diff options
author | Anders Jonsson <anders.jonsson@norsjovallen.se> | 2016-06-19 23:13:01 +0200 |
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committer | Anders Jonsson <anders.jonsson@norsjovallen.se> | 2016-06-19 23:15:48 +0200 |
commit | 89d613bab7ead1a027ddb11d6b7fca9ee64ba259 (patch) | |
tree | e4d445b6ffe5aa201d4bd95d6e891c2d92099e7f /help | |
parent | bb91cc31a576e2dfb8cf4a79f2ededbdf07d5840 (diff) |
Add beginning of Swedish help translation
Diffstat (limited to 'help')
-rw-r--r-- | help/Makefile.am | 2 | ||||
-rw-r--r-- | help/sv/sv.po | 13663 |
2 files changed, 13664 insertions, 1 deletions
diff --git a/help/Makefile.am b/help/Makefile.am index 252d6bc3..9d4ca8a7 100644 --- a/help/Makefile.am +++ b/help/Makefile.am @@ -12,7 +12,7 @@ DOC_FIGURES = figures/parametric.png \ DOC_ENTITIES = legal.xml -DOC_LINGUAS = cs de el es fr pt_BR ru +DOC_LINGUAS = cs de el es fr pt_BR ru sv # # Text version diff --git a/help/sv/sv.po b/help/sv/sv.po new file mode 100644 index 00000000..6e24e57f --- /dev/null +++ b/help/sv/sv.po @@ -0,0 +1,13663 @@ +# Swedish translation for genius. +# Copyright © 2016 genius's COPYRIGHT HOLDER +# This file is distributed under the same license as the genius package. +# Anders Jonsson <anders.jonsson@norsjovallen.se>, 2016. +# +msgid "" +msgstr "" +"Project-Id-Version: genius master\n" +"POT-Creation-Date: 2016-06-10 20:45+0000\n" +"PO-Revision-Date: 2016-06-19 18:30+0200\n" +"Language-Team: Swedish <tp-sv@listor.tp-sv.se>\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: sv\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" +"Last-Translator: Anders Jonsson <anders.jonsson@norsjovallen.se>\n" +"X-Generator: Poedit 1.8.8\n" + +#. When image changes, this message will be marked fuzzy or untranslated for you. +#. It doesn't matter what you translate it to: it's not used at all. +#: C/genius.xml:276(None) +#, fuzzy +msgid "" +"@@image: 'figures/genius_window.png'; md5=0b299ec3a83d5e0b1acddefc339f3451" +msgstr "" +"@@image: 'figures/genius_window.png'; md5=0b299ec3a83d5e0b1acddefc339f3451" + +#. When image changes, this message will be marked fuzzy or untranslated for you. +#. It doesn't matter what you translate it to: it's not used at all. +#: C/genius.xml:517(None) +#, fuzzy +msgid "@@image: 'figures/line_plot.png'; md5=3f99805e74d0b0a8ddf9e22785e6739c" +msgstr "@@image: 'figures/line_plot.png'; md5=3f99805e74d0b0a8ddf9e22785e6739c" + +#. When image changes, this message will be marked fuzzy or untranslated for you. +#. It doesn't matter what you translate it to: it's not used at all. +#: C/genius.xml:552(None) +#, fuzzy +msgid "" +"@@image: 'figures/line_plot_graph.png'; md5=72dffef41ea45f59650f90154af9df9e" +msgstr "" +"@@image: 'figures/line_plot_graph.png'; md5=72dffef41ea45f59650f90154af9df9e" + +#. When image changes, this message will be marked fuzzy or untranslated for you. +#. It doesn't matter what you translate it to: it's not used at all. +#: C/genius.xml:595(None) +#, fuzzy +msgid "@@image: 'figures/parametric.png'; md5=04adf9c9c5efb07b8bc29d127c5b5a6c" +msgstr "@@image: 'figures/parametric.png'; md5=04adf9c9c5efb07b8bc29d127c5b5a6c" + +#. When image changes, this message will be marked fuzzy or untranslated for you. +#. It doesn't matter what you translate it to: it's not used at all. +#: C/genius.xml:619(None) +#, fuzzy +msgid "" +"@@image: 'figures/parametric_graph.png'; md5=2e0a5b1b13ab5a841b749c2d5b869556" +msgstr "" +"@@image: 'figures/parametric_graph.png'; md5=2e0a5b1b13ab5a841b749c2d5b869556" + +#. When image changes, this message will be marked fuzzy or untranslated for you. +#. It doesn't matter what you translate it to: it's not used at all. +#: C/genius.xml:727(None) +#, fuzzy +msgid "" +"@@image: 'figures/surface_graph.png'; md5=b0b9f997b2e02cab5af495341f86c279" +msgstr "" +"@@image: 'figures/surface_graph.png'; md5=b0b9f997b2e02cab5af495341f86c279" + +#: C/genius.xml:36(para) +msgid "Manual for the Genius Math Tool." +msgstr "" + +#: C/genius.xml:37(title) +msgid "Genius Manual" +msgstr "" + +#: C/genius.xml:40(year) +msgid "1997-2016" +msgstr "1997-2016" + +#: C/genius.xml:41(holder) +msgid "Jiří (George) Lebl" +msgstr "Jiří (George) Lebl" + +#: C/genius.xml:44(year) +msgid "2004" +msgstr "2004" + +#: C/genius.xml:45(holder) +msgid "Kai Willadsen" +msgstr "Kai Willadsen" + +#: C/genius.xml:2(para) +msgid "" +"Permission is granted to copy, distribute and/or modify this document under " +"the terms of the GNU Free Documentation License (GFDL), Version 1.1 or any " +"later version published by the Free Software Foundation with no Invariant " +"Sections, no Front-Cover Texts, and no Back-Cover Texts. You can find a copy " +"of the GFDL at this <ulink type=\"help\" url=\"ghelp:fdl\">link</ulink> or in " +"the file COPYING-DOCS distributed with this manual." +msgstr "" + +#: C/genius.xml:12(para) +msgid "" +"This manual is part of a collection of GNOME manuals distributed under the " +"GFDL. If you want to distribute this manual separately from the collection, " +"you can do so by adding a copy of the license to the manual, as described in " +"section 6 of the license." +msgstr "" + +#: C/genius.xml:19(para) +msgid "" +"Many of the names used by companies to distinguish their products and services " +"are claimed as trademarks. Where those names appear in any GNOME " +"documentation, and the members of the GNOME Documentation Project are made " +"aware of those trademarks, then the names are in capital letters or initial " +"capital letters." +msgstr "" + +#: C/genius.xml:35(para) +msgid "" +"DOCUMENT IS PROVIDED ON AN \"AS IS\" BASIS, WITHOUT WARRANTY OF ANY KIND, " +"EITHER EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, WARRANTIES THAT " +"THE DOCUMENT OR MODIFIED VERSION OF THE DOCUMENT IS FREE OF DEFECTS " +"MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE OR NON-INFRINGING. THE ENTIRE RISK " +"AS TO THE QUALITY, ACCURACY, AND PERFORMANCE OF THE DOCUMENT OR MODIFIED " +"VERSION OF THE DOCUMENT IS WITH YOU. SHOULD ANY DOCUMENT OR MODIFIED VERSION " +"PROVE DEFECTIVE IN ANY RESPECT, YOU (NOT THE INITIAL WRITER, AUTHOR OR ANY " +"CONTRIBUTOR) ASSUME THE COST OF ANY NECESSARY SERVICING, REPAIR OR CORRECTION. " +"THIS DISCLAIMER OF WARRANTY CONSTITUTES AN ESSENTIAL PART OF THIS LICENSE. NO " +"USE OF ANY DOCUMENT OR MODIFIED VERSION OF THE DOCUMENT IS AUTHORIZED " +"HEREUNDER EXCEPT UNDER THIS DISCLAIMER; AND" +msgstr "" + +#: C/genius.xml:55(para) +msgid "" +"UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, WHETHER IN TORT (INCLUDING " +"NEGLIGENCE), CONTRACT, OR OTHERWISE, SHALL THE AUTHOR, INITIAL WRITER, ANY " +"CONTRIBUTOR, OR ANY DISTRIBUTOR OF THE DOCUMENT OR MODIFIED VERSION OF THE " +"DOCUMENT, OR ANY SUPPLIER OF ANY OF SUCH PARTIES, BE LIABLE TO ANY PERSON FOR " +"ANY DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES OF ANY " +"CHARACTER INCLUDING, WITHOUT LIMITATION, DAMAGES FOR LOSS OF GOODWILL, WORK " +"STOPPAGE, COMPUTER FAILURE OR MALFUNCTION, OR ANY AND ALL OTHER DAMAGES OR " +"LOSSES ARISING OUT OF OR RELATING TO USE OF THE DOCUMENT AND MODIFIED VERSIONS " +"OF THE DOCUMENT, EVEN IF SUCH PARTY SHALL HAVE BEEN INFORMED OF THE " +"POSSIBILITY OF SUCH DAMAGES." +msgstr "" + +#: C/genius.xml:28(para) +msgid "" +"DOCUMENT AND MODIFIED VERSIONS OF THE DOCUMENT ARE PROVIDED UNDER THE TERMS OF " +"THE GNU FREE DOCUMENTATION LICENSE WITH THE FURTHER UNDERSTANDING THAT: " +"<placeholder-1/>" +msgstr "" + +#: C/genius.xml:65(firstname) +msgid "Jiří" +msgstr "Jiří" + +#: C/genius.xml:66(surname) +msgid "Lebl" +msgstr "Lebl" + +#: C/genius.xml:68(orgname) +msgid "Oklahoma State University" +msgstr "Oklahoma State University" + +#: C/genius.xml:69(email) +msgid "jirka@5z.com" +msgstr "jirka@5z.com" + +#: C/genius.xml:73(firstname) +msgid "Kai" +msgstr "Kai" + +#: C/genius.xml:74(surname) +msgid "Willadsen" +msgstr "Willadsen" + +#: C/genius.xml:76(orgname) +msgid "University of Queensland, Australia" +msgstr "University of Queensland, Australien" + +#: C/genius.xml:77(email) +msgid "kaiw@itee.uq.edu.au" +msgstr "kaiw@itee.uq.edu.au" + +#: C/genius.xml:145(revnumber) +msgid "0.2" +msgstr "0.2" + +#: C/genius.xml:146(date) +msgid "January 2016" +msgstr "Januari 2016" + +#: C/genius.xml:148(para) +msgid "Jiri (George) Lebl <email>jirka@5z.com</email>" +msgstr "Jiri (George) Lebl <email>jirka@5z.com</email>" + +#: C/genius.xml:154(releaseinfo) +msgid "This manual describes version 1.0.21 of Genius." +msgstr "" + +#: C/genius.xml:157(title) +msgid "Feedback" +msgstr "" + +#: C/genius.xml:158(para) +msgid "" +"To report a bug or make a suggestion regarding the <application>Genius " +"Mathematics Tool</application> application or this manual, please visit the " +"<ulink url=\"http://www.jirka.org/genius.html\" type=\"http\">Genius Web page</" +"ulink> or email me at <email>jirka@5z.com</email>." +msgstr "" + +#: C/genius.xml:171(title) +msgid "Introduction" +msgstr "" + +#: C/genius.xml:172(para) +msgid "" +"The <application>Genius Mathematics Tool</application> application is a " +"general calculator for use as a desktop calculator, an educational tool in " +"mathematics, and is useful even for research. The language used in " +"<application>Genius Mathematics Tool</application> is designed to be " +"‘mathematical’ in the sense that it should be ‘what you mean is what you get’. " +"Of course that is not an entirely attainable goal. <application>Genius " +"Mathematics Tool</application> features rationals, arbitrary precision " +"integers and multiple precision floats using the GMP library. It handles " +"complex numbers using cartesian notation. It has good vector and matrix " +"manipulation and can handle basic linear algebra. The programming language " +"allows user defined functions, variables and modification of parameters." +msgstr "" + +#: C/genius.xml:186(para) +msgid "" +"<application>Genius Mathematics Tool</application> comes in two versions. One " +"version is the graphical GNOME version, which features an IDE style interface " +"and the ability to plot functions of one or two variables. The command line " +"version does not require GNOME, but of course does not implement any feature " +"that requires the graphical interface." +msgstr "" + +#: C/genius.xml:194(para) +msgid "" +"Parts of this manual describe the graphical version of the calculator, but the " +"language is of course the same. The command line only version lacks the " +"graphing capabilities and all other capabilities that require the graphical " +"user interface." +msgstr "" + +#: C/genius.xml:201(para) +msgid "" +"Generally, when some feature of the language (function, operator, etc...) is " +"new is some version past 1.0.5, it is mentioned, but below 1.0.5 you would " +"have to look at the NEWS file." +msgstr "" + +#: C/genius.xml:211(title) +msgid "Getting Started" +msgstr "" + +#: C/genius.xml:214(title) +msgid "To Start <application>Genius Mathematics Tool</application>" +msgstr "" + +#: C/genius.xml:215(para) +msgid "" +"You can start <application><application>Genius Mathematics Tool</application></" +"application> in the following ways:" +msgstr "" + +#: C/genius.xml:219(term) +msgid "<guimenu>Applications</guimenu> menu" +msgstr "" + +#: C/genius.xml:221(para) +msgid "" +"Depending on your operating system and version, the menu item for " +"<application>Genius Mathematics Tool</application> could appear in a number of " +"different places. It can be in the <guisubmenu>Education</guisubmenu>, " +"<guisubmenu>Accessories</guisubmenu>, <guisubmenu>Office</guisubmenu>, " +"<guisubmenu>Science</guisubmenu>, or similar submenu, depending on your " +"particular setup. The menu item name you are looking for is " +"<guimenuitem>Genius Math Tool</guimenuitem>. Once you locate this menu item " +"click on it to start <application>Genius Mathematics Tool</application>." +msgstr "" + +#: C/genius.xml:237(term) +msgid "<guilabel>Run</guilabel> dialog" +msgstr "" + +#: C/genius.xml:239(para) +msgid "" +"Depending on your system installation the menu item may not be available. If " +"it is not, you can open the Run dialog and execute <command>gnome-genius</" +"command>." +msgstr "" + +#: C/genius.xml:247(term) +msgid "Command line" +msgstr "" + +#: C/genius.xml:249(para) +msgid "" +"To start the GNOME version of <application>Genius Mathematics Tool</" +"application> execute <command>gnome-genius</command> from the command line." +msgstr "" + +#: C/genius.xml:253(para) +msgid "" +"To start the command line only version, execute the following command: " +"<command>genius</command>. This version does not include the graphical " +"environment and some functionality such as plotting will not be available." +msgstr "" + +#: C/genius.xml:265(title) +msgid "When You Start Genius" +msgstr "" + +#: C/genius.xml:266(para) +msgid "" +"When you start the GNOME edition of <application>Genius Mathematics Tool</" +"application>, the window pictured in <xref linkend=\"mainwindow-fig\"/> is " +"displayed." +msgstr "" + +#: C/genius.xml:271(title) +msgid "<application>Genius Mathematics Tool</application> Window" +msgstr "" + +#: C/genius.xml:0(application) +msgid "Genius Mathematics Tool" +msgstr "" + +#: C/genius.xml:280(guilabel) +msgid "File" +msgstr "" + +#: C/genius.xml:281(guilabel) +msgid "Edit" +msgstr "" + +#: C/genius.xml:281(guilabel) +msgid "Calculator" +msgstr "" + +#: C/genius.xml:282(guilabel) +msgid "Examples" +msgstr "" + +#: C/genius.xml:283(guilabel) +msgid "Programs" +msgstr "" + +#: C/genius.xml:284(guilabel) C/genius.xml:9378(title) +msgid "Settings" +msgstr "" + +#: C/genius.xml:284(guilabel) +msgid "Help" +msgstr "" + +#: C/genius.xml:279(phrase) +msgid "" +"Shows <placeholder-1/> main window. Contains titlebar, menubar, toolbar and " +"working area. Menubar contains <placeholder-2/>, <placeholder-3/>, " +"<placeholder-4/>, <placeholder-5/>, <placeholder-6/>, <placeholder-7/>, and " +"<placeholder-8/> menus." +msgstr "" + +#: C/genius.xml:290(para) +msgid "" +"The <application>Genius Mathematics Tool</application> window contains the " +"following elements:" +msgstr "" + +#: C/genius.xml:294(term) +msgid "Menubar." +msgstr "" + +#: C/genius.xml:296(para) +msgid "" +"The menus on the menubar contain all of the commands that you need to work " +"with files in <application>Genius Mathematics Tool</application>. The " +"<guilabel>File</guilabel> menu contains items for loading and saving items and " +"creating new programs. The <guilabel>Load and Run...</guilabel> command does " +"not open a new window for the program, but just executes the program directly. " +"It is equivalent to the <command>load</command> command." +msgstr "" + +#: C/genius.xml:301(para) +msgid "" +"The <guilabel>Calculator</guilabel> menu controls the calculator engine. It " +"allows you to run the currently selected program or to interrupt the current " +"calculation. You can also look at the full expression of the last answer " +"(useful if the last answer was too large to fit onto the console), or you can " +"view a listing of the values of all user defined variables. You can also " +"monitor user variables, which is especially useful while a long calculation is " +"running, or to debug a certain program. Finally the <guilabel>Calculator</" +"guilabel> allows plotting functions using a user friendly dialog box." +msgstr "" + +#: C/genius.xml:311(para) +msgid "" +"The <guilabel>Examples</guilabel> menu is a list of example programs or demos. " +"If you open the menu, it will load the example into a new program, which you " +"can run, edit, modify, and save. These programs should be well documented and " +"generally demonstrate some either feature of <application>Genius Mathematics " +"Tool</application> or some mathematical concept." +msgstr "" + +#: C/genius.xml:319(para) +msgid "" +"The <guilabel>Programs</guilabel> menu lists the currently open programs and " +"allows you to switch between them." +msgstr "" + +#: C/genius.xml:324(para) +msgid "The other menus have same familiar functions as in other applications." +msgstr "" + +#: C/genius.xml:330(term) +msgid "Toolbar." +msgstr "" + +#: C/genius.xml:332(para) +msgid "" +"The toolbar contains a subset of the commands that you can access from the " +"menubar." +msgstr "" + +#: C/genius.xml:336(term) +msgid "Working area" +msgstr "" + +#: C/genius.xml:338(para) +msgid "" +"The working area is the primary method of interacting with the application." +msgstr "" + +#: C/genius.xml:342(para) +msgid "" +"The working area initially has just the <guilabel>Console</guilabel> tab, " +"which is the main way of interacting with the calculator. Here you type " +"expressions and the results are immediately returned after you hit the Enter " +"key." +msgstr "" + +#: C/genius.xml:348(para) +msgid "" +"Alternatively you can write longer programs and those can appear in separate " +"tabs. The programs are a set of commands or functions that can be run all at " +"once rather than entering them at the command line. The programs can be saved " +"in files for later retrieval." +msgstr "" + +#: C/genius.xml:364(title) +msgid "Basic Usage" +msgstr "" + +#: C/genius.xml:367(title) +msgid "Using the Work Area" +msgstr "" + +#: C/genius.xml:369(para) +msgid "" +"Normally you interact with the calculator in the <guilabel>Console</guilabel> " +"tab of the work area. If you are running the text only version then the " +"console will be the only thing that is available to you. If you want to use " +"<application>Genius Mathematics Tool</application> as a calculator only, just " +"type in your expression in the console, it will be evaluated, and the returned " +"value will be printed." +msgstr "" + +#: C/genius.xml:377(para) +msgid "" +"To evaluate an expression, type it into the <guilabel>Console</guilabel> work " +"area and press enter. Expressions are written in a language called GEL. The " +"most simple GEL expression just looks like mathematics. For example " +"<screen><prompt>genius> </prompt><userinput>30*70 + 67^3.0 + ln(7) * " +"(88.8/100)</userinput>\n" +"</screen> or <screen><prompt>genius> </prompt><userinput>62734 + 812634 + " +"77^4 mod 5</userinput>\n" +"</screen> or <screen><prompt>genius> </prompt><userinput>| sin(37) - e^7 |</" +"userinput>\n" +"</screen> or <screen><prompt>genius> </prompt><userinput>sum n=1 to 70 do 1/" +"n</userinput>\n" +"</screen> (Last is the harmonic sum from 1 to 70)" +msgstr "" + +#: C/genius.xml:395(para) +msgid "" +"To get a list of functions and commands, type: <screen><prompt>genius> </" +"prompt><userinput>help</userinput>\n" +"</screen> If you wish to get more help on a specific function, type: " +"<screen><prompt>genius> </prompt><userinput>help FunctionName</userinput>\n" +"</screen> To view this manual, type: <screen><prompt>genius> </" +"prompt><userinput>manual</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:406(para) +msgid "" +"Suppose you have previously saved some GEL commands as a program to a file and " +"you now want to execute them. To load this program from the file " +"<filename>path/to/program.gel</filename>, type <screen><prompt>genius> </" +"prompt><userinput>load path/to/program.gel</userinput>\n" +"</screen><application>Genius Mathematics Tool</application> keeps track of the " +"current directory. To list files in the current directory type <command>ls</" +"command>, to change directory do <userinput>cd directory</userinput> as in the " +"UNIX command shell." +msgstr "" + +#: C/genius.xml:420(title) +msgid "To Create a New Program" +msgstr "" + +#: C/genius.xml:421(para) +msgid "" +"If you wish to enter several more complicated commands, or perhaps write a " +"complicated function using the <link linkend=\"genius-gel\">GEL</link> " +"language. You can create a new program." +msgstr "" + +#: C/genius.xml:426(para) +msgid "" +"To start writing a new program, choose <menuchoice><guimenu>File</" +"guimenu><guimenuitem>New Program</guimenuitem></menuchoice>. A new tab will " +"appear in the work area. You can write a <link linkend=\"genius-gel\">GEL</" +"link> program in this work area. Once you have written your program you can " +"run it by <menuchoice><guimenu>Calculator</guimenu><guimenuitem>Run</" +"guimenuitem></menuchoice> (or the <guilabel>Run</guilabel> toolbar button). " +"This will execute your program and will display any output on the " +"<guilabel>Console</guilabel> tab. Executing a program is equivalent of taking " +"the text of the program and typing it into the console. The only difference is " +"that this input is done independent of the console and just the output goes " +"onto the console. <menuchoice><guimenu>Calculator</guimenu><guimenuitem>Run</" +"guimenuitem></menuchoice> will always run the currently selected program even " +"if you are on the <guilabel>Console</guilabel> tab. The currently selected " +"program has its tab in bold type. To select a program, just click on its tab." +msgstr "" + +#: C/genius.xml:443(para) +msgid "" +"To save the program you've just written, choose <menuchoice><guimenu>File</" +"guimenu><guimenuitem>Save As...</guimenuitem></menuchoice>. Similarly as in " +"other programs you can choose <menuchoice><guimenu>File</" +"guimenu><guimenuitem>Save</guimenuitem></menuchoice> to save a program that " +"already has a filename attached to it. If you have many opened programs you " +"have edited and wish to save you can also choose <menuchoice><guimenu>File</" +"guimenu><guimenuitem>Save All Unsaved</guimenuitem></menuchoice>." +msgstr "" + +#: C/genius.xml:450(para) +msgid "" +"Programs that have unsaved changes will have a \"[+]\" next to their filename. " +"This way you can see if the file on disk and the currently opened tab differ " +"in content. Programs which have not yet had a filename associated with them " +"are always considered unsaved and no \"[+]\" is printed." +msgstr "" + +#: C/genius.xml:458(title) +msgid "To Open and Run a Program" +msgstr "" + +#: C/genius.xml:459(para) +msgid "" +"To open a file, choose <menuchoice><guimenu>File</guimenu><guimenuitem>Open</" +"guimenuitem></menuchoice>. A new tab containing the file will appear in the " +"work area. You can use this to edit the file." +msgstr "" + +#: C/genius.xml:465(para) +msgid "" +"To run a program from a file, choose <menuchoice><guimenu>File</" +"guimenu><guimenuitem>Load and Run...</guimenuitem></menuchoice>. This will run " +"the program without opening it in a separate tab. This is equivalent to the " +"<command>load</command> command." +msgstr "" + +#: C/genius.xml:471(para) +msgid "" +"If you have made edits to a file you wish to throw away and want to reload to " +"the version that's on disk, you can choose the <menuchoice><guimenu>File</" +"guimenu><guimenuitem>Reload from Disk</guimenuitem></menuchoice> menuitem. " +"This is useful for experimenting with a program and making temporary edits, to " +"run a program, but that you do not intend to keep." +msgstr "" + +#: C/genius.xml:483(title) C/genius.xml:8626(title) +msgid "Plotting" +msgstr "" + +#: C/genius.xml:485(para) +msgid "" +"Plotting support is only available in the graphical GNOME version. All " +"plotting accessible from the graphical interface is available from the " +"<guilabel>Create Plot</guilabel> window. You can access this window by either " +"clicking on the <guilabel>Plot</guilabel> button on the toolbar or selecting " +"<guilabel>Plot</guilabel> from the <guilabel>Calculator</guilabel> menu. You " +"can also access the plotting functionality by using the <link linkend=\"genius-" +"gel-function-list-plotting\">plotting functions</link> of the GEL language. " +"See <xref linkend=\"genius-gel\"/> to find out how to enter expressions that " +"Genius understands." +msgstr "" + +#: C/genius.xml:498(title) +msgid "Line Plots" +msgstr "" + +#: C/genius.xml:499(para) +msgid "" +"To graph real valued functions of one variable open the <guilabel>Create Plot</" +"guilabel> window. You can also use the <link linkend=\"gel-function-LinePlot" +"\"><function>LinePlot</function></link> function on the command line (see its " +"documentation)." +msgstr "" + +#: C/genius.xml:505(para) +msgid "" +"Once you click the <guilabel>Plot</guilabel> button, a window opens up with " +"some notebooks in it. You want to be in the <guilabel>Function line plot</" +"guilabel> notebook tab, and inside you want to be on the <guilabel>Functions / " +"Expressions</guilabel> notebook tab. See <xref linkend=\"lineplot-fig\"/>." +msgstr "" + +#: C/genius.xml:513(title) +msgid "Create Plot Window" +msgstr "" + +#: C/genius.xml:520(phrase) +msgid "Shows the line plotting window." +msgstr "" + +#: C/genius.xml:526(para) +msgid "" +"Type expressions with <userinput>x</userinput> as the independent variable " +"into the textboxes. Alternatively you can give names of functions such as " +"<userinput>cos</userinput> rather then having to type <userinput>cos(x)</" +"userinput>. You can graph up to ten functions. If you make a mistake and " +"Genius cannot parse the input it will signify this with a warning icon on the " +"right of the text input box where the error occurred, as well as giving you an " +"error dialog. You can change the ranges of the dependent and independent " +"variables in the bottom part of the dialog. The <varname>y</varname> " +"(dependent) range can be set automatically by turning on the <guilabel>Fit " +"dependent axis</guilabel> checkbox. The names of the variables can also be " +"changed. Pressing the <guilabel>Plot</guilabel> button produces the graph " +"shown in <xref linkend=\"lineplot2-fig\"/>." +msgstr "" + +#: C/genius.xml:540(para) +msgid "" +"The variables can be renamed by clicking the <guilabel>Change variable names..." +"</guilabel> button, which is useful if you wish to print or save the figure " +"and don't want to use the standard names. Finally you can also avoid printing " +"the legend and the axis labels completely, which is also useful if printing or " +"saving, when the legend might simply be clutter." +msgstr "" + +#: C/genius.xml:548(title) +msgid "Plot Window" +msgstr "" + +#: C/genius.xml:555(phrase) +msgid "The graph produced." +msgstr "" + +#: C/genius.xml:561(para) +msgid "" +"From here you can print out the plot, create encapsulated postscript or a PNG " +"version of the plot or change the zoom. If the dependent axis was not set " +"correctly you can have Genius fit it by finding out the extrema of the graphed " +"functions." +msgstr "" + +#: C/genius.xml:568(para) +msgid "" +"For plotting using the command line see the documentation of the <link linkend=" +"\"gel-function-LinePlot\"><function>LinePlot</function></link> function." +msgstr "" + +#: C/genius.xml:575(title) +msgid "Parametric Plots" +msgstr "" + +#: C/genius.xml:576(para) +msgid "" +"In the create plot window, you can also choose the <guilabel>Parametric</" +"guilabel> notebook tab to create two dimensional parametric plots. This way " +"you can plot a single parametric function. You can either specify the points " +"as <varname>x</varname> and <varname>y</varname>, or giving a single complex " +"number as a function of the variable <varname>t</varname>. The range of the " +"variable <varname>t</varname> is given explicitly, and the function is sampled " +"according to the given increment. The <varname>x</varname> and <varname>y</" +"varname> range can be set automatically by turning on the <guilabel>Fit " +"dependent axis</guilabel> checkbox, or it can be specified explicitly. See " +"<xref linkend=\"paramplot-fig\"/>." +msgstr "" + +#: C/genius.xml:591(title) +msgid "Parametric Plot Tab" +msgstr "" + +#: C/genius.xml:598(guilabel) +msgid "Create Plot" +msgstr "" + +#: C/genius.xml:598(phrase) +msgid "Parametric plotting tab in the <placeholder-1/> window." +msgstr "" + +#: C/genius.xml:604(para) +msgid "" +"An example of a parametric plot is given in <xref linkend=\"paramplot2-fig\"/" +">. Similar operations can be done on such graphs as can be done on the other " +"line plots. For plotting using the command line see the documentation of the " +"<link linkend=\"gel-function-LinePlotParametric" +"\"><function>LinePlotParametric</function></link> or <link linkend=\"gel-" +"function-LinePlotCParametric\"><function>LinePlotCParametric</function></link> " +"function." +msgstr "" + +#: C/genius.xml:615(title) +msgid "Parametric Plot" +msgstr "" + +#: C/genius.xml:622(phrase) +msgid "Parametric plot produced" +msgstr "" + +#: C/genius.xml:631(title) +msgid "Slopefield Plots" +msgstr "" + +#: C/genius.xml:632(para) +msgid "" +"In the create plot window, you can also choose the <guilabel>Slope field</" +"guilabel> notebook tab to create a two dimensional slope field plot. Similar " +"operations can be done on such graphs as can be done on the other line plots. " +"For plotting using the command line see the documentation of the <link linkend=" +"\"gel-function-SlopefieldPlot\"><function>SlopefieldPlot</function></link> " +"function." +msgstr "" + +#: C/genius.xml:641(para) +msgid "" +"When a slope field is active, there is an extra <guilabel>Solver</guilabel> " +"menu available, through which you can bring up the solver dialog. Here you can " +"have Genius plot specific solutions for the given initial conditions. You can " +"either specify initial conditions in the dialog, or you can click on the plot " +"directly to specify the initial point. While the solver dialog is active, the " +"zooming by clicking and dragging does not work. You have to close the dialog " +"first if you want to zoom using the mouse." +msgstr "" + +#: C/genius.xml:650(para) +msgid "" +"The solver uses the standard Runge-Kutta method. The plots will stay on the " +"screen until cleared. The solver will stop whenever it reaches the boundary of " +"the plot window. Zooming does not change the limits or parameters of the " +"solutions, you will have to clear and redraw them with appropriate parameters. " +"You can also use the <link linkend=\"gel-function-SlopefieldDrawSolution" +"\"><function>SlopefieldDrawSolution</function></link> function to draw " +"solutions from the command line or programs." +msgstr "" + +#: C/genius.xml:663(title) +msgid "Vectorfield Plots" +msgstr "" + +#: C/genius.xml:664(para) +msgid "" +"In the create plot window, you can also choose the <guilabel>Vector field</" +"guilabel> notebook tab to create a two dimensional vector field plot. Similar " +"operations can be done on such graphs as can be done on the other line plots. " +"For plotting using the command line see the documentation of the <link linkend=" +"\"gel-function-VectorfieldPlot\"><function>VectorfieldPlot</function></link> " +"function." +msgstr "" + +#: C/genius.xml:673(para) +msgid "" +"By default the direction and magnitude of the vector field is shown. To only " +"show direction and not the magnitude, check the appropriate checkbox to " +"normalize the arrow lengths." +msgstr "" + +#: C/genius.xml:679(para) +msgid "" +"When a vector field is active, there is an extra <guilabel>Solver</guilabel> " +"menu available, through which you can bring up the solver dialog. Here you can " +"have Genius plot specific solutions for the given initial conditions. You can " +"either specify initial conditions in the dialog, or you can click on the plot " +"directly to specify the initial point. While the solver dialog is active, the " +"zooming by clicking and dragging does not work. You have to close the dialog " +"first if you want to zoom using the mouse." +msgstr "" + +#: C/genius.xml:688(para) +msgid "" +"The solver uses the standard Runge-Kutta method. The plots will stay on the " +"screen until cleared. Zooming does not change the limits or parameters of the " +"solutions, you will have to clear and redraw them with appropriate parameters. " +"You can also use the <link linkend=\"gel-function-VectorfieldDrawSolution" +"\"><function>VectorfieldDrawSolution</function></link> function to draw " +"solutions from the command line or programs." +msgstr "" + +#: C/genius.xml:701(title) +msgid "Surface Plots" +msgstr "" + +#: C/genius.xml:702(para) +msgid "" +"Genius can also plot surfaces. Select the <guilabel>Surface plot</guilabel> " +"tab in the main notebook of the <guilabel>Create Plot</guilabel> window. Here " +"you can specify a single expression that should use either <varname>x</" +"varname> and <varname>y</varname> as real independent variables or <varname>z</" +"varname> as a complex variable (where <varname>x</varname> is the real part of " +"<varname>z</varname> and <varname>y</varname> is the imaginary part). For " +"example to plot the modulus of the cosine function for complex parameters, you " +"could enter <userinput>|cos(z)|</userinput>. This would be equivalent to " +"<userinput>|cos(x+1i*y)|</userinput>. See <xref linkend=\"surfaceplot-fig\"/>. " +"For plotting using the command line see the documentation of the <link linkend=" +"\"gel-function-SurfacePlot\"><function>SurfacePlot</function></link> function." +msgstr "" + +#: C/genius.xml:715(para) +msgid "" +"The <varname>z</varname> range can be set automatically by turning on the " +"<guilabel>Fit dependent axis</guilabel> checkbox. The variables can be renamed " +"by clicking the <guilabel>Change variable names...</guilabel> button, which is " +"useful if you wish to print or save the figure and don't want to use the " +"standard names. Finally you can also avoid printing the legend, which is also " +"useful if printing or saving, when the legend might simply be clutter." +msgstr "" + +#: C/genius.xml:723(title) +msgid "Surface Plot" +msgstr "" + +#: C/genius.xml:730(phrase) +msgid "Modulus of the complex cosine function." +msgstr "" + +#: C/genius.xml:736(para) +msgid "" +"In surface mode, left and right arrow keys on your keyboard will rotate the " +"view along the z axis. Alternatively you can rotate along any axis by " +"selecting <guilabel>Rotate axis...</guilabel> in the <guilabel>View</guilabel> " +"menu. The <guilabel>View</guilabel> menu also has a top view mode which " +"rotates the graph so that the z axis is facing straight out, that is, we view " +"the graph from the top and get essentially just the colors that define the " +"values of the function getting a temperature plot of the function. Finally you " +"should try <guilabel>Start rotate animation</guilabel>, to start a continuous " +"slow rotation. This is especially good if using <application>Genius " +"Mathematics Tool</application> to present to an audience." +msgstr "" + +#: C/genius.xml:754(title) +msgid "GEL Basics" +msgstr "" + +#: C/genius.xml:756(para) +msgid "" +"GEL stands for Genius Extension Language. It is the language you use to write " +"programs in Genius. A program in GEL is simply an expression that evaluates to " +"a number, a matrix, or another object in GEL. <application>Genius Mathematics " +"Tool</application> can be used as a simple calculator, or as a powerful " +"theoretical research tool. The syntax is meant to have as shallow of a " +"learning curve as possible, especially for use as a calculator." +msgstr "" + +#: C/genius.xml:769(title) +msgid "Values" +msgstr "" + +#: C/genius.xml:771(para) +msgid "" +"Values in GEL can be <link linkend=\"genius-gel-values-numbers\">numbers</" +"link>, <link linkend=\"genius-gel-values-booleans\">Booleans</link>, or <link " +"linkend=\"genius-gel-values-strings\">strings</link>. GEL also treats <link " +"linkend=\"genius-gel-matrices\">matrices</link> as values. Values can be used " +"in calculations, assigned to variables and returned from functions, among " +"other uses." +msgstr "" + +#: C/genius.xml:778(title) +msgid "Numbers" +msgstr "" + +#: C/genius.xml:781(programlisting) +#, no-wrap +msgid "1234\n" +msgstr "1234\n" + +#: C/genius.xml:784(programlisting) +#, no-wrap +msgid "" +"0x123ABC\n" +"01234\n" +msgstr "" +"0x123ABC\n" +"01234\n" + +#: C/genius.xml:788(programlisting) +#, no-wrap +msgid "23\\1234ABCD\n" +msgstr "23\\1234ABCD\n" + +#: C/genius.xml:779(para) +msgid "" +"Integers are the first type of number in GEL. Integers are written in the " +"normal way. <placeholder-1/> Hexadecimal and octal numbers can be written " +"using C notation. For example: <placeholder-2/> Or you can type numbers in an " +"arbitrary base using <literal><base>\\<number></literal>. Digits " +"higher than 10 use letters in a similar way to hexadecimal. For example, a " +"number in base 23 could be written: <placeholder-3/>" +msgstr "" + +#: C/genius.xml:794(programlisting) +#, no-wrap +msgid "3/4\n" +msgstr "3/4\n" + +#: C/genius.xml:797(programlisting) +#, no-wrap +msgid "1 3/10\n" +msgstr "1 3/10\n" + +#: C/genius.xml:792(para) +msgid "" +"The second type of GEL number is rationals. Rationals are simply achieved by " +"dividing two integers. So one could write: <placeholder-1/> to get three " +"quarters. Rationals also accept mixed fraction notation. So in order to get " +"one and three tenths you could write: <placeholder-2/>" +msgstr "" + +#: C/genius.xml:803(programlisting) +#, no-wrap +msgid "" +"1.315\n" +"7.887e77\n" +"7.887e-77\n" +".3\n" +"0.3\n" +"77e5\n" +msgstr "" +"1.315\n" +"7.887e77\n" +"7.887e-77\n" +".3\n" +"0.3\n" +"77e5\n" + +#: C/genius.xml:801(para) +msgid "" +"The next type if number is floating point. These are entered in a similar " +"fashion to C notation. You can use <literal>E</literal>, <literal>e</literal> " +"or <literal>@</literal> as the exponent delimiter. Note that using the " +"exponent delimiter gives a float even if there is no decimal point in the " +"number. Examples: <placeholder-1/> When Genius prints a floating point number " +"it will always append a <computeroutput>.0</computeroutput> even if the number " +"is whole. This is to indicate that floating point numbers are taken as " +"imprecise quantities. When a number is written in the scientific notation, it " +"is always a floating point number and thus Genius does not print the " +"<computeroutput>.0</computeroutput>." +msgstr "" + +#: C/genius.xml:819(programlisting) +#, no-wrap +msgid "" +"1+2i\n" +"8.01i\n" +"77*e^(1.3i)\n" +msgstr "" +"1+2i\n" +"8.01i\n" +"77*e^(1.3i)\n" + +#: C/genius.xml:817(para) +msgid "" +"The final type of number in gel is the complex numbers. You can enter a " +"complex number as a sum of real and imaginary parts. To add an imaginary part, " +"append an <literal>i</literal>. Here are examples of entering complex numbers: " +"<placeholder-1/>" +msgstr "" + +#: C/genius.xml:826(para) +msgid "" +"When entering imaginary numbers, a number must be in front of the <literal>i</" +"literal>. If you use <literal>i</literal> by itself, Genius will interpret " +"this as referring to the variable <varname>i</varname>. If you need to refer " +"to <literal>i</literal> by itself, use <literal>1i</literal> instead." +msgstr "" + +#: C/genius.xml:830(para) +msgid "" +"In order to use mixed fraction notation with imaginary numbers you must have " +"the mixed fraction in parentheses. (i.e., <userinput>(1 2/5)i</userinput>)" +msgstr "" + +#: C/genius.xml:839(title) +msgid "Booleans" +msgstr "" + +#: C/genius.xml:840(para) +msgid "" +"Genius also supports native Boolean values. The two Boolean constants are " +"defined as <constant>true</constant> and <constant>false</constant>; these " +"identifiers can be used like any other variable. You can also use the " +"identifiers <constant>True</constant>, <constant>TRUE</constant>, " +"<constant>False</constant> and <constant>FALSE</constant> as aliases for the " +"above." +msgstr "" + +#: C/genius.xml:848(para) +msgid "" +"At any place where a Boolean expression is expected, you can use a Boolean " +"value or any expression that produces either a number or a Boolean. If Genius " +"needs to evaluate a number as a Boolean it will interpret 0 as " +"<constant>false</constant> and any other number as <constant>true</constant>." +msgstr "" + +#: C/genius.xml:857(programlisting) +#, no-wrap +msgid "( (1 + true) - false ) * true\n" +msgstr "( (1 + true) - false ) * true\n" + +#: C/genius.xml:860(programlisting) +#, no-wrap +msgid "( (true or true) or not false ) and true\n" +msgstr "( (true or true) or not false ) and true\n" + +#: C/genius.xml:863(programlisting) +#, no-wrap +msgid "1 == true\n" +msgstr "1 == true\n" + +#: C/genius.xml:855(para) +msgid "" +"In addition, you can do arithmetic with Boolean values. For example: " +"<placeholder-1/> is the same as: <placeholder-2/> Only addition, subtraction " +"and multiplication are supported. If you mix numbers with Booleans in an " +"expression then the numbers are converted to Booleans as described above. This " +"means that, for example: <placeholder-3/> always evaluates to <constant>true</" +"constant> since 1 will be converted to <constant>true</constant> before being " +"compared to <constant>true</constant>." +msgstr "" + +#: C/genius.xml:871(title) +msgid "Strings" +msgstr "" + +#: C/genius.xml:874(programlisting) +#, no-wrap +msgid "a=2+3;\"The result is: \"+a\n" +msgstr "" + +#: C/genius.xml:877(programlisting) +#, no-wrap +msgid "The result is: 5\n" +msgstr "" + +#: C/genius.xml:880(programlisting) +#, no-wrap +msgid "\"Slash: \\\\ Quotes: \\\" Tabs: \\t1\\t2\\t3\"\n" +msgstr "" + +#: C/genius.xml:883(programlisting) +#, no-wrap +msgid "Slash: \\ Quotes: \" Tabs: \t1\t2\t3\n" +msgstr "" + +#: C/genius.xml:872(para) +msgid "" +"Like numbers and Booleans, strings in GEL can be stored as values inside " +"variables and passed to functions. You can also concatenate a string with " +"another value using the plus operator. For example: <placeholder-1/> will " +"create the string: <placeholder-2/> You can also use C-like escape sequences " +"such as <literal>\\n</literal>,<literal>\\t</literal>,<literal>\\b</literal>," +"<literal>\\a</literal> and <literal>\\r</literal>. To get a <literal>\\</" +"literal> or <literal>\"</literal> into the string you can quote it with a " +"<literal>\\</literal>. For example: <placeholder-3/> will make a string: " +"<placeholder-4/> Do note however that when a string is returned from a " +"function, escapes are quoted, so that the output can be used as input. If you " +"wish to print the string as it is (without escapes), use the <link linkend=" +"\"gel-function-print\"><function>print</function></link> or <link linkend=" +"\"gel-function-printn\"><function>printn</function></link> functions." +msgstr "" + +#: C/genius.xml:894(programlisting) +#, no-wrap +msgid "string(22)\n" +msgstr "string(22)\n" + +#: C/genius.xml:897(programlisting) +#, no-wrap +msgid "\"22\"\n" +msgstr "\"22\"\n" + +#: C/genius.xml:892(para) +msgid "" +"In addition, you can use the library function <link linkend=\"gel-function-" +"string\"><function>string</function></link> to convert anything to a string. " +"For example: <placeholder-1/> will return <placeholder-2/> Strings can also be " +"compared with <literal>==</literal> (equal), <literal>!=</literal> (not equal) " +"and <literal><=></literal> (comparison) operators" +msgstr "" + +#: C/genius.xml:905(title) +msgid "Null" +msgstr "Null" + +#: C/genius.xml:906(para) +msgid "" +"There is a special value called <constant>null</constant>. No operations can " +"be performed on it, and nothing is printed when it is returned. Therefore, " +"<constant>null</constant> is useful when you do not want output from an " +"expression. The value <constant>null</constant> can be obtained as an " +"expression when you type <literal>.</literal>, the constant <constant>null</" +"constant> or nothing. By nothing we mean that if you end an expression with a " +"separator <literal>;</literal>, it is equivalent to ending it with a separator " +"followed by a <constant>null</constant>." +msgstr "" + +#: C/genius.xml:919(programlisting) +#, no-wrap +msgid "" +"x=5;.\n" +"x=5;\n" +msgstr "" +"x=5;.\n" +"x=5;\n" + +#: C/genius.xml:917(para) C/genius.xml:2246(para) +msgid "Example: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:923(para) +msgid "" +"Some functions return <constant>null</constant> when no value can be returned " +"or an error happened. Also <constant>null</constant> is used as an empty " +"vector or matrix, or an empty reference." +msgstr "" + +#: C/genius.xml:933(title) +msgid "Using Variables" +msgstr "" + +#: C/genius.xml:937(programlisting) +#, no-wrap +msgid "VariableName\n" +msgstr "" + +#: C/genius.xml:935(para) +msgid "" +"Syntax: <placeholder-1/> Example: <screen><prompt>genius> </" +"prompt><userinput>e</userinput>\n" +"= 2.71828182846\n" +"</screen>" +msgstr "" + +#: C/genius.xml:945(para) +msgid "" +"To evaluate a variable by itself, just enter the name of the variable. This " +"will return the value of the variable. You can use a variable anywhere you " +"would normally use a number or string. In addition, variables are necessary " +"when defining functions that take arguments (see <xref linkend=\"genius-gel-" +"functions-defining\"/>)." +msgstr "" + +#: C/genius.xml:950(title) C/genius.xml:1039(title) +msgid "Using Tab completion" +msgstr "" + +#: C/genius.xml:951(para) +msgid "" +"You can use Tab completion to get Genius to complete variable names for you. " +"Try typing the first few letters of the name and pressing <userinput>Tab</" +"userinput>." +msgstr "" + +#: C/genius.xml:957(title) +msgid "Variable names are case sensitive" +msgstr "" + +#: C/genius.xml:958(para) +msgid "" +"The names of variables are case sensitive. That means that variables named " +"<varname>hello</varname>, <varname>HELLO</varname> and <varname>Hello</" +"varname> are all different variables." +msgstr "" + +#: C/genius.xml:965(title) +msgid "Setting Variables" +msgstr "" + +#: C/genius.xml:972(programlisting) +#, no-wrap +msgid "" +"x = 3\n" +"x := 3\n" +msgstr "" +"x = 3\n" +"x := 3\n" + +#: C/genius.xml:966(para) +msgid "Syntax: <placeholder-1/> Example: <placeholder-2/>" +msgstr "" + +#: C/genius.xml:979(programlisting) +#, no-wrap +msgid "a = b = 5\n" +msgstr "a = b = 5\n" + +#: C/genius.xml:977(para) +msgid "" +"To assign a value to a variable, use the <literal>=</literal> or <literal>:=</" +"literal> operators. These operators set the value of the variable and return " +"the value you set, so you can do things like <placeholder-1/> This will set " +"<varname>b</varname> to 5 and then also set <varname>a</varname> to 5." +msgstr "" + +#: C/genius.xml:984(para) +msgid "" +"The <literal>=</literal> and <literal>:=</literal> operators can both be used " +"to set variables. The difference between them is that the <literal>:=</" +"literal> operator always acts as an assignment operator, whereas the " +"<literal>=</literal> operator may be interpreted as testing for equality when " +"used in a context where a Boolean expression is expected." +msgstr "" + +#: C/genius.xml:988(para) +msgid "" +"For more information about the scope of variables, that is when are what " +"variables visible, see <xref linkend=\"genius-gel-variables-global\"/>." +msgstr "" + +#: C/genius.xml:995(title) +msgid "Built-in Variables" +msgstr "" + +#: C/genius.xml:996(para) +msgid "" +"GEL has a number of built-in ‘variables’, such as <varname>e</varname>, " +"<varname>pi</varname> or <varname>GoldenRatio</varname>. These are widely used " +"constants with a preset value, and they cannot be assigned new values. There " +"are a number of other built-in variables. See <xref linkend=\"genius-gel-" +"function-list-constants\"/> for a full list. Note that <varname>i</varname> is " +"not by default the square root of negative one (the imaginary number), and is " +"undefined to allow its use as a counter. If you wish to write the imaginary " +"number you need to use <userinput>1i</userinput>." +msgstr "" + +#: C/genius.xml:1009(title) +msgid "Previous Result Variable" +msgstr "" + +#: C/genius.xml:1012(programlisting) +#, no-wrap +msgid "Ans+389\n" +msgstr "Ans+389\n" + +#: C/genius.xml:1010(para) +msgid "" +"The <varname>Ans</varname> and <varname>ans</varname> variables can be used to " +"get the result of the last expression. For example, if you had performed some " +"calculation, to add 389 to the result you could do: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:1019(title) +msgid "Using Functions" +msgstr "" + +#: C/genius.xml:1023(programlisting) +#, no-wrap +msgid "FunctionName(argument1, argument2, ...)\n" +msgstr "" + +#: C/genius.xml:1026(programlisting) +#, no-wrap +msgid "" +"Factorial(5)\n" +"cos(2*pi)\n" +"gcd(921,317)\n" +msgstr "" +"Factorial(5)\n" +"cos(2*pi)\n" +"gcd(921,317)\n" + +#: C/genius.xml:1021(para) +msgid "" +"Syntax: <placeholder-1/> Example: <placeholder-2/> To evaluate a function, " +"enter the name of the function, followed by the arguments (if any) to the " +"function in parentheses. This will return the result of applying the function " +"to its arguments. The number of arguments to the function is, of course, " +"different for each function." +msgstr "" + +#: C/genius.xml:1034(para) +msgid "" +"There are many built-in functions, such as <link linkend=\"gel-function-sin" +"\"><function>sin</function></link>, <link linkend=\"gel-function-cos" +"\"><function>cos</function></link> and <link linkend=\"gel-function-tan" +"\"><function>tan</function></link>. You can use the <link linkend=\"gel-" +"command-help\"><function>help</function></link> built-in command to get a list " +"of available functions, or see <xref linkend=\"genius-gel-function-list\"/> " +"for a full listing." +msgstr "" + +#: C/genius.xml:1040(para) +msgid "" +"You can use Tab completion to get Genius to complete function names for you. " +"Try typing the first few letters of the name and pressing <userinput>Tab</" +"userinput>." +msgstr "" + +#: C/genius.xml:1046(title) +msgid "Function names are case sensitive" +msgstr "" + +#: C/genius.xml:1047(para) +msgid "" +"The names of functions are case sensitive. That means that functions named " +"<function>dosomething</function>, <function>DOSOMETHING</function> and " +"<function>DoSomething</function> are all different functions." +msgstr "" + +#: C/genius.xml:1054(title) +msgid "Defining Functions" +msgstr "" + +#: C/genius.xml:1055(para) +msgid "" +"Syntax: <placeholder-1/> The <literal>`</literal> is the backquote character, " +"and signifies an anonymous function. By setting it to a variable name you " +"effectively define a function." +msgstr "" + +#: C/genius.xml:1066(programlisting) +#, no-wrap +msgid "function addup(a,b,c) = a+b+c\n" +msgstr "function addup(a,b,c) = a+b+c\n" + +#: C/genius.xml:1063(para) +msgid "" +"A function takes zero or more comma separated arguments, and returns the " +"result of the function body. Defining your own functions is primarily a matter " +"of convenience; one possible use is to have sets of functions defined in GEL " +"files that Genius can load in order to make them available. Example: " +"<placeholder-1/> then <userinput>addup(1,4,9)</userinput> yields 14" +msgstr "" + +#: C/genius.xml:1073(title) +msgid "Variable Argument Lists" +msgstr "" + +#: C/genius.xml:1076(programlisting) +#, no-wrap +msgid "function f(a,b...) = b\n" +msgstr "function f(a,b...) = b\n" + +#: C/genius.xml:1074(para) +msgid "" +"If you include <literal>...</literal> after the last argument name in the " +"function declaration, then Genius will allow any number of arguments to be " +"passed in place of that argument. If no arguments were passed then that " +"argument will be set to <constant>null</constant>. Otherwise, it will be a " +"horizontal vector containing all the arguments. For example: <placeholder-1/> " +"Then <userinput>f(1,2,3)</userinput> yields <computeroutput>[2,3]</" +"computeroutput>, while <userinput>f(1)</userinput> yields a <constant>null</" +"constant>." +msgstr "" + +#: C/genius.xml:1084(title) +msgid "Passing Functions to Functions" +msgstr "" + +#: C/genius.xml:1086(para) +msgid "" +"In Genius, it is possible to pass a function as an argument to another " +"function. This can be done using either ‘function nodes’ or anonymous " +"functions." +msgstr "" + +#: C/genius.xml:1093(programlisting) +#, no-wrap +msgid "" +"function f(a,b) = a(b)+1;\n" +"function b(x) = x*x;\n" +"f(b,2)\n" +msgstr "" +"function f(a,b) = a(b)+1;\n" +"function b(x) = x*x;\n" +"f(b,2)\n" + +#: C/genius.xml:1090(para) +msgid "" +"If you do not enter the parentheses after a function name, instead of being " +"evaluated, the function will instead be returned as a ‘function node’. The " +"function node can then be passed to another function. Example: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:1106(programlisting) +#, no-wrap +msgid "" +"function f(a,b) = a(b)+1;\n" +"f(`(x) = x*x,2)\n" +msgstr "" +"function f(a,b) = a(b)+1;\n" +"f(`(x) = x*x,2)\n" + +#: C/genius.xml:1098(para) +msgid "" +"To pass functions that are not defined, you can use an anonymous function (see " +"<xref linkend=\"genius-gel-functions-defining\"/>). That is, you want to pass " +"a function without giving it a name. Syntax: <placeholder-1/> Example: " +"<placeholder-2/> This will return 5." +msgstr "" + +#: C/genius.xml:1115(title) +msgid "Operations on Functions" +msgstr "" + +#: C/genius.xml:1118(programlisting) +#, no-wrap +msgid "exp(sin*cos+4)\n" +msgstr "exp(sin*cos+4)\n" + +#: C/genius.xml:1122(programlisting) +#, no-wrap +msgid "`(x) = exp(sin(x)*cos(x)+4)\n" +msgstr "`(x) = exp(sin(x)*cos(x)+4)\n" + +#: C/genius.xml:1127(programlisting) +#, no-wrap +msgid "f = exp(sin*cos+4)\n" +msgstr "f = exp(sin*cos+4)\n" + +#: C/genius.xml:1130(programlisting) +#, no-wrap +msgid "LinePlot(sin^2)\n" +msgstr "" + +#: C/genius.xml:1116(para) +msgid "" +"Some functions allow arithmetic operations, and some single argument functions " +"such as <link linkend=\"gel-function-exp\"><function>exp</function></link> or " +"<link linkend=\"gel-function-ln\"><function>ln</function></link>, to operate " +"on the function. For example, <placeholder-1/> will return a function that " +"takes <varname>x</varname> and returns <userinput>exp(sin(x)*cos(x)+4)</" +"userinput>. It is functionally equivalent to typing <placeholder-2/> This " +"operation can be useful when quickly defining functions. For example to create " +"a function called <varname>f</varname> to perform the above operation, you can " +"just type: <placeholder-3/> It can also be used in plotting. For example, to " +"plot sin squared you can enter: <placeholder-4/>" +msgstr "" + +#: C/genius.xml:1135(para) +msgid "" +"Not all functions can be used in this way. For example, when you use a binary " +"operation the functions must take the same number of arguments." +msgstr "" + +#: C/genius.xml:1145(title) +msgid "Separator" +msgstr "" + +#: C/genius.xml:1154(programlisting) +#, no-wrap +msgid "3 ; 5\n" +msgstr "3 ; 5\n" + +#: C/genius.xml:1146(para) +msgid "" +"GEL is somewhat different from other languages in how it deals with multiple " +"commands and functions. In GEL you must chain commands together with a " +"separator operator. That is, if you want to type more than one expression you " +"have to use the <literal>;</literal> operator in between the expressions. This " +"is a way in which both expressions are evaluated and the result of the second " +"one (or the last one if there is more than two expressions) is returned. " +"Suppose you type the following: <placeholder-1/> This expression will yield 5." +msgstr "" + +#: C/genius.xml:1158(para) +msgid "" +"This will require some parenthesizing to make it unambiguous sometimes, " +"especially if the <literal>;</literal> is not the top most primitive. This " +"slightly differs from other programming languages where the <literal>;</" +"literal> is a terminator of statements, whereas in GEL it’s actually a binary " +"operator. If you are familiar with pascal this should be second nature. " +"However genius can let you pretend it is a terminator to some degree. If a " +"<literal>;</literal> is found at the end of a parenthesis or a block, genius " +"will append a null to it as if you would have written <userinput>;null</" +"userinput>. This is useful in case you do not want to return a value from say " +"a loop, or if you handle the return differently. Note that it will slightly " +"slow down the code if it is executed too often as there is one more operator " +"involved." +msgstr "" + +#: C/genius.xml:1171(para) +msgid "" +"If you are typing expressions in a program you do not have to add a semicolon. " +"In this case genius will simply print the return value whenever it executes " +"the expression. However, do note that if you are defining a function, the body " +"of the function is a single expression." +msgstr "" + +#: C/genius.xml:1179(title) +msgid "Comments" +msgstr "" + +#: C/genius.xml:1184(programlisting) +#, no-wrap +msgid "" +"# This is just a comment\n" +"# every line in a comment must have its own pond sign\n" +"# in the next line we set x to the value 123\n" +"x=123;\n" +msgstr "" + +#: C/genius.xml:1180(para) +msgid "" +"GEL is similar to other scripting languages in that <literal>#</literal> " +"denotes a comments, that is text that is not meant to be evaluated. Everything " +"beyond the pound sign till the end of line will just be ignored. For example, " +"<placeholder-1/>" +msgstr "" + +#: C/genius.xml:1193(title) +msgid "Modular Evaluation" +msgstr "" + +#: C/genius.xml:1194(para) +msgid "" +"Genius implements modular arithmetic. To use it you just add \"mod <" +"integer>\" after the expression. Example: <userinput>2^(5!) * 3^(6!) mod 5</" +"userinput> It could be possible to do modular arithmetic by computing with " +"integers and then modding in the end with the <literal>%</literal> operator, " +"which simply gives the remainder, but that may be time consuming if not " +"impossible when working with larger numbers. For example, " +"<userinput>10^(10^10) % 6</userinput> will simply not work (the exponent will " +"be too large), while <userinput>10^(10^10) mod 6</userinput> is instantaneous. " +"The first expression first tries to compute the integer <userinput>10^(10^10)</" +"userinput> and then find remainder after division by 6, while the second " +"expression evaluates everything modulo 6 to begin with." +msgstr "" + +#: C/genius.xml:1212(programlisting) +#, no-wrap +msgid "" +"10^-1 mod 101\n" +"1/10 mod 101" +msgstr "" +"10^-1 mod 101\n" +"1/10 mod 101" + +#: C/genius.xml:1217(programlisting) +#, no-wrap +msgid "" +"A = [1,2;3,4]\n" +"B = A^-1 mod 5\n" +"A*B mod 5" +msgstr "" +"A = [1,2;3,4]\n" +"B = A^-1 mod 5\n" +"A*B mod 5" + +#: C/genius.xml:1208(para) +msgid "" +"You can calculate the inverses of numbers mod some integer by just using " +"rational numbers (of course the inverse has to exist). Examples: " +"<placeholder-1/> You can also do modular evaluation with matrices including " +"taking inverses, powers and dividing. Example: <placeholder-2/> This should " +"yield the identity matrix as B will be the inverse of A mod 5." +msgstr "" + +#: C/genius.xml:1229(programlisting) +#, no-wrap +msgid "" +"genius> sqrt(4) mod 7\n" +"=\n" +"[2, 5]\n" +"genius> 2*2 mod 7\n" +"= 4" +msgstr "" +"genius> sqrt(4) mod 7\n" +"=\n" +"[2, 5]\n" +"genius> 2*2 mod 7\n" +"= 4" + +#: C/genius.xml:1222(para) +msgid "" +"Some functions such as <link linkend=\"gel-function-sqrt\"><function>sqrt</" +"function></link> or <link linkend=\"gel-function-log\"><function>log</" +"function></link> work in a different way when in modulo mode. These will then " +"work like their discrete versions working within the ring of integers you " +"selected. For example: <placeholder-1/><function>sqrt</function> will actually " +"return all the possible square roots." +msgstr "" + +#: C/genius.xml:1237(para) +msgid "" +"Do not chain mod operators, simply place it at the end of the computation, all " +"computations in the expression on the left will be carried out in mod " +"arithmetic. If you place a mod inside a mod, you will get unexpected results. " +"If you simply want to mod a single number and control exactly when remainders " +"are taken, best to use the <literal>%</literal> operator. When you need to " +"chain several expressions in modular arithmetic with different divisors, it " +"may be best to just split up the expression into several and use temporary " +"variables to avoid a mod inside a mod." +msgstr "" + +#: C/genius.xml:1250(title) +msgid "List of GEL Operators" +msgstr "" + +#: C/genius.xml:1252(para) +msgid "" +"Everything in gel is really just an expression. Expressions are stringed " +"together with different operators. As we have seen, even the separator is " +"simply a binary operator in GEL. Here is a list of the operators in GEL." +msgstr "" + +#: C/genius.xml:1260(userinput) +#, no-wrap +msgid "a;b" +msgstr "a;b" + +#: C/genius.xml:1262(para) +msgid "" +"The separator, just evaluates both <varname>a</varname> and <varname>b</" +"varname>, but returns only the result of <varname>b</varname>." +msgstr "" + +#: C/genius.xml:1274(userinput) +#, no-wrap +msgid "a=b" +msgstr "a=b" + +#: C/genius.xml:1276(para) +msgid "" +"The assignment operator. This assigns <varname>b</varname> to <varname>a</" +"varname> (<varname>a</varname> must be a valid <link linkend=\"genius-gel-" +"lvalues\">lvalue</link>) (note however that this operator may be translated to " +"<literal>==</literal> if used in a place where boolean expression is expected)" +msgstr "" + +#: C/genius.xml:1288(userinput) +#, no-wrap +msgid "a:=b" +msgstr "a:=b" + +#: C/genius.xml:1290(para) +msgid "" +"The assignment operator. Assigns <varname>b</varname> to <varname>a</varname> " +"(<varname>a</varname> must be a valid <link linkend=\"genius-gel-lvalues" +"\">lvalue</link>). This is different from <literal>=</literal> because it " +"never gets translated to a <literal>==</literal>." +msgstr "" + +#: C/genius.xml:1301(userinput) +#, no-wrap +msgid "|a|" +msgstr "|a|" + +#: C/genius.xml:1303(para) +msgid "" +"Absolute value. In case the expression is a complex number the result will be " +"the modulus (distance from the origin). For example: <userinput>|3 * e^(1i*pi)|" +"</userinput> returns 3." +msgstr "" + +#: C/genius.xml:1310(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/AbsoluteValue.html\">Mathworld</" +"ulink> for more information." +msgstr "" +"Se <ulink url=\"http://mathworld.wolfram.com/AbsoluteValue.html\">Mathworld</" +"ulink> för mer information." + +#: C/genius.xml:1319(userinput) +#, no-wrap +msgid "a^b" +msgstr "a^b" + +#: C/genius.xml:1321(para) +msgid "" +"Exponentiation, raises <varname>a</varname> to the <varname>b</varname>th " +"power." +msgstr "" + +#: C/genius.xml:1329(userinput) +#, no-wrap +msgid "a.^b" +msgstr "a.^b" + +#: C/genius.xml:1331(para) +msgid "" +"Element by element exponentiation. Raise each element of a matrix <varname>a</" +"varname> to the <varname>b</varname>th power. Or if <varname>b</varname> is a " +"matrix of the same size as <varname>a</varname>, then do the operation element " +"by element. If <varname>a</varname> is a number and <varname>b</varname> is a " +"matrix then it creates matrix of the same size as <varname>b</varname> with " +"<varname>a</varname> raised to all the different powers in <varname>b</" +"varname>." +msgstr "" + +#: C/genius.xml:1346(userinput) +#, no-wrap +msgid "a+b" +msgstr "a+b" + +#: C/genius.xml:1348(para) +msgid "" +"Addition. Adds two numbers, matrices, functions or strings. If you add a " +"string to anything the result will just be a string. If one is a square matrix " +"and the other a number, then the number is multiplied by the identity matrix." +msgstr "" + +#: C/genius.xml:1359(userinput) +#, no-wrap +msgid "a-b" +msgstr "a-b" + +#: C/genius.xml:1361(para) +msgid "Subtraction. Subtract two numbers, matrices or functions." +msgstr "" + +#: C/genius.xml:1369(userinput) +#, no-wrap +msgid "a*b" +msgstr "a*b" + +#: C/genius.xml:1371(para) +msgid "Multiplication. This is the normal matrix multiplication." +msgstr "" + +#: C/genius.xml:1379(userinput) +#, no-wrap +msgid "a.*b" +msgstr "a.*b" + +#: C/genius.xml:1381(para) +msgid "" +"Element by element multiplication if <varname>a</varname> and <varname>b</" +"varname> are matrices." +msgstr "" + +#: C/genius.xml:1390(userinput) +#, no-wrap +msgid "a/b" +msgstr "a/b" + +#: C/genius.xml:1392(para) +msgid "" +"Division. When <varname>a</varname> and <varname>b</varname> are just numbers " +"this is the normal division. When they are matrices, then this is equivalent " +"to <userinput>a*b^-1</userinput>." +msgstr "" + +#: C/genius.xml:1402(userinput) +#, no-wrap +msgid "a./b" +msgstr "a./b" + +#: C/genius.xml:1404(para) +msgid "" +"Element by element division. Same as <userinput>a/b</userinput> for numbers, " +"but operates element by element on matrices." +msgstr "" + +#: C/genius.xml:1413(userinput) +#, no-wrap +msgid "a\\b" +msgstr "a\\b" + +#: C/genius.xml:1415(para) +msgid "Back division. That is this is the same as <userinput>b/a</userinput>." +msgstr "" + +#: C/genius.xml:1423(userinput) +#, no-wrap +msgid "a.\\b" +msgstr "a.\\b" + +#: C/genius.xml:1425(para) +msgid "Element by element back division." +msgstr "" + +#: C/genius.xml:1433(userinput) +#, no-wrap +msgid "a%b" +msgstr "a%b" + +#: C/genius.xml:1435(para) +msgid "" +"The mod operator. This does not turn on the <link linkend=\"genius-gel-modular-" +"evaluation\">modular mode</link>, but just returns the remainder of " +"<userinput>a/b</userinput>." +msgstr "" + +#: C/genius.xml:1445(userinput) +#, no-wrap +msgid "a.%b" +msgstr "a.%b" + +#: C/genius.xml:1447(para) +msgid "" +"Element by element the mod operator. Returns the remainder after element by " +"element integer <userinput>a./b</userinput>." +msgstr "" + +#: C/genius.xml:1456(userinput) +#, no-wrap +msgid "a mod b" +msgstr "a mod b" + +#: C/genius.xml:1458(para) +msgid "" +"Modular evaluation operator. The expression <varname>a</varname> is evaluated " +"modulo <varname>b</varname>. See <xref linkend=\"genius-gel-modular-evaluation" +"\"/>. Some functions and operators behave differently modulo an integer." +msgstr "" + +#: C/genius.xml:1469(userinput) +#, no-wrap +msgid "a!" +msgstr "a!" + +#: C/genius.xml:1471(para) +msgid "" +"Factorial operator. This is like <userinput>1*...*(n-2)*(n-1)*n</userinput>." +msgstr "" + +#: C/genius.xml:1480(userinput) +#, no-wrap +msgid "a!!" +msgstr "a!!" + +#: C/genius.xml:1482(para) +msgid "" +"Double factorial operator. This is like <userinput>1*...*(n-4)*(n-2)*n</" +"userinput>." +msgstr "" + +#: C/genius.xml:1491(userinput) +#, no-wrap +msgid "a==b" +msgstr "a==b" + +#: C/genius.xml:1493(para) +msgid "" +"Equality operator. Returns <constant>true</constant> or <constant>false</" +"constant> depending on <varname>a</varname> and <varname>b</varname> being " +"equal or not." +msgstr "" + +#: C/genius.xml:1503(userinput) +#, no-wrap +msgid "a!=b" +msgstr "a!=b" + +#: C/genius.xml:1505(para) +msgid "" +"Inequality operator, returns <constant>true</constant> if <varname>a</varname> " +"does not equal <varname>b</varname> else returns <constant>false</constant>." +msgstr "" + +#: C/genius.xml:1515(userinput) +#, no-wrap +msgid "a<>b" +msgstr "a<>b" + +#: C/genius.xml:1517(para) +msgid "" +"Alternative inequality operator, returns <constant>true</constant> if " +"<varname>a</varname> does not equal <varname>b</varname> else returns " +"<constant>false</constant>." +msgstr "" + +#: C/genius.xml:1527(userinput) +#, no-wrap +msgid "a<=b" +msgstr "a<=b" + +#: C/genius.xml:1529(para) +msgid "" +"Less than or equal operator, returns <constant>true</constant> if <varname>a</" +"varname> is less than or equal to <varname>b</varname> else returns " +"<constant>false</constant>. These can be chained as in <userinput>a <= b " +"<= c</userinput> (can also be combined with the less than operator)." +msgstr "" + +#: C/genius.xml:1542(userinput) +#, no-wrap +msgid "a>=b" +msgstr "a>=b" + +#: C/genius.xml:1544(para) +msgid "" +"Greater than or equal operator, returns <constant>true</constant> if " +"<varname>a</varname> is greater than or equal to <varname>b</varname> else " +"returns <constant>false</constant>. These can be chained as in <userinput>a " +">= b >= c</userinput> (can also be combine with the greater than " +"operator)." +msgstr "" + +#: C/genius.xml:1556(userinput) +#, no-wrap +msgid "a<b" +msgstr "a<b" + +#: C/genius.xml:1558(para) +msgid "" +"Less than operator, returns <constant>true</constant> if <varname>a</varname> " +"is less than <varname>b</varname> else returns <constant>false</constant>. " +"These can be chained as in <userinput>a < b < c</userinput> (can also be " +"combine with the less than or equal to operator)." +msgstr "" + +#: C/genius.xml:1571(userinput) +#, no-wrap +msgid "a>b" +msgstr "a>b" + +#: C/genius.xml:1573(para) +msgid "" +"Greater than operator, returns <constant>true</constant> if <varname>a</" +"varname> is greater than <varname>b</varname> else returns <constant>false</" +"constant>. These can be chained as in <userinput>a > b > c</userinput> " +"(can also be combine with the greater than or equal to operator)." +msgstr "" + +#: C/genius.xml:1586(userinput) +#, no-wrap +msgid "a<=>b" +msgstr "a<=>b" + +#: C/genius.xml:1588(para) +msgid "" +"Comparison operator. If <varname>a</varname> is equal to <varname>b</varname> " +"it returns 0, if <varname>a</varname> is less than <varname>b</varname> it " +"returns -1 and if <varname>a</varname> is greater than <varname>b</varname> it " +"returns 1." +msgstr "" + +#: C/genius.xml:1600(userinput) +#, no-wrap +msgid "a and b" +msgstr "a and b" + +#: C/genius.xml:1602(para) +msgid "" +"Logical and. Returns true if both <varname>a</varname> and <varname>b</" +"varname> are true, else returns false. If given numbers, nonzero numbers are " +"treated as true." +msgstr "" + +#: C/genius.xml:1613(userinput) +#, no-wrap +msgid "a or b" +msgstr "a or b" + +#: C/genius.xml:1615(para) +msgid "" +"Logical or. Returns true if both <varname>a</varname> or <varname>b</varname> " +"are true, else returns false. If given numbers, nonzero numbers are treated as " +"true." +msgstr "" + +#: C/genius.xml:1627(userinput) +#, no-wrap +msgid "a xor b" +msgstr "a xor b" + +#: C/genius.xml:1629(para) +msgid "" +"Logical xor. Returns true exactly one of <varname>a</varname> or <varname>b</" +"varname> is true, else returns false. If given numbers, nonzero numbers are " +"treated as true." +msgstr "" + +#: C/genius.xml:1641(userinput) +#, no-wrap +msgid "not a" +msgstr "not a" + +#: C/genius.xml:1643(para) +msgid "Logical not. Returns the logical negation of <varname>a</varname>" +msgstr "" + +#: C/genius.xml:1651(userinput) +#, no-wrap +msgid "-a" +msgstr "-a" + +#: C/genius.xml:1653(para) +msgid "" +"Negation operator. Returns the negative of a number or a matrix (works element-" +"wise on a matrix)." +msgstr "" + +#: C/genius.xml:1661(userinput) +#, no-wrap +msgid "&a" +msgstr "&a" + +#: C/genius.xml:1663(para) +msgid "" +"Variable referencing (to pass a reference to a variable). See <xref linkend=" +"\"genius-gel-references\"/>." +msgstr "" + +#: C/genius.xml:1672(userinput) C/genius.xml:2319(userinput) +#, no-wrap +msgid "*a" +msgstr "*a" + +#: C/genius.xml:1674(para) +msgid "" +"Variable dereferencing (to access a referenced variable). See <xref linkend=" +"\"genius-gel-references\"/>." +msgstr "" + +#: C/genius.xml:1683(userinput) +#, no-wrap +msgid "a'" +msgstr "a'" + +#: C/genius.xml:1685(para) +msgid "" +"Matrix conjugate transpose. That is, rows and columns get swapped and we take " +"complex conjugate of all entries. That is if the i,j element of <varname>a</" +"varname> is x+iy, then the j,i element of <userinput>a'</userinput> is x-iy." +msgstr "" + +#: C/genius.xml:1694(userinput) +#, no-wrap +msgid "a.'" +msgstr "a.'" + +#: C/genius.xml:1696(para) +msgid "" +"Matrix transpose, does not conjugate the entries. That is, the i,j element of " +"<varname>a</varname> becomes the j,i element of <userinput>a.'</userinput>." +msgstr "" + +#: C/genius.xml:1705(userinput) +#, no-wrap +msgid "a@(b,c)" +msgstr "a@(b,c)" + +#: C/genius.xml:1707(para) +msgid "" +"Get element of a matrix in row <varname>b</varname> and column <varname>c</" +"varname>. If <varname>b</varname>, <varname>c</varname> are vectors, then this " +"gets the corresponding rows columns or submatrices." +msgstr "" + +#: C/genius.xml:1718(userinput) +#, no-wrap +msgid "a@(b,)" +msgstr "a@(b,)" + +#: C/genius.xml:1720(para) +msgid "" +"Get row of a matrix (or multiple rows if <varname>b</varname> is a vector)." +msgstr "" + +#: C/genius.xml:1728(userinput) +#, no-wrap +msgid "a@(b,:)" +msgstr "a@(b,:)" + +#: C/genius.xml:1730(para) C/genius.xml:1751(para) +msgid "Same as above." +msgstr "" + +#: C/genius.xml:1738(userinput) +#, no-wrap +msgid "a@(,c)" +msgstr "a@(,c)" + +#: C/genius.xml:1740(para) +msgid "Get column of a matrix (or columns if <varname>c</varname> is a vector)." +msgstr "" + +#: C/genius.xml:1749(userinput) +#, no-wrap +msgid "a@(:,c)" +msgstr "a@(:,c)" + +#: C/genius.xml:1759(userinput) +#, no-wrap +msgid "a@(b)" +msgstr "a@(b)" + +#: C/genius.xml:1761(para) +msgid "" +"Get an element from a matrix treating it as a vector. This will traverse the " +"matrix row-wise." +msgstr "" + +#: C/genius.xml:1770(userinput) +#, no-wrap +msgid "a:b" +msgstr "a:b" + +#: C/genius.xml:1774(programlisting) +#, no-wrap +msgid "" +"A@(2:4,)\n" +"\t " +msgstr "" +"A@(2:4,)\n" +"\t " + +#: C/genius.xml:1772(para) +msgid "" +"Build a vector from <varname>a</varname> to <varname>b</varname> (or specify a " +"row, column region for the <literal>@</literal> operator). For example to get " +"rows 2 to 4 of matrix <varname>A</varname> we could do <placeholder-1/> as " +"<userinput>2:4</userinput> will return a vector <userinput>[2,3,4]</userinput>." +msgstr "" + +#: C/genius.xml:1784(userinput) +#, no-wrap +msgid "a:b:c" +msgstr "a:b:c" + +#: C/genius.xml:1789(programlisting) +#, no-wrap +msgid "" +"genius> 1:2:9\n" +"=\n" +"`[1, 3, 5, 7, 9]\n" +msgstr "" +"genius> 1:2:9\n" +"=\n" +"`[1, 3, 5, 7, 9]\n" + +#: C/genius.xml:1786(para) +msgid "" +"Build a vector from <varname>a</varname> to <varname>c</varname> with " +"<varname>b</varname> as a step. That is for example <placeholder-1/>" +msgstr "" + +#: C/genius.xml:1794(para) +msgid "" +"When the numbers involved are floating point numbers, for example " +"<userinput>1.0:0.4:3.0</userinput>, the output is what is expected even though " +"adding 0.4 to 1.0 five times is actually just slightly more than 3.0 due to " +"the way that floating point numbers are stored in base 2 (there is no 0.4, the " +"actual number stored is just ever so slightly bigger). The way this is handled " +"is the same as in the for, sum, and prod loops. If the end is within " +"<userinput>2^-20</userinput> times the step size of the endpoint, the endpoint " +"is used and we assume there were roundoff errors. This is not perfect, but it " +"handles the majority of the cases. This check is done only from version 1.0.18 " +"onwards, so execution of your code may differ on older versions. If you want " +"to avoid dealing with this issue, use actual rational numbers, possibly using " +"the <function>float</function> if you wish to get floating point numbers in " +"the end. For example <userinput>1:2/5:3</userinput> does the right thing and " +"<userinput>float(1:2/5:3)</userinput> even gives you floating point numbers " +"and is ever so slightly more precise than <userinput>1.0:0.4:3.0</userinput>." +msgstr "" + +#: C/genius.xml:1820(userinput) +#, no-wrap +msgid "(a)i" +msgstr "(a)i" + +#: C/genius.xml:1826(programlisting) +#, no-wrap +msgid "" +"(a)*1i\n" +"\t " +msgstr "" +"(a)*1i\n" +"\t " + +#: C/genius.xml:1822(para) +msgid "" +"Make a imaginary number (multiply <varname>a</varname> by the imaginary). Note " +"that normally the number <varname>i</varname> is written as <userinput>1i</" +"userinput>. So the above is equal to <placeholder-1/>" +msgstr "" + +#: C/genius.xml:1834(userinput) +#, no-wrap +msgid "`a" +msgstr "`a" + +#: C/genius.xml:1836(para) +msgid "" +"Quote an identifier so that it doesn't get evaluated. Or quote a matrix so " +"that it doesn't get expanded." +msgstr "" + +#: C/genius.xml:1844(userinput) +#, no-wrap +msgid "a swapwith b" +msgstr "a swapwith b" + +#: C/genius.xml:1846(para) +msgid "" +"Swap value of <varname>a</varname> with the value of <varname>b</varname>. " +"Currently does not operate on ranges of matrix elements. It returns " +"<constant>null</constant>. Available from version 1.0.13." +msgstr "" + +#: C/genius.xml:1857(userinput) +#, no-wrap +msgid "increment a" +msgstr "increment a" + +#: C/genius.xml:1859(para) +msgid "" +"Increment the variable <varname>a</varname> by 1. If <varname>a</varname> is a " +"matrix, then increment each element. This is equivalent to <userinput>a=a+1</" +"userinput>, but it is somewhat faster. It returns <constant>null</constant>. " +"Available from version 1.0.13." +msgstr "" + +#: C/genius.xml:1870(userinput) +#, no-wrap +msgid "increment a by b" +msgstr "increment a by b" + +#: C/genius.xml:1872(para) +msgid "" +"Increment the variable <varname>a</varname> by <varname>b</varname>. If " +"<varname>a</varname> is a matrix, then increment each element. This is " +"equivalent to <userinput>a=a+b</userinput>, but it is somewhat faster. It " +"returns <constant>null</constant>. Available from version 1.0.13." +msgstr "" + +#: C/genius.xml:1886(para) +msgid "" +"The @() operator makes the : operator most useful. With this you can specify " +"regions of a matrix. So that a@(2:4,6) is the rows 2,3,4 of the column 6. Or " +"a@(,1:2) will get you the first two columns of a matrix. You can also assign " +"to the @() operator, as long as the right value is a matrix that matches the " +"region in size, or if it is any other type of value." +msgstr "" + +#: C/genius.xml:1892(para) +msgid "" +"The comparison operators (except for the <=> operator, which behaves " +"normally), are not strictly binary operators, they can in fact be grouped in " +"the normal mathematical way, e.g.: (1<x<=y<5) is a legal boolean " +"expression and means just what it should, that is (1<x and x≤y and y<5)" +msgstr "" + +#: C/genius.xml:1898(para) +msgid "" +"The unitary minus operates in a different fashion depending on where it " +"appears. If it appears before a number it binds very closely, if it appears in " +"front of an expression it binds less than the power and factorial operators. " +"So for example <userinput>-1^k</userinput> is really <userinput>(-1)^k</" +"userinput>, but <userinput>-foo(1)^k</userinput> is really <userinput>-" +"(foo(1)^k)</userinput>. So be careful how you use it and if in doubt, add " +"parentheses." +msgstr "" + +#: C/genius.xml:1913(title) +msgid "Programming with GEL" +msgstr "" + +#: C/genius.xml:1916(title) +msgid "Conditionals" +msgstr "" + +#: C/genius.xml:1917(para) +msgid "" +"Syntax: <placeholder-1/> If <literal>else</literal> is omitted, then if the " +"<literal>expression1</literal> yields <constant>false</constant> or 0, " +"<literal>NULL</literal> is returned." +msgstr "" + +#: C/genius.xml:1931(programlisting) +#, no-wrap +msgid "if a=5 then a=a-1\n" +msgstr "if a=5 then a=a-1\n" + +#: C/genius.xml:1934(programlisting) +#, no-wrap +msgid "if a==5 then a:=a-1\n" +msgstr "if a==5 then a:=a-1\n" + +#: C/genius.xml:1923(para) +msgid "" +"Examples: <placeholder-1/> Note that <literal>=</literal> will be translated " +"to <literal>==</literal> if used inside the expression for <literal>if</" +"literal>, so <placeholder-2/> will be interpreted as: <placeholder-3/>" +msgstr "" + +#: C/genius.xml:1940(title) +msgid "Loops" +msgstr "" + +#: C/genius.xml:1943(title) +msgid "While Loops" +msgstr "" + +#: C/genius.xml:1944(para) +msgid "" +"Syntax: <placeholder-1/> These are similar to other languages. However, as in " +"gel it is simply an expression that must have some return value, these " +"constructs will simply return the result of the last iteration or " +"<literal>NULL</literal> if no iteration was done. In the boolean expression, " +"<literal>=</literal> is translated into <literal>==</literal> just as for the " +"<literal>if</literal> statement." +msgstr "" + +#: C/genius.xml:1957(title) +msgid "For Loops" +msgstr "" + +#: C/genius.xml:1964(programlisting) +#, no-wrap +msgid "for i = 1 to 20 by 2 do print(i)\n" +msgstr "for i = 1 to 20 by 2 do print(i)\n" + +#: C/genius.xml:1958(para) +msgid "" +"Syntax: <placeholder-1/> Loop with identifier being set to all values from " +"<literal><from></literal> to <literal><to></literal>, optionally " +"using an increment other than 1. These are faster, nicer and more compact than " +"the normal loops such as above, but less flexible. The identifier must be an " +"identifier and can't be a dereference. The value of identifier is the last " +"value of identifier, or <literal><from></literal> if body was never " +"evaluated. The variable is guaranteed to be initialized after a loop, so you " +"can safely use it. Also the <literal><from></literal>, <literal><" +"to></literal> and <literal><increment></literal> must be non complex " +"values. The <literal><to></literal> is not guaranteed to be hit, but " +"will never be overshot, for example the following prints out odd numbers from " +"1 to 19: <placeholder-2/>" +msgstr "" + +#: C/genius.xml:1972(programlisting) +#, no-wrap +msgid "for x = 0 to 1 by 0.1 do print(x)\n" +msgstr "for x = 0 to 1 by 0.1 do print(x)\n" + +#: C/genius.xml:1977(programlisting) +#, no-wrap +msgid "for x = 0 to 1 by 1/10 do print(x)\n" +msgstr "for x = 0 to 1 by 1/10 do print(x)\n" + +#: C/genius.xml:1967(para) +msgid "" +"When one of the values is a floating point number, then the final check is " +"done to within 2^-20 of the step size. That is, even if we overshoot by 2^-20 " +"times the \"by\" above, we still execute the last iteration. This way " +"<placeholder-1/> does the expected even though adding 0.1 ten times becomes " +"just slightly more 1.0 due to the way that floating point numbers are stored " +"in base 2 (there is no 0.1, the actual number stored is just ever so slightly " +"bigger). This is not perfect but it handles the majority of the cases. If you " +"want to avoid dealing with this issue, use actual rational numbers for " +"example: <placeholder-2/> This check is done only from version 1.0.16 onwards, " +"so execution of your code may differ on older versions." +msgstr "" + +#: C/genius.xml:1984(title) +msgid "Foreach Loops" +msgstr "" + +#: C/genius.xml:1992(programlisting) +#, no-wrap +msgid "for n in [1,2:3,4] do print(n)\n" +msgstr "for n in [1,2:3,4] do print(n)\n" + +#: C/genius.xml:1997(programlisting) +#, no-wrap +msgid "for n in RowsOf ([1,2:3,4]) do print(n)\n" +msgstr "for n in RowsOf ([1,2:3,4]) do print(n)\n" + +#: C/genius.xml:1985(para) +msgid "" +"Syntax: <placeholder-1/> For each element in the matrix, going row by row from " +"left to right we execute the body with the identifier set to the current " +"element. To print numbers 1,2,3 and 4 in this order you could do: " +"<placeholder-2/> If you wish to run through the rows and columns of a matrix, " +"you can use the RowsOf and ColumnsOf functions, which return a vector of the " +"rows or columns of the matrix. So, <placeholder-3/> will print out [1,2] and " +"then [3,4]." +msgstr "" + +#: C/genius.xml:2004(title) +msgid "Break and Continue" +msgstr "" + +#: C/genius.xml:2005(para) +msgid "" +"You can also use the <literal>break</literal> and <literal>continue</literal> " +"commands in loops. The continue <literal>continue</literal> command will " +"restart the current loop at its next iteration, while the <literal>break</" +"literal> command exits the current loop. <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2018(title) +msgid "Sums and Products" +msgstr "" + +#: C/genius.xml:2019(para) +msgid "" +"Syntax: <placeholder-1/> If you substitute <literal>for</literal> with " +"<literal>sum</literal> or <literal>prod</literal>, then you will get a sum or " +"a product instead of a <literal>for</literal> loop. Instead of returning the " +"last value, these will return the sum or the product of the values " +"respectively." +msgstr "" + +#: C/genius.xml:2030(para) +msgid "" +"If no body is executed (for example <userinput>sum i=1 to 0 do ...</" +"userinput>) then <literal>sum</literal> returns 0 and <literal>prod</literal> " +"returns 1 as is the standard convention." +msgstr "" + +#: C/genius.xml:2033(para) +msgid "" +"For floating point numbers the same roundoff error protection is done as in " +"the for loop. See <xref linkend=\"genius-gel-loops-for\"/>." +msgstr "" + +#: C/genius.xml:2040(title) +msgid "Comparison Operators" +msgstr "" + +#: C/genius.xml:2041(para) +msgid "" +"The following standard comparison operators are supported in GEL and have the " +"obvious meaning: <literal>==</literal>, <literal>>=</literal>, <literal><" +"=</literal>, <literal>!=</literal>, <literal><></literal>, <literal><" +"</literal>, <literal>></literal>. They return <constant>true</constant> or " +"<constant>false</constant>. The operators <literal>!=</literal> and " +"<literal><></literal> are the same thing and mean \"is not equal to\". " +"GEL also supports the operator <literal><=></literal>, which returns -1 " +"if left side is smaller, 0 if both sides are equal, 1 if left side is larger." +msgstr "" + +#: C/genius.xml:2060(programlisting) +#, no-wrap +msgid "" +"if a=b then c\n" +"if a==b then c\n" +msgstr "" +"if a=b then c\n" +"if a==b then c\n" + +#: C/genius.xml:2056(para) +msgid "" +"Normally <literal>=</literal> is translated to <literal>==</literal> if it " +"happens to be somewhere where GEL is expecting a condition such as in the if " +"condition. For example <placeholder-1/> are the same thing in GEL. However you " +"should really use <literal>==</literal> or <literal>:=</literal> when you want " +"to compare or assign respectively if you want your code to be easy to read and " +"to avoid mistakes." +msgstr "" + +#: C/genius.xml:2069(para) +msgid "" +"All the comparison operators (except for the <literal><=></literal> " +"operator, which behaves normally), are not strictly binary operators, they can " +"in fact be grouped in the normal mathematical way, e.g.: (<literal>1<x<" +"=y<5</literal>) is a legal boolean expression and means just what it " +"should, that is (1<x and x≤y and y<5)" +msgstr "" + +#: C/genius.xml:2078(para) +msgid "" +"To build up logical expressions use the words <literal>not</literal>, " +"<literal>and</literal>, <literal>or</literal>, <literal>xor</literal>. The " +"operators <literal>or</literal> and <literal>and</literal> are special beasts " +"as they evaluate their arguments one by one, so the usual trick for " +"conditional evaluation works here as well. For example, <literal>1 or a=1</" +"literal> will not set <literal>a=1</literal> since the first argument was true." +msgstr "" + +#: C/genius.xml:2089(title) +msgid "Global Variables and Scope of Variables" +msgstr "" + +#: C/genius.xml:2090(para) +msgid "" +"GEL is a <ulink url=\"http://en.wikipedia.org/wiki/Scope_%28programming%29\"> " +"dynamically scoped language</ulink>. We will explain what this means below. " +"That is, normal variables and functions are dynamically scoped. The exception " +"are <link linkend=\"genius-gel-parameters\">parameter variables</link>, which " +"are always global." +msgstr "" + +#: C/genius.xml:2113(programlisting) +#, no-wrap +msgid "" +"function f() = (a:=5; g());\n" +"function g() = print(a);\n" +"f();\n" +msgstr "" +"function f() = (a:=5; g());\n" +"function g() = print(a);\n" +"f();\n" + +#: C/genius.xml:2099(para) +msgid "" +"Like most programming languages, GEL has different types of variables. " +"Normally when a variable is defined in a function, it is visible from that " +"function and from all functions that are called (all higher contexts). For " +"example, suppose a function <function>f</function> defines a variable " +"<varname>a</varname> and then calls function <function>g</function>. Then " +"function <function>g</function> can reference <varname>a</varname>. But once " +"<function>f</function> returns, the variable <varname>a</varname> goes out of " +"scope. For example, the following code will print out 5. The function " +"<function>g</function> cannot be called on the top level (outside <function>f</" +"function> as <varname>a</varname> will not be defined). <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2122(programlisting) +#, no-wrap +msgid "" +"function f() = (a:=5; g());\n" +"function g() = print(a);\n" +"a:=10;\n" +"f();\n" +msgstr "" +"function f() = (a:=5; g());\n" +"function g() = print(a);\n" +"a:=10;\n" +"f();\n" + +#: C/genius.xml:2118(para) +msgid "" +"If you define a variable inside a function it will override any variables " +"defined in calling functions. For example, we modify the above code and write: " +"<placeholder-1/> This code will still print out 5. But if you call " +"<function>g</function> outside of <function>f</function> then you will get a " +"printout of 10. Note that setting <varname>a</varname> to 5 inside " +"<function>f</function> does not change the value of <varname>a</varname> at " +"the top (global) level, so if you now check the value of <varname>a</varname> " +"it will still be 10." +msgstr "" + +#: C/genius.xml:2136(para) +msgid "" +"Function arguments are exactly like variables defined inside the function, " +"except that they are initialized with the value that was passed to the " +"function. Other than this point, they are treated just like all other " +"variables defined inside the function." +msgstr "" + +#: C/genius.xml:2143(para) +msgid "" +"Functions are treated exactly like variables. Hence you can locally redefine " +"functions. Normally (on the top level) you cannot redefine protected variables " +"and functions. But locally you can do this. Consider the following session: " +"<screen><prompt>genius> </prompt><userinput>function f(x) = sin(x)^2</" +"userinput>\n" +"= (`(x)=(sin(x)^2))\n" +"<prompt>genius> </prompt><userinput>function f(x) = sin(x)^2</userinput>\n" +"= (`(x)=(sin(x)^2))\n" +"<prompt>genius> </prompt><userinput>function g(x) = ((function sin(x)=x^10);" +"f(x))</userinput>\n" +"= (`(x)=((sin:=(`(x)=(x^10)));f(x)))\n" +"<prompt>genius> </prompt><userinput>g(10)</userinput>\n" +"= 1e20\n" +"</screen>" +msgstr "" + +#: C/genius.xml:2163(programlisting) +#, no-wrap +msgid "" +"a=6;\n" +"function f() = (a:=5);\n" +"f();\n" +msgstr "" +"a=6;\n" +"function f() = (a:=5);\n" +"f();\n" + +#: C/genius.xml:2174(programlisting) +#, no-wrap +msgid "set(`a,3)\n" +msgstr "set(`a,3)\n" + +#: C/genius.xml:2177(programlisting) +#, no-wrap +msgid "set(\"a\",3)\n" +msgstr "set(\"a\",3)\n" + +#: C/genius.xml:2158(para) +msgid "" +"Functions and variables defined at the top level are considered global. They " +"are visible from anywhere. As we said the following function <function>f</" +"function> will not change the value of <varname>a</varname> to 5. " +"<placeholder-1/> Sometimes, however, it is necessary to set a global variable " +"from inside a function. When this behavior is needed, use the <link linkend=" +"\"gel-function-set\"><function>set</function></link> function. Passing a " +"string or a quoted identifier to this function sets the variable globally (on " +"the top level). For example, to set <varname>a</varname> to the value 3 you " +"could call: <placeholder-2/> or: <placeholder-3/>" +msgstr "" + +#: C/genius.xml:2180(para) +msgid "" +"The <function>set</function> function always sets the toplevel global. There " +"is no way to set a local variable in some function from a subroutine. If this " +"is required, must use passing by reference." +msgstr "" + +#: C/genius.xml:2186(para) +msgid "" +"See also the <link linkend=\"gel-function-SetElement\"><function>SetElement</" +"function></link> and <link linkend=\"gel-function-SetVElement" +"\"><function>SetVElement</function></link> functions." +msgstr "" + +#: C/genius.xml:2191(para) +msgid "" +"So to recap in a more technical language: Genius operates with different " +"numbered contexts. The top level is the context 0 (zero). Whenever a function " +"is entered, the context is raised, and when the function returns the context " +"is lowered. A function or a variable is always visible from all higher " +"numbered contexts. When a variable was defined in a lower numbered context, " +"then setting this variable has the effect of creating a new local variable in " +"the current context number and this variable will now be visible from all " +"higher numbered contexts." +msgstr "" + +#: C/genius.xml:2202(para) +msgid "" +"There are also true local variables that are not seen from anywhere but the " +"current context. Also when returning functions by value it may reference " +"variables not visible from higher context and this may be a problem. See the " +"sections <link linkend=\"genius-gel-true-local-variables\">True Local " +"Variables</link> and <link linkend=\"genius-gel-returning-functions" +"\">Returning Functions</link>." +msgstr "" + +#: C/genius.xml:2215(title) +msgid "Parameter variables" +msgstr "" + +#: C/genius.xml:2216(para) +msgid "" +"As we said before, there exist special variables called parameters that exist " +"in all scopes. To declare a parameter called <varname>foo</varname> with the " +"initial value 1, we write <placeholder-1/> From then on, <varname>foo</" +"varname> is a strictly global variable. Setting <varname>foo</varname> inside " +"any function will modify the variable in all contexts, that is, functions do " +"not have a private copy of parameters." +msgstr "" + +#: C/genius.xml:2227(para) +msgid "" +"When you undefine a parameter using the <link linkend=\"gel-function-undefine" +"\"><function>undefine</function></link> function, it stops being a parameter." +msgstr "" + +#: C/genius.xml:2233(para) +msgid "Some parameters are built-in and modify the behavior of genius." +msgstr "" + +#: C/genius.xml:2239(title) +msgid "Returning" +msgstr "" + +#: C/genius.xml:2240(para) +msgid "" +"Normally a function is one or several expressions separated by a semicolon, " +"and the value of the last expression is returned. This is fine for simple " +"functions, but sometimes you do not want a function to return the last thing " +"calculated. You may, for example, want to return from a middle of a function. " +"In this case, you can use the <literal>return</literal> keyword. " +"<literal>return</literal> takes one argument, which is the value to be " +"returned." +msgstr "" + +#: C/genius.xml:2262(title) +msgid "References" +msgstr "" + +#: C/genius.xml:2263(para) +msgid "" +"It may be necessary for some functions to return more than one value. This may " +"be accomplished by returning a vector of values, but many times it is " +"convenient to use passing a reference to a variable. You pass a reference to a " +"variable to a function, and the function will set the variable for you using a " +"dereference. You do not have to use references only for this purpose, but this " +"is their main use." +msgstr "" + +#: C/genius.xml:2271(para) +msgid "" +"When using functions that return values through references in the argument " +"list, just pass the variable name with an ampersand. For example the following " +"code will compute an eigenvalue of a matrix <varname>A</varname> with initial " +"eigenvector guess <varname>x</varname>, and store the computed eigenvector " +"into the variable named <varname>v</varname>: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2281(para) +msgid "" +"The details of how references work and the syntax is similar to the C " +"language. The operator <literal>&</literal> references a variable and " +"<literal>*</literal> dereferences a variable. Both can only be applied to an " +"identifier, so <literal>**a</literal> is not a legal expression in GEL." +msgstr "" + +#: C/genius.xml:2288(para) +msgid "" +"References are best explained by an example: <placeholder-1/> now <varname>a</" +"varname> contains 2. You can also reference functions: <placeholder-2/> gives " +"us 4." +msgstr "" + +#: C/genius.xml:2304(title) +msgid "Lvalues" +msgstr "" + +#: C/genius.xml:2310(userinput) +#, no-wrap +msgid "a" +msgstr "a" + +#: C/genius.xml:2312(para) +msgid "" +"Identifier. Here we would be setting the variable of name <varname>a</varname>." +msgstr "" + +#: C/genius.xml:2321(para) +msgid "" +"Dereference of an identifier. This will set whatever variable <varname>a</" +"varname> points to." +msgstr "" + +#: C/genius.xml:2328(userinput) +#, no-wrap +msgid "a@(<region>)" +msgstr "a@(<region>)" + +#: C/genius.xml:2330(para) +msgid "" +"A region of a matrix. Here the region is specified normally as with the " +"regular @() operator, and can be a single entry, or an entire region of the " +"matrix." +msgstr "" + +#: C/genius.xml:2305(para) +msgid "" +"An lvalue is the left hand side of an assignment. In other words, an lvalue is " +"what you assign something to. Valid lvalues are: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2341(programlisting) +#, no-wrap +msgid "" +"a:=4\n" +"*tmp := 89\n" +"a@(1,1) := 5\n" +"a@(4:8,3) := [1,2,3,4,5]'\n" +msgstr "" +"a:=4\n" +"*tmp := 89\n" +"a@(1,1) := 5\n" +"a@(4:8,3) := [1,2,3,4,5]'\n" + +#: C/genius.xml:2339(para) +msgid "" +"Examples: <placeholder-1/> Note that both <literal>:=</literal> and " +"<literal>=</literal> can be used interchangeably. Except if the assignment " +"appears in a condition. It is thus always safer to just use <literal>:=</" +"literal> when you mean assignment, and <literal>==</literal> when you mean " +"comparison." +msgstr "" + +#: C/genius.xml:2357(title) +msgid "Advanced Programming with GEL" +msgstr "" + +#: C/genius.xml:2360(title) +msgid "Error Handling" +msgstr "" + +#: C/genius.xml:2361(para) +msgid "" +"If you detect an error in your function, you can bail out of it. For normal " +"errors, such as wrong types of arguments, you can fail to compute the function " +"by adding the statement <literal>bailout</literal>. If something went really " +"wrong and you want to completely kill the current computation, you can use " +"<literal>exception</literal>." +msgstr "" + +#: C/genius.xml:2371(programlisting) +#, no-wrap +msgid "" +"function f(M) = (\n" +" if not IsMatrix (M) then (\n" +" error (\"M not a matrix!\");\n" +" bailout\n" +" );\n" +" ...\n" +")\n" +msgstr "" +"function f(M) = (\n" +" if not IsMatrix (M) then (\n" +" error (\"M not a matrix!\");\n" +" bailout\n" +" );\n" +" ...\n" +")\n" + +#: C/genius.xml:2368(para) +msgid "" +"For example if you want to check for arguments in your function. You could use " +"the following code. <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2383(title) +msgid "Toplevel Syntax" +msgstr "" + +#: C/genius.xml:2384(para) +msgid "" +"The syntax is slightly different if you enter statements on the top level " +"versus when they are inside parentheses or inside functions. On the top level, " +"enter acts the same as if you press return on the command line. Therefore " +"think of programs as just sequence of lines as if were entered on the command " +"line. In particular, you do not need to enter the separator at the end of the " +"line (unless it is of course part of several statements inside parentheses)." +msgstr "" + +#: C/genius.xml:2397(programlisting) +#, no-wrap +msgid "" +"if Something() then\n" +" DoSomething()\n" +"else\n" +" DoSomethingElse()\n" +msgstr "" + +#: C/genius.xml:2394(para) +msgid "" +"The following code will produce an error when entered on the top level of a " +"program, while it will work just fine in a function. <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2411(programlisting) +#, no-wrap +msgid "" +"if Something() then (\n" +" DoSomething()\n" +") else (\n" +" DoSomethingElse()\n" +")\n" +msgstr "" + +#: C/genius.xml:2403(para) +msgid "" +"The problem is that after <application>Genius Mathematics Tool</application> " +"sees the end of line after the second line, it will decide that we have whole " +"statement and it will execute it. After the execution is done, " +"<application>Genius Mathematics Tool</application> will go on to the next " +"line, it will see <literal>else</literal>, and it will produce a parsing " +"error. To fix this, use parentheses. <application>Genius Mathematics Tool</" +"application> will not be satisfied until it has found that all parentheses are " +"closed. <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2421(title) +msgid "Returning Functions" +msgstr "" + +#: C/genius.xml:2434(programlisting) +#, no-wrap +msgid "" +"function f() = (\n" +" k = 5;\n" +" `(x) = (x+k)\n" +")\n" +msgstr "" +"function f() = (\n" +" k = 5;\n" +" `(x) = (x+k)\n" +")\n" + +#: C/genius.xml:2441(programlisting) +#, no-wrap +msgid "" +"g = f();\n" +"g(5)\n" +msgstr "" +"g = f();\n" +"g(5)\n" + +#: C/genius.xml:2422(para) +msgid "" +"It is possible to return functions as value. This way you can build functions " +"that construct special purpose functions according to some parameters. The " +"tricky bit is what variables does the function see. The way this works in GEL " +"is that when a function returns another function, all identifiers referenced " +"in the function body that went out of scope are prepended a private dictionary " +"of the returned function. So the function will see all variables that were in " +"scope when it was defined. For example, we define a function that returns a " +"function that adds 5 to its argument. <placeholder-1/> Notice that the " +"function adds <varname>k</varname> to <varname>x</varname>. You could use this " +"as follows. <placeholder-2/> And <userinput>g(5)</userinput> should return 10." +msgstr "" + +#: C/genius.xml:2450(programlisting) +#, no-wrap +msgid "" +"function f() = (\n" +" k := 5;\n" +" function r(x) = (x+k);\n" +" k := 10;\n" +" r\n" +")\n" +msgstr "" +"function f() = (\n" +" k := 5;\n" +" function r(x) = (x+k);\n" +" k := 10;\n" +" r\n" +")\n" + +#: C/genius.xml:2446(para) +msgid "" +"One thing to note is that the value of <varname>k</varname> that is used is " +"the one that's in effect when the <function>f</function> returns. For example: " +"<placeholder-1/> will return a function that adds 10 to its argument rather " +"than 5. This is because the extra dictionary is created only when the context " +"in which the function was defined ends, which is when the function " +"<function>f</function> returns. This is consistent with how you would expect " +"the function <function>r</function> to work inside the function <function>f</" +"function> according to the rules of scope of variables in GEL. Only those " +"variables are added to the extra dictionary that are in the context that just " +"ended and no longer exists. Variables used in the function that are in still " +"valid contexts will work as usual, using the current value of the variable. " +"The only difference is with global variables and functions. All identifiers " +"that referenced global variables at time of the function definition are not " +"added to the private dictionary. This is to avoid much unnecessary work when " +"returning functions and would rarely be a problem. For example, suppose that " +"you delete the \"k=5\" from the function <function>f</function>, and at the " +"top level you define <varname>k</varname> to be say 5. Then when you run " +"<function>f</function>, the function <function>r</function> will not put " +"<varname>k</varname> into the private dictionary because it was global " +"(toplevel) at the time of definition of <function>r</function>." +msgstr "" + +#: C/genius.xml:2492(programlisting) +#, no-wrap +msgid "" +"function f() = (\n" +" k := 5;\n" +" function r(x) [k] = (x+k);\n" +" k := 10;\n" +" r\n" +")\n" +msgstr "" +"function f() = (\n" +" k := 5;\n" +" function r(x) [k] = (x+k);\n" +" k := 10;\n" +" r\n" +")\n" + +#: C/genius.xml:2481(para) +msgid "" +"Sometimes it is better to have more control over how variables are copied into " +"the private dictionary. Since version 1.0.7, you can specify which variables " +"are copied into the private dictionary by putting extra square brackets after " +"the arguments with the list of variables to be copied separated by commas. If " +"you do this, then variables are copied into the private dictionary at time of " +"the function definition, and the private dictionary is not touched afterwards. " +"For example <placeholder-1/> will return a function that when called will add " +"5 to its argument. The local copy of <varname>k</varname> was created when the " +"function was defined." +msgstr "" + +#: C/genius.xml:2514(programlisting) +#, no-wrap +msgid "" +"function f() = (\n" +" k := 5;\n" +" function r(x) [] = (x+k);\n" +" r\n" +");\n" +"k := 10;\n" +"g = f();\n" +"g(10)\n" +msgstr "" +"function f() = (\n" +" k := 5;\n" +" function r(x) [] = (x+k);\n" +" r\n" +");\n" +"k := 10;\n" +"g = f();\n" +"g(10)\n" + +#: C/genius.xml:2503(para) +msgid "" +"When you want the function to not have any private dictionary then put empty " +"square brackets after the argument list. Then no private dictionary will be " +"created at all. Doing this is good to increase efficiency when a private " +"dictionary is not needed or when you want the function to lookup all variables " +"as it sees them when called. For example suppose you want the function " +"returned from <function>f</function> to see the value of <varname>k</varname> " +"from the toplevel despite there being a local variable of the same name during " +"definition. So the code <placeholder-1/> will return 20 and not 15, which " +"would happen if <varname>k</varname> with a value of 5 was added to the " +"private dictionary." +msgstr "" + +#: C/genius.xml:2530(title) +msgid "True Local Variables" +msgstr "" + +#: C/genius.xml:2534(programlisting) +#, no-wrap +msgid "" +"k := 10;\n" +"function r(x) = (x+k);\n" +"function f(g,x) = (\n" +" k := 5;\n" +" g(x)\n" +");\n" +"f(r,1)\n" +msgstr "" +"k := 10;\n" +"function r(x) = (x+k);\n" +"function f(g,x) = (\n" +" k := 5;\n" +" g(x)\n" +");\n" +"f(r,1)\n" + +#: C/genius.xml:2531(para) +msgid "" +"When passing functions into other functions, the normal scoping of variables " +"might be undesired. For example: <placeholder-1/> you probably want the " +"function <function>r</function> when passed as <function>g</function> into " +"<function>f</function> to see <varname>k</varname> as 10 rather than 5, so " +"that the code returns 11 and not 6. However, as written, the function when " +"executed will see the <varname>k</varname> that is equal to 5. There are two " +"ways to solve this. One would be to have <function>r</function> get " +"<varname>k</varname> in a private dictionary using the square bracket notation " +"section <link linkend=\"genius-gel-returning-functions\">Returning Functions</" +"link>." +msgstr "" + +#: C/genius.xml:2563(programlisting) +#, no-wrap +msgid "" +"function f(g,x) = (\n" +" local g,x,k;\n" +" k := 5;\n" +" g(x)\n" +");\n" +msgstr "" +"function f(g,x) = (\n" +" local g,x,k;\n" +" k := 5;\n" +" g(x)\n" +");\n" + +#: C/genius.xml:2553(para) +msgid "" +"But there is another solution. Since version 1.0.7 there are true local " +"variables. These are variables that are visible only from the current context " +"and not from any called functions. We could define <varname>k</varname> as a " +"local variable in the function <function>f</function>. To do this add a " +"<command>local</command> statement as the first statement in the function (it " +"must always be the first statement in the function). You can also make any " +"arguments be local variables as well. That is, <placeholder-1/> Then the code " +"will work as expected and prints out 11. Note that the <command>local</" +"command> statement initializes all the referenced variables (except for " +"function arguments) to a <constant>null</constant>." +msgstr "" + +#: C/genius.xml:2580(programlisting) +#, no-wrap +msgid "" +"function f(g,x) = (\n" +" local *;\n" +" k := 5;\n" +" g(x)\n" +");\n" +msgstr "" +"function f(g,x) = (\n" +" local *;\n" +" k := 5;\n" +" g(x)\n" +");\n" + +#: C/genius.xml:2574(para) +msgid "" +"If all variables are to be created as locals you can just pass an asterisk " +"instead of a list of variables. In this case the variables will not be " +"initialized until they are actually set of course. So the following definition " +"of <function>f</function> will also work: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2587(para) +msgid "" +"It is good practice that all functions that take other functions as arguments " +"use local variables. This way the passed function does not see implementation " +"details and get confused." +msgstr "" + +#: C/genius.xml:2595(title) +msgid "GEL Startup Procedure" +msgstr "" + +#: C/genius.xml:2596(para) +msgid "" +"First the program looks for the installed library file (the compiled version " +"<filename>lib.cgel</filename>) in the installed directory, then it looks into " +"the current directory, and then it tries to load an uncompiled file called " +"<filename>~/.geniusinit</filename>." +msgstr "" + +#: C/genius.xml:2600(para) +msgid "" +"If you ever change the library in its installed place, you’ll have to first " +"compile it with <command>genius --compile loader.gel > lib.cgel</command>" +msgstr "" + +#: C/genius.xml:2607(title) +msgid "Loading Programs" +msgstr "" + +#: C/genius.xml:2610(programlisting) +#, no-wrap +msgid "" +"load program1.gel program2.gel\n" +"load \"Weird File Name With SPACES.gel\"\n" +msgstr "" + +#: C/genius.xml:2614(programlisting) +#, no-wrap +msgid "" +"cd directory_with_gel_programs\n" +"ls *.gel\n" +msgstr "" + +#: C/genius.xml:2608(para) +msgid "" +"Sometimes you have a larger program you wrote into a file and want to read " +"that file into <application>Genius Mathematics Tool</application>. In these " +"situations, you have two options. You can keep the functions you use most " +"inside the <filename>~/.geniusinit</filename> file. Or if you want to load up " +"a file in a middle of a session (or from within another file), you can type " +"<command>load <list of filenames></command> at the prompt. This has to " +"be done on the top level and not inside any function or whatnot, and it cannot " +"be part of any expression. It also has a slightly different syntax than the " +"rest of genius, more similar to a shell. You can enter the file in quotes. If " +"you use the '' quotes, you will get exactly the string that you typed, if you " +"use the \"\" quotes, special characters will be unescaped as they are for " +"strings. Example: <placeholder-1/> There are also <command>cd</command>, " +"<command>pwd</command> and <command>ls</command> commands built in. " +"<command>cd</command> will take one argument, <command>ls</command> will take " +"an argument that is like the glob in the UNIX shell (i.e., you can use " +"wildcards). <command>pwd</command> takes no arguments. For example: " +"<placeholder-2/>" +msgstr "" + +#: C/genius.xml:2624(title) +msgid "Matrices in GEL" +msgstr "" + +#: C/genius.xml:2626(para) +msgid "" +"Genius has support for vectors and matrices and possesses a sizable library of " +"matrix manipulation and linear algebra functions." +msgstr "" + +#: C/genius.xml:2632(title) +msgid "Entering Matrices" +msgstr "" + +#: C/genius.xml:2641(programlisting) +#, no-wrap +msgid "[1,2,3;4,5,6;7,8,9]\n" +msgstr "[1,2,3;4,5,6;7,8,9]\n" + +#: C/genius.xml:2644(programlisting) +#, no-wrap +msgid "" +"[1, 2, 3\n" +" 4, 5, 6\n" +" 7, 8, 9]\n" +msgstr "" +"[1, 2, 3\n" +" 4, 5, 6\n" +" 7, 8, 9]\n" + +#: C/genius.xml:2633(para) +msgid "" +"To enter matrices, you can use one of the following two syntaxes. You can " +"either enter the matrix on one line, separating values by commas and rows by " +"semicolons. Or you can enter each row on one line, separating values by " +"commas. You can also just combine the two methods. So to enter a 3x3 matrix of " +"numbers 1-9 you could do <placeholder-1/> or <placeholder-2/> Do not use both " +"';' and return at once on the same line though." +msgstr "" + +#: C/genius.xml:2654(programlisting) +#, no-wrap +msgid "" +"a = [ 1, 2, 3\n" +" 4, 5, 6\n" +" 7, 8, 9]\n" +"b = [ a, 10\n" +" 11, 12]\n" +msgstr "" +"a = [ 1, 2, 3\n" +" 4, 5, 6\n" +" 7, 8, 9]\n" +"b = [ a, 10\n" +" 11, 12]\n" + +#: C/genius.xml:2661(programlisting) +#, no-wrap +msgid "" +"[1, 2, 3, 10\n" +" 4, 5, 6, 10\n" +" 7, 8, 9, 10\n" +" 11, 11, 11, 12]\n" +msgstr "" +"[1, 2, 3, 10\n" +" 4, 5, 6, 10\n" +" 7, 8, 9, 10\n" +" 11, 11, 11, 12]\n" + +#: C/genius.xml:2651(para) +msgid "" +"You can also use the matrix expansion functionality to enter matrices. For " +"example you can do: <placeholder-1/> and you should get <placeholder-2/> " +"similarly you can build matrices out of vectors and other stuff like that." +msgstr "" + +#: C/genius.xml:2671(programlisting) +#, no-wrap +msgid "" +"[1, 2, 3\n" +" 4, 5\n" +" 6]\n" +msgstr "" +"[1, 2, 3\n" +" 4, 5\n" +" 6]\n" + +#: C/genius.xml:2676(programlisting) +#, no-wrap +msgid "" +"\n" +"[1, 2, 3\n" +" 4, 5, 0\n" +" 6, 0, 0]\n" +msgstr "" +"\n" +"[1, 2, 3\n" +" 4, 5, 0\n" +" 6, 0, 0]\n" + +#: C/genius.xml:2669(para) +msgid "" +"Another thing is that non-specified spots are initialized to 0, so " +"<placeholder-1/> will end up being <placeholder-2/>" +msgstr "" + +#: C/genius.xml:2683(para) +msgid "" +"When matrices are evaluated, they are evaluated and traversed row-wise. This " +"is just like the <literal>M@(j)</literal> operator, which traverses the matrix " +"row-wise." +msgstr "" + +#: C/genius.xml:2689(para) +msgid "" +"Be careful about using returns for expressions inside the <literal>[ ]</" +"literal> brackets, as they have a slightly different meaning there. You will " +"start a new row." +msgstr "" + +#: C/genius.xml:2699(title) +msgid "Conjugate Transpose and Transpose Operator" +msgstr "" + +#: C/genius.xml:2707(programlisting) +#, no-wrap +msgid "[1,2,3]*[4,5,6]'\n" +msgstr "[1,2,3]*[4,5,6]'\n" + +#: C/genius.xml:2712(programlisting) +#, no-wrap +msgid "[1,2,3]*[4,5,6i].'\n" +msgstr "[1,2,3]*[4,5,6i].'\n" + +#: C/genius.xml:2700(para) +msgid "" +"You can conjugate transpose a matrix by using the <literal>'</literal> " +"operator. That is the entry in the <varname>i</varname>th column and the " +"<varname>j</varname>th row will be the complex conjugate of the entry in the " +"<varname>j</varname>th column and the <varname>i</varname>th row of the " +"original matrix. For example: <placeholder-1/> We transpose the second vector " +"to make matrix multiplication possible. If you just want to transpose a matrix " +"without conjugating it, you would use the <literal>.'</literal> operator. For " +"example: <placeholder-2/>" +msgstr "" + +#: C/genius.xml:2715(para) +msgid "" +"Note that normal transpose, that is the <literal>.'</literal> operator, is " +"much faster and will not create a new copy of the matrix in memory. The " +"conjugate transpose does create a new copy unfortunately. It is recommended to " +"always use the <literal>.'</literal> operator when working with real matrices " +"and vectors." +msgstr "" + +#: C/genius.xml:2725(title) C/genius.xml:5869(title) +msgid "Linear Algebra" +msgstr "" + +#: C/genius.xml:2726(para) +msgid "" +"Genius implements many useful linear algebra and matrix manipulation routines. " +"See the <link linkend=\"genius-gel-function-list-linear-algebra\">Linear " +"Algebra</link> and <link linkend=\"genius-gel-function-list-matrix\">Matrix " +"Manipulation</link> sections of the GEL function listing." +msgstr "" + +#: C/genius.xml:2733(para) +msgid "" +"The linear algebra routines implemented in GEL do not currently come from a " +"well tested numerical package, and thus should not be used for critical " +"numerical computation. On the other hand, Genius implements very well many " +"linear algebra operations with rational and integer coefficients. These are " +"inherently exact and in fact will give you much better results than common " +"double precision routines for linear algebra." +msgstr "" + +#: C/genius.xml:2741(para) +msgid "" +"For example, it is pointless to compute the rank and nullspace of a floating " +"point matrix since for all practical purposes, we need to consider the matrix " +"as having some slight errors. You are likely to get a different result than " +"you expect. The problem is that under a small perturbation every matrix is of " +"full rank and invertible. If the matrix however is of rational numbers, then " +"the rank and nullspace are always exact." +msgstr "" + +#: C/genius.xml:2749(para) +msgid "" +"In general when Genius computes the basis of a certain vectorspace (for " +"example with the <link linkend=\"gel-function-NullSpace\"><function>NullSpace</" +"function></link>) it will give the basis as a matrix, in which the columns are " +"the vectors of the basis. That is, when Genius talks of a linear subspace it " +"means a matrix whose column space is the given linear subspace." +msgstr "" + +#: C/genius.xml:2756(para) +msgid "" +"It should be noted that Genius can remember certain properties of a matrix. " +"For example, it will remember that a matrix is in row reduced form. If many " +"calls are made to functions that internally use row reduced form of the " +"matrix, we can just row reduce the matrix beforehand once. Successive calls to " +"<link linkend=\"gel-function-rref\"><function>rref</function></link> will be " +"very fast." +msgstr "" + +#: C/genius.xml:2769(title) +msgid "Polynomials in GEL" +msgstr "" + +#: C/genius.xml:2771(para) +msgid "" +"Currently Genius can handle polynomials of one variable written out as " +"vectors, and do some basic operations with these. It is planned to expand this " +"support further." +msgstr "" + +#: C/genius.xml:2778(title) +msgid "Using Polynomials" +msgstr "" + +#: C/genius.xml:2784(programlisting) +#, no-wrap +msgid "[1,2,3]\n" +msgstr "[1,2,3]\n" + +#: C/genius.xml:2787(programlisting) +#, no-wrap +msgid "1 + 2*x + 3*x^2\n" +msgstr "1 + 2*x + 3*x^2\n" + +#: C/genius.xml:2779(para) +msgid "" +"Currently polynomials in one variable are just horizontal vectors with value " +"only nodes. The power of the term is the position in the vector, with the " +"first position being 0. So, <placeholder-1/> translates to a polynomial of " +"<placeholder-2/>" +msgstr "" + +#: C/genius.xml:2799(programlisting) +#, no-wrap +msgid "PolyToString([1,2,3],\"y\")\n" +msgstr "PolyToString([1,2,3],\"y\")\n" + +#: C/genius.xml:2802(programlisting) +#, no-wrap +msgid "3*y^2 + 2*y + 1\n" +msgstr "3*y^2 + 2*y + 1\n" + +#: C/genius.xml:2809(programlisting) +#, no-wrap +msgid "" +"f = PolyToFunction([0,1,1])\n" +"f(2)\n" +msgstr "" +"f = PolyToFunction([0,1,1])\n" +"f(2)\n" + +#: C/genius.xml:2790(para) +msgid "" +"You can add, subtract and multiply polynomials using the <link linkend=\"gel-" +"function-AddPoly\"><function>AddPoly</function></link>, <link linkend=\"gel-" +"function-SubtractPoly\"><function>SubtractPoly</function></link>, and <link " +"linkend=\"gel-function-MultiplyPoly\"><function>MultiplyPoly</function></link> " +"functions respectively. You can print a polynomial using the <link linkend=" +"\"gel-function-PolyToString\"><function>PolyToString</function></link> " +"function. For example, <placeholder-1/> gives <placeholder-2/> You can also " +"get a function representation of the polynomial so that you can evaluate it. " +"This is done by using <link linkend=\"gel-function-PolyToFunction" +"\"><function>PolyToFunction</function></link>, which returns an anonymous " +"function. <placeholder-3/>" +msgstr "" + +#: C/genius.xml:2813(para) +msgid "" +"It is also possible to find roots of polynomials of degrees 1 through 4 by " +"using the function <link linkend=\"gel-function-PolynomialRoots" +"\"><function>PolynomialRoots</function></link>, which calls the appropriate " +"formula function. Higher degree polynomials must be converted to functions and " +"solved numerically using a function such as <link linkend=\"gel-function-" +"FindRootBisection\"><function>FindRootBisection</function></link>, <link " +"linkend=\"gel-function-FindRootFalsePosition" +"\"><function>FindRootFalsePosition</function></link>, <link linkend=\"gel-" +"function-FindRootMullersMethod\"><function>FindRootMullersMethod</function></" +"link>, or <link linkend=\"gel-function-FindRootSecant" +"\"><function>FindRootSecant</function></link>." +msgstr "" + +#: C/genius.xml:2825(para) +msgid "" +"See <xref linkend=\"genius-gel-function-list-polynomials\"/> in the function " +"list for the rest of functions acting on polynomials." +msgstr "" + +#: C/genius.xml:2835(title) +msgid "Set Theory in GEL" +msgstr "" + +#: C/genius.xml:2837(para) +msgid "" +"Genius has some basic set theoretic functionality built in. Currently a set is " +"just a vector (or a matrix). Every distinct object is treated as a different " +"element." +msgstr "" + +#: C/genius.xml:2843(title) +msgid "Using Sets" +msgstr "" + +#: C/genius.xml:2844(para) +msgid "" +"Just like vectors, objects in sets can include numbers, strings, " +"<constant>null</constant>, matrices and vectors. It is planned in the future " +"to have a dedicated type for sets, rather than using vectors. Note that " +"floating point numbers are distinct from integers, even if they appear the " +"same. That is, Genius will treat <constant>0</constant> and <constant>0.0</" +"constant> as two distinct elements. The <constant>null</constant> is treated " +"as an empty set." +msgstr "" + +#: C/genius.xml:2852(para) +msgid "" +"To build a set out of a vector, use the <link linkend=\"gel-function-MakeSet" +"\"><function>MakeSet</function></link> function. Currently, it will just " +"return a new vector where every element is unique. <screen><prompt>genius> " +"</prompt><userinput>MakeSet([1,2,2,3])</userinput>\n" +"= [1, 2, 3]\n" +"</screen>" +msgstr "" + +#: C/genius.xml:2861(para) +msgid "" +"Similarly there are functions <link linkend=\"gel-function-Union" +"\"><function>Union</function></link>, <link linkend=\"gel-function-Intersection" +"\"><function>Intersection</function></link>, <link linkend=\"gel-function-" +"SetMinus\"><function>SetMinus</function></link>, which are rather self " +"explanatory. For example: <screen><prompt>genius> </" +"prompt><userinput>Union([1,2,3], [1,2,4])</userinput>\n" +"= [1, 2, 4, 3]\n" +"</screen> Note that no order is guaranteed for the return values. If you wish " +"to sort the vector you should use the <link linkend=\"gel-function-SortVector" +"\"><function>SortVector</function></link> function." +msgstr "" + +#: C/genius.xml:2875(para) +msgid "" +"For testing membership, there are functions <link linkend=\"gel-function-IsIn" +"\"><function>IsIn</function></link> and <link linkend=\"gel-function-IsSubset" +"\"><function>IsSubset</function></link>, which return a boolean value. For " +"example: <screen><prompt>genius> </prompt><userinput>IsIn (1, [0,1,2])</" +"userinput>\n" +"= true\n" +"</screen> The input <userinput>IsIn(x,X)</userinput> is of course equivalent " +"to <userinput>IsSubset([x],X)</userinput>. Note that since the empty set is a " +"subset of every set, <userinput>IsSubset(null,X)</userinput> is always true." +msgstr "" + +#: C/genius.xml:2894(title) +msgid "List of GEL functions" +msgstr "" + +#: C/genius.xml:2900(programlisting) +#, no-wrap +msgid "help FunctionName\n" +msgstr "" + +#. &gel-function-list; +#: C/genius.xml:2898(para) +msgid "" +"To get help on a specific function from the console type: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:2905(title) +msgid "Commands" +msgstr "" + +#: C/genius.xml:2908(term) +msgid "<anchor id=\"gel-command-help\"/>help" +msgstr "<anchor id=\"gel-command-help\"/>help" + +#: C/genius.xml:2910(synopsis) +#, no-wrap +msgid "help" +msgstr "help" + +#: C/genius.xml:2911(synopsis) +#, no-wrap +msgid "help FunctionName" +msgstr "" + +#: C/genius.xml:2912(para) +msgid "Print help (or help on a function/command)." +msgstr "" + +#: C/genius.xml:2917(term) +msgid "<anchor id=\"gel-command-load\"/>load" +msgstr "<anchor id=\"gel-command-load\"/>load" + +#: C/genius.xml:2919(synopsis) +#, no-wrap +msgid "load \"file.gel\"" +msgstr "" + +#: C/genius.xml:2920(para) +msgid "" +"Load a file into the interpreter. The file will execute as if it were typed " +"onto the command line." +msgstr "" + +#: C/genius.xml:2926(term) +msgid "<anchor id=\"gel-command-cd\"/>cd" +msgstr "<anchor id=\"gel-command-cd\"/>cd" + +#: C/genius.xml:2928(synopsis) +#, no-wrap +msgid "cd /directory/name" +msgstr "" + +#: C/genius.xml:2929(para) +msgid "Change working directory to <filename>/directory/name</filename>." +msgstr "" + +#: C/genius.xml:2934(term) +msgid "<anchor id=\"gel-command-pwd\"/>pwd" +msgstr "<anchor id=\"gel-command-pwd\"/>pwd" + +#: C/genius.xml:2936(synopsis) +#, no-wrap +msgid "pwd" +msgstr "pwd" + +#: C/genius.xml:2937(para) +msgid "Print the current working directory." +msgstr "" + +#: C/genius.xml:2942(term) +msgid "<anchor id=\"gel-command-ls\"/>ls" +msgstr "<anchor id=\"gel-command-ls\"/>ls" + +#: C/genius.xml:2944(synopsis) +#, no-wrap +msgid "ls" +msgstr "ls" + +#: C/genius.xml:2945(para) +msgid "List files in the current directory." +msgstr "" + +#: C/genius.xml:2950(term) +msgid "<anchor id=\"gel-command-plugin\"/>plugin" +msgstr "<anchor id=\"gel-command-plugin\"/>plugin" + +#: C/genius.xml:2952(synopsis) +#, no-wrap +msgid "plugin plugin_name" +msgstr "" + +#: C/genius.xml:2953(para) +msgid "" +"Load a plugin. Plugin of that name must be installed on the system in the " +"proper directory." +msgstr "" + +#: C/genius.xml:2961(title) +msgid "Basic" +msgstr "" + +#: C/genius.xml:2964(term) +msgid "<anchor id=\"gel-function-AskButtons\"/>AskButtons" +msgstr "<anchor id=\"gel-function-AskButtons\"/>AskButtons" + +#: C/genius.xml:2966(synopsis) +#, no-wrap +msgid "AskButtons (query)" +msgstr "" + +#: C/genius.xml:2967(synopsis) +#, no-wrap +msgid "AskButtons (query, button1, ...)" +msgstr "" + +#: C/genius.xml:2968(para) +msgid "" +"Asks a question and presents a list of buttons to the user (or a menu of " +"options in text mode). Returns the 1-based index of the button pressed. That " +"is, returns 1 if the first button was pressed, 2 if the second button was " +"pressed, and so on. If the user closes the window (or simply hits enter in " +"text mode), then <constant>null</constant> is returned. The execution of the " +"program is blocked until the user responds." +msgstr "" + +#: C/genius.xml:2974(para) C/genius.xml:3592(para) C/genius.xml:3722(para) +#: C/genius.xml:3770(para) C/genius.xml:3799(para) C/genius.xml:7953(para) +#: C/genius.xml:8195(para) +msgid "Version 1.0.10 onwards." +msgstr "Version 1.0.10 och framåt." + +#: C/genius.xml:2979(term) +msgid "<anchor id=\"gel-function-AskString\"/>AskString" +msgstr "<anchor id=\"gel-function-AskString\"/>AskString" + +#: C/genius.xml:2981(synopsis) +#, no-wrap +msgid "AskString (query)" +msgstr "" + +#: C/genius.xml:2982(synopsis) +#, no-wrap +msgid "AskString (query, default)" +msgstr "" + +#: C/genius.xml:2983(para) +msgid "" +"Asks a question and lets the user enter a string, which it then returns. If " +"the user cancels or closes the window, then <constant>null</constant> is " +"returned. The execution of the program is blocked until the user responds. If " +"<varname>default</varname> is given, then it is pre-typed in for the user to " +"just press enter on (version 1.0.6 onwards)." +msgstr "" + +#: C/genius.xml:2991(term) +msgid "<anchor id=\"gel-function-Compose\"/>Compose" +msgstr "<anchor id=\"gel-function-Compose\"/>Compose" + +#: C/genius.xml:2993(synopsis) +#, no-wrap +msgid "Compose (f,g)" +msgstr "Compose (f,g)" + +#: C/genius.xml:2994(para) +msgid "" +"Compose two functions and return a function that is the composition of " +"<function>f</function> and <function>g</function>." +msgstr "" + +#: C/genius.xml:2999(term) +msgid "<anchor id=\"gel-function-ComposePower\"/>ComposePower" +msgstr "<anchor id=\"gel-function-ComposePower\"/>ComposePower" + +#: C/genius.xml:3001(synopsis) +#, no-wrap +msgid "ComposePower (f,n,x)" +msgstr "ComposePower (f,n,x)" + +#: C/genius.xml:3002(para) +msgid "" +"Compose and execute a function with itself <varname>n</varname> times, passing " +"<varname>x</varname> as argument. Returning <varname>x</varname> if " +"<varname>n</varname> equals 0. Example: <screen><prompt>genius></prompt> " +"<userinput>function f(x) = x^2 ;</userinput>\n" +"<prompt>genius></prompt> <userinput>ComposePower (f,3,7)</userinput>\n" +"= 5764801\n" +"<prompt>genius></prompt> <userinput>f(f(f(7)))</userinput>\n" +"= 5764801\n" +"</screen>" +msgstr "" + +#: C/genius.xml:3016(term) +msgid "<anchor id=\"gel-function-Evaluate\"/>Evaluate" +msgstr "<anchor id=\"gel-function-Evaluate\"/>Evaluate" + +#: C/genius.xml:3018(synopsis) +#, no-wrap +msgid "Evaluate (str)" +msgstr "Evaluate (str)" + +#: C/genius.xml:3019(para) +msgid "Parses and evaluates a string." +msgstr "" + +#: C/genius.xml:3025(term) +msgid "<anchor id=\"gel-function-GetCurrentModulo\"/>GetCurrentModulo" +msgstr "<anchor id=\"gel-function-GetCurrentModulo\"/>GetCurrentModulo" + +#: C/genius.xml:3027(synopsis) +#, no-wrap +msgid "GetCurrentModulo" +msgstr "" + +#: C/genius.xml:3028(para) +msgid "" +"Get current modulo from the context outside the function. That is, if outside " +"of the function was executed in modulo (using <literal>mod</literal>) then " +"this returns what this modulo was. Normally the body of the function called is " +"not executed in modular arithmetic, and this builtin function makes it " +"possible to make GEL functions aware of modular arithmetic." +msgstr "" + +#: C/genius.xml:3036(term) +msgid "<anchor id=\"gel-function-Identity\"/>Identity" +msgstr "<anchor id=\"gel-function-Identity\"/>Identity" + +#: C/genius.xml:3038(synopsis) +#, no-wrap +msgid "Identity (x)" +msgstr "Identity (x)" + +#: C/genius.xml:3039(para) +msgid "" +"Identity function, returns its argument. It is equivalent to " +"<userinput>function Identity(x)=x</userinput>." +msgstr "" + +#: C/genius.xml:3044(term) +msgid "<anchor id=\"gel-function-IntegerFromBoolean\"/>IntegerFromBoolean" +msgstr "<anchor id=\"gel-function-IntegerFromBoolean\"/>IntegerFromBoolean" + +#: C/genius.xml:3046(synopsis) +#, no-wrap +msgid "IntegerFromBoolean (bval)" +msgstr "" + +#: C/genius.xml:3047(para) +msgid "" +"Make integer (0 for <constant>false</constant> or 1 for <constant>true</" +"constant>) from a boolean value. <varname>bval</varname> can also be a number " +"in which case a non-zero value will be interpreted as <constant>true</" +"constant> and zero will be interpreted as <constant>false</constant>." +msgstr "" + +#: C/genius.xml:3058(term) +msgid "<anchor id=\"gel-function-IsBoolean\"/>IsBoolean" +msgstr "<anchor id=\"gel-function-IsBoolean\"/>IsBoolean" + +#: C/genius.xml:3060(synopsis) +#, no-wrap +msgid "IsBoolean (arg)" +msgstr "IsBoolean (arg)" + +#: C/genius.xml:3061(para) +msgid "Check if argument is a boolean (and not a number)." +msgstr "" + +#: C/genius.xml:3066(term) +msgid "<anchor id=\"gel-function-IsDefined\"/>IsDefined" +msgstr "<anchor id=\"gel-function-IsDefined\"/>IsDefined" + +#: C/genius.xml:3068(synopsis) +#, no-wrap +msgid "IsDefined (id)" +msgstr "IsDefined (id)" + +#: C/genius.xml:3069(para) +msgid "" +"Check if an id is defined. You should pass a string or and identifier. If you " +"pass a matrix, each entry will be evaluated separately and the matrix should " +"contain strings or identifiers." +msgstr "" + +#: C/genius.xml:3077(term) +msgid "<anchor id=\"gel-function-IsFunction\"/>IsFunction" +msgstr "<anchor id=\"gel-function-IsFunction\"/>IsFunction" + +#: C/genius.xml:3079(synopsis) +#, no-wrap +msgid "IsFunction (arg)" +msgstr "IsFunction (arg)" + +#: C/genius.xml:3080(para) +msgid "Check if argument is a function." +msgstr "" + +#: C/genius.xml:3085(term) +msgid "" +"<anchor id=\"gel-function-IsFunctionOrIdentifier\"/>IsFunctionOrIdentifier" +msgstr "" +"<anchor id=\"gel-function-IsFunctionOrIdentifier\"/>IsFunctionOrIdentifier" + +#: C/genius.xml:3087(synopsis) +#, no-wrap +msgid "IsFunctionOrIdentifier (arg)" +msgstr "IsFunctionOrIdentifier (arg)" + +#: C/genius.xml:3088(para) +msgid "Check if argument is a function or an identifier." +msgstr "" + +#: C/genius.xml:3093(term) +msgid "<anchor id=\"gel-function-IsFunctionRef\"/>IsFunctionRef" +msgstr "<anchor id=\"gel-function-IsFunctionRef\"/>IsFunctionRef" + +#: C/genius.xml:3095(synopsis) +#, no-wrap +msgid "IsFunctionRef (arg)" +msgstr "IsFunctionRef (arg)" + +#: C/genius.xml:3096(para) +msgid "" +"Check if argument is a function reference. This includes variable references." +msgstr "" + +#: C/genius.xml:3102(term) +msgid "<anchor id=\"gel-function-IsMatrix\"/>IsMatrix" +msgstr "<anchor id=\"gel-function-IsMatrix\"/>IsMatrix" + +#: C/genius.xml:3104(synopsis) +#, no-wrap +msgid "IsMatrix (arg)" +msgstr "IsMatrix (arg)" + +#: C/genius.xml:3105(para) +msgid "" +"Check if argument is a matrix. Even though <constant>null</constant> is " +"sometimes considered an empty matrix, the function <function>IsMatrix</" +"function> does not consider <constant>null</constant> a matrix." +msgstr "" + +#: C/genius.xml:3112(term) +msgid "<anchor id=\"gel-function-IsNull\"/>IsNull" +msgstr "<anchor id=\"gel-function-IsNull\"/>IsNull" + +#: C/genius.xml:3114(synopsis) +#, no-wrap +msgid "IsNull (arg)" +msgstr "IsNull (arg)" + +#: C/genius.xml:3115(para) +msgid "Check if argument is a <constant>null</constant>." +msgstr "" + +#: C/genius.xml:3120(term) +msgid "<anchor id=\"gel-function-IsString\"/>IsString" +msgstr "<anchor id=\"gel-function-IsString\"/>IsString" + +#: C/genius.xml:3122(synopsis) +#, no-wrap +msgid "IsString (arg)" +msgstr "IsString (arg)" + +#: C/genius.xml:3123(para) +msgid "Check if argument is a text string." +msgstr "" + +#: C/genius.xml:3128(term) +msgid "<anchor id=\"gel-function-IsValue\"/>IsValue" +msgstr "<anchor id=\"gel-function-IsValue\"/>IsValue" + +#: C/genius.xml:3130(synopsis) +#, no-wrap +msgid "IsValue (arg)" +msgstr "IsValue (arg)" + +#: C/genius.xml:3131(para) +msgid "Check if argument is a number." +msgstr "" + +#: C/genius.xml:3136(term) +msgid "<anchor id=\"gel-function-Parse\"/>Parse" +msgstr "<anchor id=\"gel-function-Parse\"/>Parse" + +#: C/genius.xml:3138(synopsis) +#, no-wrap +msgid "Parse (str)" +msgstr "Parse (str)" + +#: C/genius.xml:3139(para) +msgid "" +"Parses but does not evaluate a string. Note that certain pre-computation is " +"done during the parsing stage." +msgstr "" + +#: C/genius.xml:3145(term) +msgid "<anchor id=\"gel-function-SetFunctionFlags\"/>SetFunctionFlags" +msgstr "<anchor id=\"gel-function-SetFunctionFlags\"/>SetFunctionFlags" + +#: C/genius.xml:3147(synopsis) +#, no-wrap +msgid "SetFunctionFlags (id,flags...)" +msgstr "" + +#: C/genius.xml:3148(para) +msgid "" +"Set flags for a function, currently <literal>\"PropagateMod\"</literal> and " +"<literal>\"NoModuloArguments\"</literal>. If <literal>\"PropagateMod\"</" +"literal> is set, then the body of the function is evaluated in modular " +"arithmetic when the function is called inside a block that was evaluated using " +"modular arithmetic (using <literal>mod</literal>). If <literal>" +"\"NoModuloArguments\"</literal>, then the arguments of the function are never " +"evaluated using modular arithmetic." +msgstr "" + +#: C/genius.xml:3157(term) +msgid "<anchor id=\"gel-function-SetHelp\"/>SetHelp" +msgstr "<anchor id=\"gel-function-SetHelp\"/>SetHelp" + +#: C/genius.xml:3159(synopsis) +#, no-wrap +msgid "SetHelp (id,category,desc)" +msgstr "" + +#: C/genius.xml:3160(para) +msgid "Set the category and help description line for a function." +msgstr "" + +#: C/genius.xml:3165(term) +msgid "<anchor id=\"gel-function-SetHelpAlias\"/>SetHelpAlias" +msgstr "<anchor id=\"gel-function-SetHelpAlias\"/>SetHelpAlias" + +#: C/genius.xml:3167(synopsis) +#, no-wrap +msgid "SetHelpAlias (id,alias)" +msgstr "SetHelpAlias (id,alias)" + +#: C/genius.xml:3168(para) +msgid "Sets up a help alias." +msgstr "" + +#: C/genius.xml:3173(term) +msgid "<anchor id=\"gel-function-chdir\"/>chdir" +msgstr "<anchor id=\"gel-function-chdir\"/>chdir" + +#: C/genius.xml:3175(synopsis) +#, no-wrap +msgid "chdir (dir)" +msgstr "chdir (kat)" + +#: C/genius.xml:3176(para) +msgid "Changes current directory, same as the <command>cd</command>." +msgstr "" + +#: C/genius.xml:3181(term) +msgid "<anchor id=\"gel-function-CurrentTime\"/>CurrentTime" +msgstr "<anchor id=\"gel-function-CurrentTime\"/>CurrentTime" + +#: C/genius.xml:3183(synopsis) +#, no-wrap +msgid "CurrentTime" +msgstr "" + +#: C/genius.xml:3184(para) +msgid "" +"Returns the current UNIX time with microsecond precision as a floating point " +"number. That is, returns the number of seconds since January 1st 1970." +msgstr "" + +#: C/genius.xml:3185(para) C/genius.xml:8502(para) C/genius.xml:8511(para) +#: C/genius.xml:8520(para) +msgid "Version 1.0.15 onwards." +msgstr "Version 1.0.15 och framåt." + +#: C/genius.xml:3190(term) +msgid "<anchor id=\"gel-function-display\"/>display" +msgstr "<anchor id=\"gel-function-display\"/>display" + +#: C/genius.xml:3192(synopsis) +#, no-wrap +msgid "display (str,expr)" +msgstr "" + +#: C/genius.xml:3193(para) +msgid "Display a string and an expression with a colon to separate them." +msgstr "" + +#: C/genius.xml:3198(term) +msgid "<anchor id=\"gel-function-DisplayVariables\"/>DisplayVariables" +msgstr "<anchor id=\"gel-function-DisplayVariables\"/>DisplayVariables" + +#: C/genius.xml:3200(synopsis) +#, no-wrap +msgid "DisplayVariables (var1,var2,...)" +msgstr "DisplayVariables (var1,var2,...)" + +#: C/genius.xml:3203(programlisting) +#, no-wrap +msgid "" +"DisplayVariables(`x,`y,`z)\n" +"\t " +msgstr "" +"DisplayVariables(`x,`y,`z)\n" +"\t " + +#: C/genius.xml:3201(para) +msgid "" +"Display set of variables. The variables can be given as strings or " +"identifiers. For example: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:3208(programlisting) +#, no-wrap +msgid "" +"DisplayVariables()\n" +"\t " +msgstr "" +"DisplayVariables()\n" +"\t " + +#: C/genius.xml:3206(para) +msgid "" +"If called without arguments (must supply empty argument list) as " +"<placeholder-1/> then all variables are printed including a stacktrace similar " +"to <guilabel>Show user variables</guilabel> in the graphical version." +msgstr "" + +#: C/genius.xml:3213(para) C/genius.xml:3281(para) C/genius.xml:5692(para) +#: C/genius.xml:5701(para) C/genius.xml:6312(para) C/genius.xml:7667(para) +#: C/genius.xml:8026(para) C/genius.xml:8052(para) C/genius.xml:8888(para) +#: C/genius.xml:8902(para) +msgid "Version 1.0.18 onwards." +msgstr "Version 1.0.18 och framåt." + +#: C/genius.xml:3218(term) +msgid "<anchor id=\"gel-function-error\"/>error" +msgstr "<anchor id=\"gel-function-error\"/>error" + +#: C/genius.xml:3220(synopsis) +#, no-wrap +msgid "error (str)" +msgstr "error (str)" + +#: C/genius.xml:3221(para) +msgid "Prints a string to the error stream (onto the console)." +msgstr "" + +#: C/genius.xml:3226(term) +msgid "<anchor id=\"gel-function-exit\"/>exit" +msgstr "<anchor id=\"gel-function-exit\"/>exit" + +#: C/genius.xml:3228(synopsis) +#, no-wrap +msgid "exit" +msgstr "exit" + +#: C/genius.xml:3229(para) +msgid "Aliases: <function>quit</function>" +msgstr "Alias: <function>quit</function>" + +#: C/genius.xml:3230(para) +msgid "Exits the program." +msgstr "" + +#: C/genius.xml:3235(term) +msgid "<anchor id=\"gel-function-false\"/>false" +msgstr "<anchor id=\"gel-function-false\"/>false" + +#: C/genius.xml:3237(synopsis) +#, no-wrap +msgid "false" +msgstr "" + +#: C/genius.xml:3238(para) +msgid "Aliases: <function>False</function><function>FALSE</function>" +msgstr "" + +#: C/genius.xml:3239(para) +msgid "The <constant>false</constant> boolean value." +msgstr "" + +#: C/genius.xml:3244(term) +msgid "<anchor id=\"gel-function-manual\"/>manual" +msgstr "<anchor id=\"gel-function-manual\"/>manual" + +#: C/genius.xml:3246(synopsis) +#, no-wrap +msgid "manual" +msgstr "manual" + +#: C/genius.xml:3247(para) +msgid "Displays the user manual." +msgstr "" + +#: C/genius.xml:3252(term) +msgid "<anchor id=\"gel-function-print\"/>print" +msgstr "<anchor id=\"gel-function-print\"/>print" + +#: C/genius.xml:3254(synopsis) +#, no-wrap +msgid "print (str)" +msgstr "print (str)" + +#: C/genius.xml:3255(para) +msgid "" +"Prints an expression and then print a newline. The argument <varname>str</" +"varname> can be any expression. It is made into a string before being printed." +msgstr "" + +#: C/genius.xml:3261(term) +msgid "<anchor id=\"gel-function-printn\"/>printn" +msgstr "<anchor id=\"gel-function-printn\"/>printn" + +#: C/genius.xml:3263(synopsis) +#, no-wrap +msgid "printn (str)" +msgstr "printn (str)" + +#: C/genius.xml:3264(para) +msgid "" +"Prints an expression without a trailing newline. The argument <varname>str</" +"varname> can be any expression. It is made into a string before being printed." +msgstr "" + +#: C/genius.xml:3270(term) +msgid "<anchor id=\"gel-function-PrintTable\"/>PrintTable" +msgstr "<anchor id=\"gel-function-PrintTable\"/>PrintTable" + +#: C/genius.xml:3272(synopsis) +#, no-wrap +msgid "PrintTable (f,v)" +msgstr "PrintTable (f,v)" + +#: C/genius.xml:3276(programlisting) +#, no-wrap +msgid "" +"PrintTable (f,[0:10])\n" +"\t " +msgstr "" +"PrintTable (f,[0:10])\n" +"\t " + +#: C/genius.xml:3273(para) +msgid "" +"Print a table of values for a function. The values are in the vector " +"<varname>v</varname>. You can use the vector building notation as follows: " +"<placeholder-1/> If <varname>v</varname> is a positive integer, then the table " +"of integers from 1 up to and including v will be used." +msgstr "" + +#: C/genius.xml:3286(term) +msgid "<anchor id=\"gel-function-protect\"/>protect" +msgstr "<anchor id=\"gel-function-protect\"/>protect" + +#: C/genius.xml:3288(synopsis) +#, no-wrap +msgid "protect (id)" +msgstr "protect (id)" + +#: C/genius.xml:3289(para) +msgid "" +"Protect a variable from being modified. This is used on the internal GEL " +"functions to avoid them being accidentally overridden." +msgstr "" + +#: C/genius.xml:3295(term) +msgid "<anchor id=\"gel-function-ProtectAll\"/>ProtectAll" +msgstr "<anchor id=\"gel-function-ProtectAll\"/>ProtectAll" + +#: C/genius.xml:3297(synopsis) +#, no-wrap +msgid "ProtectAll ()" +msgstr "ProtectAll ()" + +#: C/genius.xml:3298(para) +msgid "" +"Protect all currently defined variables, parameters and functions from being " +"modified. This is used on the internal GEL functions to avoid them being " +"accidentally overridden. Normally <application>Genius Mathematics Tool</" +"application> considers unprotected variables as user defined." +msgstr "" + +#: C/genius.xml:3302(para) C/genius.xml:3403(para) C/genius.xml:3421(para) +#: C/genius.xml:7149(para) C/genius.xml:7272(para) C/genius.xml:7292(para) +#: C/genius.xml:7317(para) C/genius.xml:7338(para) C/genius.xml:7360(para) +#: C/genius.xml:7381(para) C/genius.xml:7432(para) C/genius.xml:7465(para) +msgid "Version 1.0.7 onwards." +msgstr "Version 1.0.7 och framåt." + +#: C/genius.xml:3307(term) +msgid "<anchor id=\"gel-function-set\"/>set" +msgstr "<anchor id=\"gel-function-set\"/>set" + +#: C/genius.xml:3309(synopsis) +#, no-wrap +msgid "set (id,val)" +msgstr "" + +#: C/genius.xml:3313(programlisting) +#, no-wrap +msgid "" +"set(`x,1)\n" +"\t " +msgstr "" +"set(`x,1)\n" +"\t " + +#: C/genius.xml:3310(para) +msgid "" +"Set a global variable. The <varname>id</varname> can be either a string or a " +"quoted identifier. For example: <placeholder-1/> will set the global variable " +"<varname>x</varname> to the value 1." +msgstr "" + +#: C/genius.xml:3317(para) C/genius.xml:3336(para) C/genius.xml:3356(para) +msgid "" +"The function returns the <varname>val</varname>, to be usable in chaining." +msgstr "" + +#: C/genius.xml:3323(term) +msgid "<anchor id=\"gel-function-SetElement\"/>SetElement" +msgstr "<anchor id=\"gel-function-SetElement\"/>SetElement" + +#: C/genius.xml:3325(synopsis) +#, no-wrap +msgid "SetElement (id,row,col,val)" +msgstr "" + +#: C/genius.xml:3330(programlisting) +#, no-wrap +msgid "" +"SetElement(`x,2,3,1)\n" +"\t " +msgstr "" +"SetElement(`x,2,3,1)\n" +"\t " + +#: C/genius.xml:3326(para) +msgid "" +"Set an element of a global variable which is a matrix. The <varname>id</" +"varname> can be either a string or a quoted identifier. For example: " +"<placeholder-1/> will set the second row third column element of the global " +"variable <varname>x</varname> to the value 1. If no global variable of the " +"name exists, or if it is set to something that's not a matrix, a new zero " +"matrix of appropriate size will be created." +msgstr "" + +#: C/genius.xml:3334(para) +msgid "" +"The <varname>row</varname> and <varname>col</varname> can also be ranges, and " +"the semantics are the same as for regular setting of the elements with an " +"equals sign." +msgstr "" + +#: C/genius.xml:3338(para) C/genius.xml:3358(para) +msgid "Available from 1.0.18 onwards." +msgstr "" + +#: C/genius.xml:3343(term) +msgid "<anchor id=\"gel-function-SetVElement\"/>SetVElement" +msgstr "<anchor id=\"gel-function-SetVElement\"/>SetVElement" + +#: C/genius.xml:3345(synopsis) +#, no-wrap +msgid "SetElement (id,elt,val)" +msgstr "" + +#: C/genius.xml:3350(programlisting) +#, no-wrap +msgid "" +"SetElement(`x,2,1)\n" +"\t " +msgstr "" +"SetElement(`x,2,1)\n" +"\t " + +#: C/genius.xml:3346(para) +msgid "" +"Set an element of a global variable which is a vector. The <varname>id</" +"varname> can be either a string or a quoted identifier. For example: " +"<placeholder-1/> will set the second element of the global vector variable " +"<varname>x</varname> to the value 1. If no global variable of the name exists, " +"or if it is set to something that's not a vector (matrix), a new zero row " +"vector of appropriate size will be created." +msgstr "" + +#: C/genius.xml:3354(para) +msgid "" +"The <varname>elt</varname> can also be a range, and the semantics are the same " +"as for regular setting of the elements with an equals sign." +msgstr "" + +#: C/genius.xml:3363(term) +msgid "<anchor id=\"gel-function-string\"/>string" +msgstr "<anchor id=\"gel-function-string\"/>string" + +#: C/genius.xml:3365(synopsis) +#, no-wrap +msgid "string (s)" +msgstr "string (s)" + +#: C/genius.xml:3366(para) +msgid "Make a string. This will make a string out of any argument." +msgstr "" + +#: C/genius.xml:3371(term) +msgid "<anchor id=\"gel-function-true\"/>true" +msgstr "<anchor id=\"gel-function-true\"/>true" + +#: C/genius.xml:3373(synopsis) +#, no-wrap +msgid "true" +msgstr "" + +#: C/genius.xml:3374(para) +msgid "Aliases: <function>True</function><function>TRUE</function>" +msgstr "" + +#: C/genius.xml:3375(para) +msgid "The <constant>true</constant> boolean value." +msgstr "" + +#: C/genius.xml:3380(term) +msgid "<anchor id=\"gel-function-undefine\"/>undefine" +msgstr "<anchor id=\"gel-function-undefine\"/>undefine" + +#: C/genius.xml:3382(synopsis) +#, no-wrap +msgid "undefine (id)" +msgstr "undefine (id)" + +#: C/genius.xml:3383(para) +msgid "Alias: <function>Undefine</function>" +msgstr "Alias: <function>Undefine</function>" + +#: C/genius.xml:3384(para) +msgid "" +"Undefine a variable. This includes locals and globals, every value on all " +"context levels is wiped. This function should really not be used on local " +"variables. A vector of identifiers can also be passed to undefine several " +"variables." +msgstr "" + +#: C/genius.xml:3393(term) +msgid "<anchor id=\"gel-function-UndefineAll\"/>UndefineAll" +msgstr "<anchor id=\"gel-function-UndefineAll\"/>UndefineAll" + +#: C/genius.xml:3395(synopsis) +#, no-wrap +msgid "UndefineAll ()" +msgstr "UndefineAll ()" + +#: C/genius.xml:3396(para) +msgid "" +"Undefine all unprotected global variables (including functions and " +"parameters). Normally <application>Genius Mathematics Tool</application> " +"considers protected variables as system defined functions and variables. Note " +"that <function>UndefineAll</function> only removes the global definition of " +"symbols not local ones, so that it may be run from inside other functions " +"safely." +msgstr "" + +#: C/genius.xml:3408(term) +msgid "<anchor id=\"gel-function-unprotect\"/>unprotect" +msgstr "<anchor id=\"gel-function-unprotect\"/>unprotect" + +#: C/genius.xml:3410(synopsis) +#, no-wrap +msgid "unprotect (id)" +msgstr "unprotect (id)" + +#: C/genius.xml:3411(para) +msgid "Unprotect a variable from being modified." +msgstr "" + +#: C/genius.xml:3416(term) +msgid "<anchor id=\"gel-function-UserVariables\"/>UserVariables" +msgstr "<anchor id=\"gel-function-UserVariables\"/>UserVariables" + +#: C/genius.xml:3418(synopsis) +#, no-wrap +msgid "UserVariables ()" +msgstr "UserVariables ()" + +#: C/genius.xml:3419(para) +msgid "" +"Return a vector of identifiers of user defined (unprotected) global variables." +msgstr "" + +#: C/genius.xml:3426(term) +msgid "<anchor id=\"gel-function-wait\"/>wait" +msgstr "<anchor id=\"gel-function-wait\"/>wait" + +#: C/genius.xml:3428(synopsis) +#, no-wrap +msgid "wait (secs)" +msgstr "" + +#: C/genius.xml:3429(para) +msgid "" +"Waits a specified number of seconds. <varname>secs</varname> must be non-" +"negative. Zero is accepted and nothing happens in this case, except possibly " +"user interface events are processed." +msgstr "" + +#: C/genius.xml:3432(para) +msgid "" +"Since version 1.0.18, <varname>secs</varname> can be a noninteger number, so " +"<userinput>wait(0.1)</userinput> will wait for one tenth of a second." +msgstr "" + +#: C/genius.xml:3438(term) +msgid "<anchor id=\"gel-function-version\"/>version" +msgstr "<anchor id=\"gel-function-version\"/>version" + +#: C/genius.xml:3440(synopsis) +#, no-wrap +msgid "version" +msgstr "version" + +#: C/genius.xml:3441(para) +msgid "" +"Returns the version of Genius as a horizontal 3-vector with major version " +"first, then minor version and finally the patch level." +msgstr "" + +#: C/genius.xml:3447(term) +msgid "<anchor id=\"gel-function-warranty\"/>warranty" +msgstr "<anchor id=\"gel-function-warranty\"/>warranty" + +#: C/genius.xml:3449(synopsis) +#, no-wrap +msgid "warranty" +msgstr "warranty" + +#: C/genius.xml:3450(para) +msgid "Gives the warranty information." +msgstr "" + +#: C/genius.xml:3458(title) +msgid "Parameters" +msgstr "" + +#: C/genius.xml:3461(term) +msgid "<anchor id=\"gel-function-ChopTolerance\"/>ChopTolerance" +msgstr "<anchor id=\"gel-function-ChopTolerance\"/>ChopTolerance" + +#: C/genius.xml:3463(synopsis) +#, no-wrap +msgid "ChopTolerance = number" +msgstr "" + +#: C/genius.xml:3464(para) +msgid "Tolerance of the <function>Chop</function> function." +msgstr "" + +#: C/genius.xml:3469(term) +msgid "" +"<anchor id=\"gel-function-ContinuousNumberOfTries\"/>ContinuousNumberOfTries" +msgstr "" +"<anchor id=\"gel-function-ContinuousNumberOfTries\"/>ContinuousNumberOfTries" + +#: C/genius.xml:3471(synopsis) +#, no-wrap +msgid "ContinuousNumberOfTries = number" +msgstr "" + +#: C/genius.xml:3472(para) +msgid "How many iterations to try to find the limit for continuity and limits." +msgstr "" + +#: C/genius.xml:3477(term) +msgid "<anchor id=\"gel-function-ContinuousSFS\"/>ContinuousSFS" +msgstr "<anchor id=\"gel-function-ContinuousSFS\"/>ContinuousSFS" + +#: C/genius.xml:3479(synopsis) +#, no-wrap +msgid "ContinuousSFS = number" +msgstr "" + +#: C/genius.xml:3480(para) +msgid "" +"How many successive steps to be within tolerance for calculation of continuity." +msgstr "" + +#: C/genius.xml:3485(term) +msgid "<anchor id=\"gel-function-ContinuousTolerance\"/>ContinuousTolerance" +msgstr "<anchor id=\"gel-function-ContinuousTolerance\"/>ContinuousTolerance" + +#: C/genius.xml:3487(synopsis) +#, no-wrap +msgid "ContinuousTolerance = number" +msgstr "" + +#: C/genius.xml:3488(para) +msgid "Tolerance for continuity of functions and for calculating the limit." +msgstr "" + +#: C/genius.xml:3493(term) +msgid "" +"<anchor id=\"gel-function-DerivativeNumberOfTries\"/>DerivativeNumberOfTries" +msgstr "" +"<anchor id=\"gel-function-DerivativeNumberOfTries\"/>DerivativeNumberOfTries" + +#: C/genius.xml:3495(synopsis) +#, no-wrap +msgid "DerivativeNumberOfTries = number" +msgstr "" + +#: C/genius.xml:3496(para) +msgid "How many iterations to try to find the limit for derivative." +msgstr "" + +#: C/genius.xml:3501(term) +msgid "<anchor id=\"gel-function-DerivativeSFS\"/>DerivativeSFS" +msgstr "<anchor id=\"gel-function-DerivativeSFS\"/>DerivativeSFS" + +#: C/genius.xml:3503(synopsis) +#, no-wrap +msgid "DerivativeSFS = number" +msgstr "" + +#: C/genius.xml:3504(para) +msgid "" +"How many successive steps to be within tolerance for calculation of derivative." +msgstr "" + +#: C/genius.xml:3509(term) +msgid "<anchor id=\"gel-function-DerivativeTolerance\"/>DerivativeTolerance" +msgstr "<anchor id=\"gel-function-DerivativeTolerance\"/>DerivativeTolerance" + +#: C/genius.xml:3511(synopsis) +#, no-wrap +msgid "DerivativeTolerance = number" +msgstr "" + +#: C/genius.xml:3512(para) +msgid "Tolerance for calculating the derivatives of functions." +msgstr "" + +#: C/genius.xml:3517(term) +msgid "" +"<anchor id=\"gel-function-ErrorFunctionTolerance\"/>ErrorFunctionTolerance" +msgstr "" +"<anchor id=\"gel-function-ErrorFunctionTolerance\"/>ErrorFunctionTolerance" + +#: C/genius.xml:3519(synopsis) +#, no-wrap +msgid "ErrorFunctionTolerance = number" +msgstr "" + +#: C/genius.xml:3520(para) +msgid "" +"Tolerance of the <link linkend=\"gel-function-ErrorFunction" +"\"><function>ErrorFunction</function></link>." +msgstr "" + +#: C/genius.xml:3525(term) +msgid "<anchor id=\"gel-function-FloatPrecision\"/>FloatPrecision" +msgstr "<anchor id=\"gel-function-FloatPrecision\"/>FloatPrecision" + +#: C/genius.xml:3527(synopsis) +#, no-wrap +msgid "FloatPrecision = number" +msgstr "" + +#: C/genius.xml:3528(para) +msgid "Floating point precision." +msgstr "" + +#: C/genius.xml:3533(term) +msgid "<anchor id=\"gel-function-FullExpressions\"/>FullExpressions" +msgstr "<anchor id=\"gel-function-FullExpressions\"/>FullExpressions" + +#: C/genius.xml:3535(synopsis) +#, no-wrap +msgid "FullExpressions = boolean" +msgstr "" + +#: C/genius.xml:3536(para) +msgid "Print full expressions, even if more than a line." +msgstr "" + +#: C/genius.xml:3541(term) +msgid "" +"<anchor id=\"gel-function-GaussDistributionTolerance\"/" +">GaussDistributionTolerance" +msgstr "" +"<anchor id=\"gel-function-GaussDistributionTolerance\"/" +">GaussDistributionTolerance" + +#: C/genius.xml:3543(synopsis) +#, no-wrap +msgid "GaussDistributionTolerance = number" +msgstr "" + +#: C/genius.xml:3544(para) +msgid "" +"Tolerance of the <link linkend=\"gel-function-GaussDistribution" +"\"><function>GaussDistribution</function></link> function." +msgstr "" + +#: C/genius.xml:3549(term) +msgid "<anchor id=\"gel-function-IntegerOutputBase\"/>IntegerOutputBase" +msgstr "<anchor id=\"gel-function-IntegerOutputBase\"/>IntegerOutputBase" + +#: C/genius.xml:3551(synopsis) +#, no-wrap +msgid "IntegerOutputBase = number" +msgstr "" + +#: C/genius.xml:3552(para) +msgid "Integer output base." +msgstr "" + +#: C/genius.xml:3557(term) +msgid "" +"<anchor id=\"gel-function-IsPrimeMillerRabinReps\"/>IsPrimeMillerRabinReps" +msgstr "" +"<anchor id=\"gel-function-IsPrimeMillerRabinReps\"/>IsPrimeMillerRabinReps" + +#: C/genius.xml:3559(synopsis) +#, no-wrap +msgid "IsPrimeMillerRabinReps = number" +msgstr "" + +#: C/genius.xml:3560(para) +msgid "" +"Number of extra Miller-Rabin tests to run on a number before declaring it a " +"prime in <link linkend=\"gel-function-IsPrime\"><function>IsPrime</function></" +"link>." +msgstr "" + +#: C/genius.xml:3565(term) +msgid "<anchor id=\"gel-function-LinePlotDrawLegends\"/>LinePlotDrawLegends" +msgstr "<anchor id=\"gel-function-LinePlotDrawLegends\"/>LinePlotDrawLegends" + +#: C/genius.xml:3567(synopsis) +#, no-wrap +msgid "LinePlotDrawLegends = true" +msgstr "" + +#: C/genius.xml:3568(para) +msgid "" +"Tells genius to draw the legends for <link linkend=\"genius-gel-function-list-" +"plotting\">line plotting functions</link> such as <link linkend=\"gel-function-" +"LinePlot\"><function>LinePlot</function></link>." +msgstr "" + +#: C/genius.xml:3575(term) +msgid "" +"<anchor id=\"gel-function-LinePlotDrawAxisLabels\"/>LinePlotDrawAxisLabels" +msgstr "" +"<anchor id=\"gel-function-LinePlotDrawAxisLabels\"/>LinePlotDrawAxisLabels" + +#: C/genius.xml:3577(synopsis) +#, no-wrap +msgid "LinePlotDrawAxisLabels = true" +msgstr "" + +#: C/genius.xml:3578(para) +msgid "" +"Tells genius to draw the axis labels for <link linkend=\"genius-gel-function-" +"list-plotting\">line plotting functions</link> such as <link linkend=\"gel-" +"function-LinePlot\"><function>LinePlot</function></link>." +msgstr "" + +#: C/genius.xml:3581(para) C/genius.xml:3757(para) C/genius.xml:7517(para) +#: C/genius.xml:7530(para) C/genius.xml:7543(para) C/genius.xml:7556(para) +#: C/genius.xml:7569(para) C/genius.xml:7582(para) C/genius.xml:7838(para) +#: C/genius.xml:8653(para) C/genius.xml:9063(para) C/genius.xml:9100(para) +msgid "Version 1.0.16 onwards." +msgstr "Version 1.0.16 och framåt." + +#: C/genius.xml:3586(term) +msgid "<anchor id=\"gel-function-LinePlotVariableNames\"/>LinePlotVariableNames" +msgstr "<anchor id=\"gel-function-LinePlotVariableNames\"/>LinePlotVariableNames" + +#: C/genius.xml:3588(synopsis) +#, no-wrap +msgid "LinePlotVariableNames = [\"x\",\"y\",\"z\",\"t\"]" +msgstr "LinePlotVariableNames = [\"x\",\"y\",\"z\",\"t\"]" + +#: C/genius.xml:3589(para) +msgid "" +"Tells genius which variable names are used as default names for <link linkend=" +"\"genius-gel-function-list-plotting\">line plotting functions</link> such as " +"<link linkend=\"gel-function-LinePlot\"><function>LinePlot</function></link> " +"and friends." +msgstr "" + +#: C/genius.xml:3597(term) +msgid "<anchor id=\"gel-function-LinePlotWindow\"/>LinePlotWindow" +msgstr "<anchor id=\"gel-function-LinePlotWindow\"/>LinePlotWindow" + +#: C/genius.xml:3599(synopsis) +#, no-wrap +msgid "LinePlotWindow = [x1,x2,y1,y2]" +msgstr "LinePlotWindow = [x1,x2,y1,y2]" + +#: C/genius.xml:3600(para) +msgid "" +"Sets the limits for <link linkend=\"genius-gel-function-list-plotting\">line " +"plotting functions</link> such as <link linkend=\"gel-function-LinePlot" +"\"><function>LinePlot</function></link>." +msgstr "" + +#: C/genius.xml:3608(term) +msgid "<anchor id=\"gel-function-MaxDigits\"/>MaxDigits" +msgstr "<anchor id=\"gel-function-MaxDigits\"/>MaxDigits" + +#: C/genius.xml:3610(synopsis) +#, no-wrap +msgid "MaxDigits = number" +msgstr "" + +#: C/genius.xml:3611(para) +msgid "Maximum digits to display." +msgstr "" + +#: C/genius.xml:3616(term) +msgid "<anchor id=\"gel-function-MaxErrors\"/>MaxErrors" +msgstr "<anchor id=\"gel-function-MaxErrors\"/>MaxErrors" + +#: C/genius.xml:3618(synopsis) +#, no-wrap +msgid "MaxErrors = number" +msgstr "" + +#: C/genius.xml:3619(para) +msgid "Maximum errors to display." +msgstr "" + +#: C/genius.xml:3624(term) +msgid "<anchor id=\"gel-function-MixedFractions\"/>MixedFractions" +msgstr "<anchor id=\"gel-function-MixedFractions\"/>MixedFractions" + +#: C/genius.xml:3626(synopsis) +#, no-wrap +msgid "MixedFractions = boolean" +msgstr "" + +#: C/genius.xml:3627(para) +msgid "If true, mixed fractions are printed." +msgstr "" + +#: C/genius.xml:3632(term) +msgid "" +"<anchor id=\"gel-function-NumericalIntegralFunction\"/" +">NumericalIntegralFunction" +msgstr "" +"<anchor id=\"gel-function-NumericalIntegralFunction\"/" +">NumericalIntegralFunction" + +#: C/genius.xml:3634(synopsis) +#, no-wrap +msgid "NumericalIntegralFunction = function" +msgstr "" + +#: C/genius.xml:3635(para) +msgid "" +"The function used for numerical integration in <link linkend=\"gel-function-" +"NumericalIntegral\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:3640(term) +msgid "" +"<anchor id=\"gel-function-NumericalIntegralSteps\"/>NumericalIntegralSteps" +msgstr "" +"<anchor id=\"gel-function-NumericalIntegralSteps\"/>NumericalIntegralSteps" + +#: C/genius.xml:3642(synopsis) +#, no-wrap +msgid "NumericalIntegralSteps = number" +msgstr "" + +#: C/genius.xml:3643(para) +msgid "" +"Steps to perform in <link linkend=\"gel-function-NumericalIntegral" +"\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:3648(term) +msgid "<anchor id=\"gel-function-OutputChopExponent\"/>OutputChopExponent" +msgstr "<anchor id=\"gel-function-OutputChopExponent\"/>OutputChopExponent" + +#: C/genius.xml:3650(synopsis) +#, no-wrap +msgid "OutputChopExponent = number" +msgstr "" + +#: C/genius.xml:3651(para) +msgid "" +"When another number in the object being printed (a matrix or a value) is " +"greater than 10<superscript>-OutputChopWhenExponent</superscript>, and the " +"number being printed is less than 10<superscript>-OutputChopExponent</" +"superscript>, then display <computeroutput>0.0</computeroutput> instead of the " +"number." +msgstr "" + +#: C/genius.xml:3658(para) +msgid "" +"Output is never chopped if <function>OutputChopExponent</function> is zero. It " +"must be a non-negative integer." +msgstr "" + +#: C/genius.xml:3662(para) +msgid "" +"If you want output always chopped according to <function>OutputChopExponent</" +"function>, then set <function>OutputChopWhenExponent</function>, to something " +"greater than or equal to <function>OutputChopExponent</function>." +msgstr "" + +#: C/genius.xml:3673(term) +msgid "" +"<anchor id=\"gel-function-OutputChopWhenExponent\"/>OutputChopWhenExponent" +msgstr "" +"<anchor id=\"gel-function-OutputChopWhenExponent\"/>OutputChopWhenExponent" + +#: C/genius.xml:3675(synopsis) +#, no-wrap +msgid "OutputChopWhenExponent = number" +msgstr "" + +#: C/genius.xml:3676(para) +msgid "" +"When to chop output. See <link linkend=\"gel-function-OutputChopExponent" +"\"><function>OutputChopExponent</function></link>." +msgstr "" + +#: C/genius.xml:3683(term) +msgid "<anchor id=\"gel-function-OutputStyle\"/>OutputStyle" +msgstr "<anchor id=\"gel-function-OutputStyle\"/>OutputStyle" + +#: C/genius.xml:3685(synopsis) +#, no-wrap +msgid "OutputStyle = string" +msgstr "" + +#: C/genius.xml:3686(para) +msgid "" +"Output style, this can be <literal>normal</literal>, <literal>latex</literal>, " +"<literal>mathml</literal> or <literal>troff</literal>." +msgstr "" + +#: C/genius.xml:3693(programlisting) +#, no-wrap +msgid "OutputStyle = \"latex\"\n" +msgstr "" + +#: C/genius.xml:3689(para) +msgid "" +"This affects mostly how matrices and fractions are printed out and is useful " +"for pasting into documents. For example you can set this to the latex by: " +"<placeholder-1/>" +msgstr "" + +#: C/genius.xml:3700(term) +msgid "<anchor id=\"gel-function-ResultsAsFloats\"/>ResultsAsFloats" +msgstr "<anchor id=\"gel-function-ResultsAsFloats\"/>ResultsAsFloats" + +#: C/genius.xml:3702(synopsis) +#, no-wrap +msgid "ResultsAsFloats = boolean" +msgstr "" + +#: C/genius.xml:3703(para) +msgid "Convert all results to floats before printing." +msgstr "" + +#: C/genius.xml:3708(term) +msgid "<anchor id=\"gel-function-ScientificNotation\"/>ScientificNotation" +msgstr "<anchor id=\"gel-function-ScientificNotation\"/>ScientificNotation" + +#: C/genius.xml:3710(synopsis) +#, no-wrap +msgid "ScientificNotation = boolean" +msgstr "" + +#: C/genius.xml:3711(para) +msgid "Use scientific notation." +msgstr "" + +#: C/genius.xml:3716(term) +msgid "<anchor id=\"gel-function-SlopefieldTicks\"/>SlopefieldTicks" +msgstr "<anchor id=\"gel-function-SlopefieldTicks\"/>SlopefieldTicks" + +#: C/genius.xml:3718(synopsis) +#, no-wrap +msgid "SlopefieldTicks = [vertical,horizontal]" +msgstr "" + +#: C/genius.xml:3719(para) +msgid "" +"Sets the number of vertical and horizontal ticks in a slopefield plot. (See " +"<link linkend=\"gel-function-SlopefieldPlot\"><function>SlopefieldPlot</" +"function></link>)." +msgstr "" + +#: C/genius.xml:3727(term) +msgid "" +"<anchor id=\"gel-function-SumProductNumberOfTries\"/>SumProductNumberOfTries" +msgstr "" +"<anchor id=\"gel-function-SumProductNumberOfTries\"/>SumProductNumberOfTries" + +#: C/genius.xml:3729(synopsis) +#, no-wrap +msgid "SumProductNumberOfTries = number" +msgstr "" + +#: C/genius.xml:3730(para) +msgid "" +"How many iterations to try for <link linkend=\"gel-function-InfiniteSum" +"\"><function>InfiniteSum</function></link> and <link linkend=\"gel-function-" +"InfiniteProduct\"><function>InfiniteProduct</function></link>." +msgstr "" + +#: C/genius.xml:3735(term) +msgid "<anchor id=\"gel-function-SumProductSFS\"/>SumProductSFS" +msgstr "<anchor id=\"gel-function-SumProductSFS\"/>SumProductSFS" + +#: C/genius.xml:3737(synopsis) +#, no-wrap +msgid "SumProductSFS = number" +msgstr "" + +#: C/genius.xml:3738(para) +msgid "" +"How many successive steps to be within tolerance for <link linkend=\"gel-" +"function-InfiniteSum\"><function>InfiniteSum</function></link> and <link " +"linkend=\"gel-function-InfiniteProduct\"><function>InfiniteProduct</function></" +"link>." +msgstr "" + +#: C/genius.xml:3743(term) +msgid "<anchor id=\"gel-function-SumProductTolerance\"/>SumProductTolerance" +msgstr "" + +#: C/genius.xml:3745(synopsis) +#, no-wrap +msgid "SumProductTolerance = number" +msgstr "" + +#: C/genius.xml:3746(para) +msgid "" +"Tolerance for <link linkend=\"gel-function-InfiniteSum" +"\"><function>InfiniteSum</function></link> and <link linkend=\"gel-function-" +"InfiniteProduct\"><function>InfiniteProduct</function></link>." +msgstr "" + +#: C/genius.xml:3751(term) +msgid "" +"<anchor id=\"gel-function-SurfacePlotDrawLegends\"/>SurfacePlotDrawLegends" +msgstr "" +"<anchor id=\"gel-function-SurfacePlotDrawLegends\"/>SurfacePlotDrawLegends" + +#: C/genius.xml:3753(synopsis) +#, no-wrap +msgid "SurfacePlotDrawLegends = true" +msgstr "" + +#: C/genius.xml:3754(para) +msgid "" +"Tells genius to draw the legends for <link linkend=\"genius-gel-function-list-" +"plotting\">surface plotting functions</link> such as <link linkend=\"gel-" +"function-SurfacePlot\"><function>SurfacePlot</function></link>." +msgstr "" + +#: C/genius.xml:3762(term) +msgid "" +"<anchor id=\"gel-function-SurfacePlotVariableNames\"/>SurfacePlotVariableNames" +msgstr "" +"<anchor id=\"gel-function-SurfacePlotVariableNames\"/>SurfacePlotVariableNames" + +#: C/genius.xml:3764(synopsis) +#, no-wrap +msgid "SurfacePlotVariableNames = [\"x\",\"y\",\"z\"]" +msgstr "SurfacePlotVariableNames = [\"x\",\"y\",\"z\"]" + +#: C/genius.xml:3765(para) +msgid "" +"Tells genius which variable names are used as default names for <link linkend=" +"\"genius-gel-function-list-plotting\">surface plotting functions</link> using " +"<link linkend=\"gel-function-SurfacePlot\"><function>SurfacePlot</function></" +"link>. Note that the <varname>z</varname> does not refer to the dependent " +"(vertical) axis, but to the independent complex variable <userinput>z=x+iy</" +"userinput>." +msgstr "" + +#: C/genius.xml:3775(term) +msgid "<anchor id=\"gel-function-SurfacePlotWindow\"/>SurfacePlotWindow" +msgstr "<anchor id=\"gel-function-SurfacePlotWindow\"/>SurfacePlotWindow" + +#: C/genius.xml:3777(synopsis) +#, no-wrap +msgid "SurfacePlotWindow = [x1,x2,y1,y2,z1,z2]" +msgstr "SurfacePlotWindow = [x1,x2,y1,y2,z1,z2]" + +#: C/genius.xml:3778(para) +msgid "" +"Sets the limits for surface plotting (See <link linkend=\"gel-function-" +"SurfacePlot\"><function>SurfacePlot</function></link>)." +msgstr "" + +#: C/genius.xml:3783(term) +msgid "<anchor id=\"gel-function-VectorfieldNormalized\"/>VectorfieldNormalized" +msgstr "<anchor id=\"gel-function-VectorfieldNormalized\"/>VectorfieldNormalized" + +#: C/genius.xml:3785(synopsis) +#, no-wrap +msgid "VectorfieldNormalized = true" +msgstr "" + +#: C/genius.xml:3786(para) +msgid "" +"Should the vectorfield plotting have normalized arrow length. If true, vector " +"fields will only show direction and not magnitude. (See <link linkend=\"gel-" +"function-VectorfieldPlot\"><function>VectorfieldPlot</function></link>)." +msgstr "" + +#: C/genius.xml:3793(term) +msgid "<anchor id=\"gel-function-VectorfieldTicks\"/>VectorfieldTicks" +msgstr "<anchor id=\"gel-function-VectorfieldTicks\"/>VectorfieldTicks" + +#: C/genius.xml:3795(synopsis) +#, no-wrap +msgid "VectorfieldTicks = [vertical,horizontal]" +msgstr "" + +#: C/genius.xml:3796(para) +msgid "" +"Sets the number of vertical and horizontal ticks in a vectorfield plot. (See " +"<link linkend=\"gel-function-VectorfieldPlot\"><function>VectorfieldPlot</" +"function></link>)." +msgstr "" + +#: C/genius.xml:3807(title) +msgid "Constants" +msgstr "" + +#: C/genius.xml:3810(term) +msgid "<anchor id=\"gel-function-CatalanConstant\"/>CatalanConstant" +msgstr "<anchor id=\"gel-function-CatalanConstant\"/>CatalanConstant" + +#: C/genius.xml:3812(synopsis) +#, no-wrap +msgid "CatalanConstant" +msgstr "CatalanConstant" + +#: C/genius.xml:3813(para) +msgid "" +"Catalan's Constant, approximately 0.915... It is defined to be the series " +"where terms are <userinput>(-1^k)/((2*k+1)^2)</userinput>, where <varname>k</" +"varname> ranges from 0 to infinity." +msgstr "" + +#: C/genius.xml:3816(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Catalan%27s_constant" +"\">Wikipedia</ulink>, or <ulink url=\"http://mathworld.wolfram.com/" +"CatalansConstant.html\">Mathworld</ulink> for more information." +msgstr "" +"Se <ulink url=\"http://en.wikipedia.org/wiki/Catalan%27s_constant\">Wikipedia</" +"ulink> eller <ulink url=\"http://mathworld.wolfram.com/CatalansConstant.html" +"\">Mathworld</ulink> för mer information." + +#: C/genius.xml:3825(term) +msgid "<anchor id=\"gel-function-EulerConstant\"/>EulerConstant" +msgstr "<anchor id=\"gel-function-EulerConstant\"/>EulerConstant" + +#: C/genius.xml:3827(synopsis) +#, no-wrap +msgid "EulerConstant" +msgstr "EulerConstant" + +#: C/genius.xml:3828(para) +msgid "Aliases: <function>gamma</function>" +msgstr "Alias: <function>gamma</function>" + +#: C/genius.xml:3829(para) +msgid "Euler's constant gamma. Sometimes called the Euler-Mascheroni constant." +msgstr "" + +#: C/genius.xml:3833(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Euler-Mascheroni_constant" +"\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/encyclopedia/" +"MascheroniConstant.html\">Planetmath</ulink> or <ulink url=\"http://mathworld." +"wolfram.com/Euler-MascheroniConstant.html\">Mathworld</ulink> for more " +"information." +msgstr "" + +#: C/genius.xml:3843(term) +msgid "<anchor id=\"gel-function-GoldenRatio\"/>GoldenRatio" +msgstr "<anchor id=\"gel-function-GoldenRatio\"/>GoldenRatio" + +#: C/genius.xml:3845(synopsis) +#, no-wrap +msgid "GoldenRatio" +msgstr "GoldenRatio" + +#: C/genius.xml:3846(para) +msgid "The Golden Ratio." +msgstr "" + +#: C/genius.xml:3847(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Golden_ratio\">Wikipedia</ulink> " +"or <ulink url=\"http://planetmath.org/encyclopedia/GoldenRatio.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/GoldenRatio." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:3857(term) +msgid "<anchor id=\"gel-function-Gravity\"/>Gravity" +msgstr "<anchor id=\"gel-function-Gravity\"/>Gravity" + +#: C/genius.xml:3859(synopsis) +#, no-wrap +msgid "Gravity" +msgstr "" + +#: C/genius.xml:3860(para) +msgid "" +"Free fall acceleration at sea level in meters per second squared. This is the " +"standard gravity constant 9.80665. The gravity in your particular neck of the " +"woods might be different due to different altitude and the fact that the earth " +"is not perfectly round and uniform." +msgstr "" + +#: C/genius.xml:3863(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Standard_gravity\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:3871(term) +msgid "<anchor id=\"gel-function-e\"/>e" +msgstr "<anchor id=\"gel-function-e\"/>e" + +#: C/genius.xml:3873(synopsis) +#, no-wrap +msgid "e" +msgstr "e" + +#: C/genius.xml:3874(para) +msgid "" +"The base of the natural logarithm. <userinput>e^x</userinput> is the " +"exponential function <link linkend=\"gel-function-exp\"><function>exp</" +"function></link>. It is approximately 2.71828182846... This number is " +"sometimes called Euler's number, although there are several numbers that are " +"also called Euler's. An example is the gamma constant: <link linkend=\"gel-" +"function-EulerConstant\"><function>EulerConstant</function></link>." +msgstr "" + +#: C/genius.xml:3881(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/" +"E_(mathematical_constant)\">Wikipedia</ulink> or <ulink url=\"http://" +"planetmath.org/encyclopedia/E.html\">Planetmath</ulink> or <ulink url=\"http://" +"mathworld.wolfram.com/e.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:3891(term) +msgid "<anchor id=\"gel-function-pi\"/>pi" +msgstr "<anchor id=\"gel-function-pi\"/>pi" + +#: C/genius.xml:3893(synopsis) +#, no-wrap +msgid "pi" +msgstr "pi" + +#: C/genius.xml:3894(para) +msgid "" +"The number pi, that is the ratio of a circle's circumference to its diameter. " +"This is approximately 3.14159265359..." +msgstr "" + +#: C/genius.xml:3898(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Pi\">Wikipedia</ulink> or <ulink " +"url=\"http://planetmath.org/encyclopedia/Pi.html\">Planetmath</ulink> or " +"<ulink url=\"http://mathworld.wolfram.com/Pi.html\">Mathworld</ulink> for more " +"information." +msgstr "" + +#: C/genius.xml:3911(title) +msgid "Numeric" +msgstr "" + +#: C/genius.xml:3914(term) +msgid "<anchor id=\"gel-function-AbsoluteValue\"/>AbsoluteValue" +msgstr "<anchor id=\"gel-function-AbsoluteValue\"/>AbsoluteValue" + +#: C/genius.xml:3916(synopsis) +#, no-wrap +msgid "AbsoluteValue (x)" +msgstr "AbsoluteValue (x)" + +#: C/genius.xml:3917(para) +msgid "Aliases: <function>abs</function>" +msgstr "Alias: <function>abs</function>" + +#: C/genius.xml:3918(para) +msgid "" +"Absolute value of a number and if <varname>x</varname> is a complex value the " +"modulus of <varname>x</varname>. I.e. this the distance of <varname>x</" +"varname> to the origin. This is equivalent to <userinput>|x|</userinput>." +msgstr "" + +#: C/genius.xml:3924(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Absolute_value\">Wikipedia</" +"ulink>, <ulink url=\"http://planetmath.org/encyclopedia/AbsoluteValue.html" +"\">Planetmath (absolute value)</ulink>, <ulink url=\"http://planetmath.org/" +"encyclopedia/ModulusOfComplexNumber.html\">Planetmath (modulus)</ulink>, " +"<ulink url=\"http://mathworld.wolfram.com/AbsoluteValue.html\">Mathworld " +"(absolute value)</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"ComplexModulus.html\">Mathworld (complex modulus)</ulink> for more information." +msgstr "" + +#: C/genius.xml:3937(term) +msgid "<anchor id=\"gel-function-Chop\"/>Chop" +msgstr "<anchor id=\"gel-function-Chop\"/>Chop" + +#: C/genius.xml:3939(synopsis) +#, no-wrap +msgid "Chop (x)" +msgstr "" + +#: C/genius.xml:3940(para) +msgid "Replace very small number with zero." +msgstr "" + +#: C/genius.xml:3945(term) +msgid "<anchor id=\"gel-function-ComplexConjugate\"/>ComplexConjugate" +msgstr "<anchor id=\"gel-function-ComplexConjugate\"/>ComplexConjugate" + +#: C/genius.xml:3947(synopsis) +#, no-wrap +msgid "ComplexConjugate (z)" +msgstr "ComplexConjugate (z)" + +#: C/genius.xml:3948(para) +msgid "Aliases: <function>conj</function><function>Conj</function>" +msgstr "Alias: <function>conj</function><function>Conj</function>" + +#: C/genius.xml:3949(para) +msgid "" +"Calculates the complex conjugate of the complex number <varname>z</varname>. " +"If <varname>z</varname> is a vector or matrix, all its elements are conjugated." +msgstr "" + +#: C/genius.xml:3951(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Complex_conjugate\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:3959(term) +msgid "<anchor id=\"gel-function-Denominator\"/>Denominator" +msgstr "<anchor id=\"gel-function-Denominator\"/>Denominator" + +#: C/genius.xml:3961(synopsis) +#, no-wrap +msgid "Denominator (x)" +msgstr "Denominator (x)" + +#: C/genius.xml:3962(para) +msgid "Get the denominator of a rational number." +msgstr "" + +#: C/genius.xml:3963(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Denominator\">Wikipedia</ulink> " +"for more information." +msgstr "" + +#: C/genius.xml:3971(term) +msgid "<anchor id=\"gel-function-FractionalPart\"/>FractionalPart" +msgstr "<anchor id=\"gel-function-FractionalPart\"/>FractionalPart" + +#: C/genius.xml:3973(synopsis) +#, no-wrap +msgid "FractionalPart (x)" +msgstr "FractionalPart (x)" + +#: C/genius.xml:3974(para) +msgid "Return the fractional part of a number." +msgstr "" + +#: C/genius.xml:3975(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Fractional_part\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:3983(term) +msgid "<anchor id=\"gel-function-Im\"/>Im" +msgstr "<anchor id=\"gel-function-Im\"/>Im" + +#: C/genius.xml:3985(synopsis) +#, no-wrap +msgid "Im (z)" +msgstr "Im (z)" + +#: C/genius.xml:3986(para) +msgid "Aliases: <function>ImaginaryPart</function>" +msgstr "Alias: <function>ImaginaryPart</function>" + +#: C/genius.xml:3987(para) +msgid "" +"Get the imaginary part of a complex number. For example <userinput>Re(3+4i)</" +"userinput> yields 4." +msgstr "" + +#: C/genius.xml:3988(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Imaginary_part\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:3996(term) +msgid "<anchor id=\"gel-function-IntegerQuotient\"/>IntegerQuotient" +msgstr "<anchor id=\"gel-function-IntegerQuotient\"/>IntegerQuotient" + +#: C/genius.xml:3998(synopsis) +#, no-wrap +msgid "IntegerQuotient (m,n)" +msgstr "IntegerQuotient (m,n)" + +#: C/genius.xml:3999(para) +msgid "Division without remainder." +msgstr "" + +#: C/genius.xml:4004(term) +msgid "<anchor id=\"gel-function-IsComplex\"/>IsComplex" +msgstr "<anchor id=\"gel-function-IsComplex\"/>IsComplex" + +#: C/genius.xml:4006(synopsis) +#, no-wrap +msgid "IsComplex (num)" +msgstr "" + +#: C/genius.xml:4007(para) +msgid "" +"Check if argument is a complex (non-real) number. Do note that we really mean " +"nonreal number. That is, <userinput>IsComplex(3)</userinput> yields false, " +"while <userinput>IsComplex(3-1i)</userinput> yields true." +msgstr "" + +#: C/genius.xml:4014(term) +msgid "<anchor id=\"gel-function-IsComplexRational\"/>IsComplexRational" +msgstr "<anchor id=\"gel-function-IsComplexRational\"/>IsComplexRational" + +#: C/genius.xml:4016(synopsis) +#, no-wrap +msgid "IsComplexRational (num)" +msgstr "" + +#: C/genius.xml:4017(para) +msgid "" +"Check if argument is a possibly complex rational number. That is, if both real " +"and imaginary parts are given as rational numbers. Of course rational simply " +"means \"not stored as a floating point number.\"" +msgstr "" + +#: C/genius.xml:4023(term) +msgid "<anchor id=\"gel-function-IsFloat\"/>IsFloat" +msgstr "<anchor id=\"gel-function-IsFloat\"/>IsFloat" + +#: C/genius.xml:4025(synopsis) +#, no-wrap +msgid "IsFloat (num)" +msgstr "" + +#: C/genius.xml:4026(para) +msgid "Check if argument is a real floating point number (non-complex)." +msgstr "" + +#: C/genius.xml:4031(term) +msgid "<anchor id=\"gel-function-IsGaussInteger\"/>IsGaussInteger" +msgstr "<anchor id=\"gel-function-IsGaussInteger\"/>IsGaussInteger" + +#: C/genius.xml:4033(synopsis) +#, no-wrap +msgid "IsGaussInteger (num)" +msgstr "" + +#: C/genius.xml:4034(para) +msgid "Aliases: <function>IsComplexInteger</function>" +msgstr "Alias: <function>IsComplexInteger</function>" + +#: C/genius.xml:4035(para) +msgid "" +"Check if argument is a possibly complex integer. That is a complex integer is " +"a number of the form <userinput>n+1i*m</userinput> where <varname>n</varname> " +"and <varname>m</varname> are integers." +msgstr "" + +#: C/genius.xml:4042(term) +msgid "<anchor id=\"gel-function-IsInteger\"/>IsInteger" +msgstr "<anchor id=\"gel-function-IsInteger\"/>IsInteger" + +#: C/genius.xml:4044(synopsis) +#, no-wrap +msgid "IsInteger (num)" +msgstr "" + +#: C/genius.xml:4045(para) +msgid "Check if argument is an integer (non-complex)." +msgstr "" + +#: C/genius.xml:4050(term) +msgid "<anchor id=\"gel-function-IsNonNegativeInteger\"/>IsNonNegativeInteger" +msgstr "<anchor id=\"gel-function-IsNonNegativeInteger\"/>IsNonNegativeInteger" + +#: C/genius.xml:4052(synopsis) +#, no-wrap +msgid "IsNonNegativeInteger (num)" +msgstr "" + +#: C/genius.xml:4053(para) +msgid "" +"Check if argument is a non-negative real integer. That is, either a positive " +"integer or zero." +msgstr "" + +#: C/genius.xml:4058(term) +msgid "<anchor id=\"gel-function-IsPositiveInteger\"/>IsPositiveInteger" +msgstr "<anchor id=\"gel-function-IsPositiveInteger\"/>IsPositiveInteger" + +#: C/genius.xml:4060(synopsis) +#, no-wrap +msgid "IsPositiveInteger (num)" +msgstr "" + +#: C/genius.xml:4061(para) +msgid "Aliases: <function>IsNaturalNumber</function>" +msgstr "Alias: <function>IsNaturalNumber</function>" + +#: C/genius.xml:4062(para) +msgid "" +"Check if argument is a positive real integer. Note that we accept the " +"convention that 0 is not a natural number." +msgstr "" + +#: C/genius.xml:4068(term) +msgid "<anchor id=\"gel-function-IsRational\"/>IsRational" +msgstr "<anchor id=\"gel-function-IsRational\"/>IsRational" + +#: C/genius.xml:4070(synopsis) +#, no-wrap +msgid "IsRational (num)" +msgstr "" + +#: C/genius.xml:4071(para) +msgid "" +"Check if argument is a rational number (non-complex). Of course rational " +"simply means \"not stored as a floating point number.\"" +msgstr "" + +#: C/genius.xml:4076(term) +msgid "<anchor id=\"gel-function-IsReal\"/>IsReal" +msgstr "<anchor id=\"gel-function-IsReal\"/>IsReal" + +#: C/genius.xml:4078(synopsis) +#, no-wrap +msgid "IsReal (num)" +msgstr "" + +#: C/genius.xml:4079(para) +msgid "Check if argument is a real number." +msgstr "" + +#: C/genius.xml:4084(term) +msgid "<anchor id=\"gel-function-Numerator\"/>Numerator" +msgstr "<anchor id=\"gel-function-Numerator\"/>Numerator" + +#: C/genius.xml:4086(synopsis) +#, no-wrap +msgid "Numerator (x)" +msgstr "Numerator (x)" + +#: C/genius.xml:4087(para) +msgid "Get the numerator of a rational number." +msgstr "" + +#: C/genius.xml:4088(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Numerator\">Wikipedia</ulink> " +"for more information." +msgstr "" + +#: C/genius.xml:4096(term) +msgid "<anchor id=\"gel-function-Re\"/>Re" +msgstr "<anchor id=\"gel-function-Re\"/>Re" + +#: C/genius.xml:4098(synopsis) +#, no-wrap +msgid "Re (z)" +msgstr "Re (z)" + +#: C/genius.xml:4099(para) +msgid "Aliases: <function>RealPart</function>" +msgstr "Alias: <function>RealPart</function>" + +#: C/genius.xml:4100(para) +msgid "" +"Get the real part of a complex number. For example <userinput>Re(3+4i)</" +"userinput> yields 3." +msgstr "" + +#: C/genius.xml:4101(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Real_part\">Wikipedia</ulink> " +"for more information." +msgstr "" + +#: C/genius.xml:4109(term) +msgid "<anchor id=\"gel-function-Sign\"/>Sign" +msgstr "<anchor id=\"gel-function-Sign\"/>Sign" + +#: C/genius.xml:4111(synopsis) +#, no-wrap +msgid "Sign (x)" +msgstr "Sign (x)" + +#: C/genius.xml:4112(para) +msgid "Aliases: <function>sign</function>" +msgstr "Alias: <function>sign</function>" + +#: C/genius.xml:4113(para) +msgid "" +"Return the sign of a number. That is returns <literal>-1</literal> if value is " +"negative, <literal>0</literal> if value is zero and <literal>1</literal> if " +"value is positive. If <varname>x</varname> is a complex value then " +"<function>Sign</function> returns the direction or 0." +msgstr "" + +#: C/genius.xml:4123(term) +msgid "<anchor id=\"gel-function-ceil\"/>ceil" +msgstr "<anchor id=\"gel-function-ceil\"/>ceil" + +#: C/genius.xml:4125(synopsis) +#, no-wrap +msgid "ceil (x)" +msgstr "ceil (x)" + +#: C/genius.xml:4126(para) +msgid "Aliases: <function>Ceiling</function>" +msgstr "Alias: <function>Ceiling</function>" + +#: C/genius.xml:4127(para) +msgid "" +"Get the lowest integer more than or equal to <varname>n</varname>. Examples: " +"<screen><prompt>genius></prompt> <userinput>ceil(1.1)</userinput>\n" +"= 2\n" +"<prompt>genius></prompt> <userinput>ceil(-1.1)</userinput>\n" +"= -1\n" +"</screen>" +msgstr "" + +#: C/genius.xml:4134(para) +msgid "" +"Note that you should be careful and notice that floating point numbers are " +"stored an binary and so may not be what you expect. For example " +"<userinput>ceil(420/4.2)</userinput> returns 101 instead of the expected 100. " +"This is because 4.2 is actually very slightly less than 4.2. Use rational " +"representation <userinput>42/10</userinput> if you want exact arithmetic." +msgstr "" + +#: C/genius.xml:4146(term) +msgid "<anchor id=\"gel-function-exp\"/>exp" +msgstr "<anchor id=\"gel-function-exp\"/>exp" + +#: C/genius.xml:4148(synopsis) +#, no-wrap +msgid "exp (x)" +msgstr "exp (x)" + +#: C/genius.xml:4149(para) +msgid "" +"The exponential function. This is the function <userinput>e^x</userinput> " +"where <varname>e</varname> is the <link linkend=\"gel-function-e\">base of the " +"natural logarithm</link>." +msgstr "" + +#: C/genius.xml:4155(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Exponential_function" +"\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/encyclopedia/" +"LogarithmFunction.html\">Planetmath</ulink> or <ulink url=\"http://mathworld." +"wolfram.com/ExponentialFunction.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4165(term) +msgid "<anchor id=\"gel-function-float\"/>float" +msgstr "<anchor id=\"gel-function-float\"/>float" + +#: C/genius.xml:4167(synopsis) +#, no-wrap +msgid "float (x)" +msgstr "float (x)" + +#: C/genius.xml:4168(para) +msgid "" +"Make number a floating point value. That is returns the floating point " +"representation of the number <varname>x</varname>." +msgstr "" + +#: C/genius.xml:4173(term) +msgid "<anchor id=\"gel-function-floor\"/>floor" +msgstr "<anchor id=\"gel-function-floor\"/>floor" + +#: C/genius.xml:4175(synopsis) +#, no-wrap +msgid "floor (x)" +msgstr "floor (x)" + +#: C/genius.xml:4176(para) +msgid "Aliases: <function>Floor</function>" +msgstr "Alias: <function>Floor</function>" + +#: C/genius.xml:4177(para) +msgid "Get the highest integer less than or equal to <varname>n</varname>." +msgstr "" + +#: C/genius.xml:4182(term) +msgid "<anchor id=\"gel-function-ln\"/>ln" +msgstr "<anchor id=\"gel-function-ln\"/>ln" + +#: C/genius.xml:4184(synopsis) +#, no-wrap +msgid "ln (x)" +msgstr "ln (x)" + +#: C/genius.xml:4185(para) +msgid "The natural logarithm, the logarithm to base <varname>e</varname>." +msgstr "" + +#: C/genius.xml:4186(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Natural_logarithm\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/LogarithmFunction." +"html\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"NaturalLogarithm.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4196(term) +msgid "<anchor id=\"gel-function-log\"/>log" +msgstr "<anchor id=\"gel-function-log\"/>log" + +#: C/genius.xml:4198(synopsis) +#, no-wrap +msgid "log (x)" +msgstr "log (x)" + +#: C/genius.xml:4199(synopsis) +#, no-wrap +msgid "log (x,b)" +msgstr "log (x,b)" + +#: C/genius.xml:4200(para) +msgid "" +"Logarithm of <varname>x</varname> base <varname>b</varname> (calls <link " +"linkend=\"gel-function-DiscreteLog\"><function>DiscreteLog</function></link> " +"if in modulo mode), if base is not given, <link linkend=\"gel-function-e" +"\"><varname>e</varname></link> is used." +msgstr "" + +#: C/genius.xml:4205(term) +msgid "<anchor id=\"gel-function-log10\"/>log10" +msgstr "<anchor id=\"gel-function-log10\"/>log10" + +#: C/genius.xml:4207(synopsis) +#, no-wrap +msgid "log10 (x)" +msgstr "log10 (x)" + +#: C/genius.xml:4208(para) +msgid "Logarithm of <varname>x</varname> base 10." +msgstr "" + +#: C/genius.xml:4213(term) +msgid "<anchor id=\"gel-function-log2\"/>log2" +msgstr "<anchor id=\"gel-function-log2\"/>log2" + +#: C/genius.xml:4215(synopsis) +#, no-wrap +msgid "log2 (x)" +msgstr "log2 (x)" + +#: C/genius.xml:4216(para) +msgid "Aliases: <function>lg</function>" +msgstr "Alias: <function>lg</function>" + +#: C/genius.xml:4217(para) +msgid "Logarithm of <varname>x</varname> base 2." +msgstr "" + +#: C/genius.xml:4222(term) +msgid "<anchor id=\"gel-function-max\"/>max" +msgstr "<anchor id=\"gel-function-max\"/>max" + +#: C/genius.xml:4224(synopsis) +#, no-wrap +msgid "max (a,args...)" +msgstr "" + +#: C/genius.xml:4225(para) +msgid "Aliases: <function>Max</function><function>Maximum</function>" +msgstr "Alias: <function>Max</function><function>Maximum</function>" + +#: C/genius.xml:4226(para) +msgid "Returns the maximum of arguments or matrix." +msgstr "" + +#: C/genius.xml:4231(term) +msgid "<anchor id=\"gel-function-min\"/>min" +msgstr "<anchor id=\"gel-function-min\"/>min" + +#: C/genius.xml:4233(synopsis) +#, no-wrap +msgid "min (a,args...)" +msgstr "" + +#: C/genius.xml:4234(para) +msgid "Aliases: <function>Min</function><function>Minimum</function>" +msgstr "Alias: <function>Min</function><function>Minimum</function>" + +#: C/genius.xml:4235(para) +msgid "Returns the minimum of arguments or matrix." +msgstr "" + +#: C/genius.xml:4240(term) +msgid "<anchor id=\"gel-function-rand\"/>rand" +msgstr "<anchor id=\"gel-function-rand\"/>rand" + +#: C/genius.xml:4242(synopsis) +#, no-wrap +msgid "rand (size...)" +msgstr "" + +#: C/genius.xml:4243(para) +msgid "" +"Generate random float in the range <literal>[0,1)</literal>. If size is given " +"then a matrix (if two numbers are specified) or vector (if one number is " +"specified) of the given size returned." +msgstr "" + +#: C/genius.xml:4250(term) +msgid "<anchor id=\"gel-function-randint\"/>randint" +msgstr "<anchor id=\"gel-function-randint\"/>randint" + +#: C/genius.xml:4252(synopsis) +#, no-wrap +msgid "randint (max,size...)" +msgstr "" + +#: C/genius.xml:4253(para) +msgid "" +"Generate random integer in the range <literal>[0,max)</literal>. If size is " +"given then a matrix (if two numbers are specified) or vector (if one number is " +"specified) of the given size returned. For example, <screen><prompt>genius>" +"</prompt> <userinput>randint(4)</userinput>\n" +"= 3\n" +"<prompt>genius></prompt> <userinput>randint(4,2)</userinput>\n" +"=\n" +"[0 1]\n" +"<prompt>genius></prompt> <userinput>randint(4,2,3)</userinput>\n" +"=\n" +"[2 2 1\n" +" 0 0 3]\n" +"</screen>" +msgstr "" + +#: C/genius.xml:4272(term) +msgid "<anchor id=\"gel-function-round\"/>round" +msgstr "<anchor id=\"gel-function-round\"/>round" + +#: C/genius.xml:4274(synopsis) +#, no-wrap +msgid "round (x)" +msgstr "round (x)" + +#: C/genius.xml:4275(para) +msgid "Aliases: <function>Round</function>" +msgstr "Alias: <function>Round</function>" + +#: C/genius.xml:4276(para) +msgid "Round a number." +msgstr "" + +#: C/genius.xml:4281(term) +msgid "<anchor id=\"gel-function-sqrt\"/>sqrt" +msgstr "<anchor id=\"gel-function-sqrt\"/>sqrt" + +#: C/genius.xml:4283(synopsis) +#, no-wrap +msgid "sqrt (x)" +msgstr "sqrt (x)" + +#: C/genius.xml:4284(para) +msgid "Aliases: <function>SquareRoot</function>" +msgstr "Alias: <function>SquareRoot</function>" + +#: C/genius.xml:4285(para) +msgid "" +"The square root. When operating modulo some integer will return either a " +"<constant>null</constant> or a vector of the square roots. Examples: " +"<screen><prompt>genius></prompt> <userinput>sqrt(2)</userinput>\n" +"= 1.41421356237\n" +"<prompt>genius></prompt> <userinput>sqrt(-1)</userinput>\n" +"= 1i\n" +"<prompt>genius></prompt> <userinput>sqrt(4) mod 7</userinput>\n" +"=\n" +"[2 5]\n" +"<prompt>genius></prompt> <userinput>2*2 mod 7</userinput>\n" +"= 4\n" +"</screen>" +msgstr "" + +#: C/genius.xml:4297(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/SquareRoot.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:4305(term) +msgid "<anchor id=\"gel-function-trunc\"/>trunc" +msgstr "<anchor id=\"gel-function-trunc\"/>trunc" + +#: C/genius.xml:4307(synopsis) +#, no-wrap +msgid "trunc (x)" +msgstr "trunc (x)" + +#: C/genius.xml:4308(para) +msgid "Aliases: <function>Truncate</function><function>IntegerPart</function>" +msgstr "Alias: <function>Truncate</function><function>IntegerPart</function>" + +#: C/genius.xml:4309(para) +msgid "Truncate number to an integer (return the integer part)." +msgstr "" + +#: C/genius.xml:4317(title) +msgid "Trigonometry" +msgstr "" + +#: C/genius.xml:4320(term) +msgid "<anchor id=\"gel-function-acos\"/>acos" +msgstr "<anchor id=\"gel-function-acos\"/>acos" + +#: C/genius.xml:4322(synopsis) +#, no-wrap +msgid "acos (x)" +msgstr "acos (x)" + +#: C/genius.xml:4323(para) +msgid "Aliases: <function>arccos</function>" +msgstr "Alias: <function>arccos</function>" + +#: C/genius.xml:4324(para) +msgid "The arccos (inverse cos) function." +msgstr "" + +#: C/genius.xml:4329(term) +msgid "<anchor id=\"gel-function-acosh\"/>acosh" +msgstr "<anchor id=\"gel-function-acosh\"/>acosh" + +#: C/genius.xml:4331(synopsis) +#, no-wrap +msgid "acosh (x)" +msgstr "acosh (x)" + +#: C/genius.xml:4332(para) +msgid "Aliases: <function>arccosh</function>" +msgstr "Alias: <function>arccosh</function>" + +#: C/genius.xml:4333(para) +msgid "The arccosh (inverse cosh) function." +msgstr "" + +#: C/genius.xml:4338(term) +msgid "<anchor id=\"gel-function-acot\"/>acot" +msgstr "<anchor id=\"gel-function-acot\"/>acot" + +#: C/genius.xml:4340(synopsis) +#, no-wrap +msgid "acot (x)" +msgstr "acot (x)" + +#: C/genius.xml:4341(para) +msgid "Aliases: <function>arccot</function>" +msgstr "Alias: <function>arccot</function>" + +#: C/genius.xml:4342(para) +msgid "The arccot (inverse cot) function." +msgstr "" + +#: C/genius.xml:4347(term) +msgid "<anchor id=\"gel-function-acoth\"/>acoth" +msgstr "<anchor id=\"gel-function-acoth\"/>acoth" + +#: C/genius.xml:4349(synopsis) +#, no-wrap +msgid "acoth (x)" +msgstr "acoth (x)" + +#: C/genius.xml:4350(para) +msgid "Aliases: <function>arccoth</function>" +msgstr "Alias: <function>arccoth</function>" + +#: C/genius.xml:4351(para) +msgid "The arccoth (inverse coth) function." +msgstr "" + +#: C/genius.xml:4356(term) +msgid "<anchor id=\"gel-function-acsc\"/>acsc" +msgstr "<anchor id=\"gel-function-acsc\"/>acsc" + +#: C/genius.xml:4358(synopsis) +#, no-wrap +msgid "acsc (x)" +msgstr "acsc (x)" + +#: C/genius.xml:4359(para) +msgid "Aliases: <function>arccsc</function>" +msgstr "Alias: <function>arccsc</function>" + +#: C/genius.xml:4360(para) +msgid "The inverse cosecant function." +msgstr "" + +#: C/genius.xml:4365(term) +msgid "<anchor id=\"gel-function-acsch\"/>acsch" +msgstr "<anchor id=\"gel-function-acsch\"/>acsch" + +#: C/genius.xml:4367(synopsis) +#, no-wrap +msgid "acsch (x)" +msgstr "acsch (x)" + +#: C/genius.xml:4368(para) +msgid "Aliases: <function>arccsch</function>" +msgstr "Alias: <function>arccsch</function>" + +#: C/genius.xml:4369(para) +msgid "The inverse hyperbolic cosecant function." +msgstr "" + +#: C/genius.xml:4374(term) +msgid "<anchor id=\"gel-function-asec\"/>asec" +msgstr "<anchor id=\"gel-function-asec\"/>asec" + +#: C/genius.xml:4376(synopsis) +#, no-wrap +msgid "asec (x)" +msgstr "asec (x)" + +#: C/genius.xml:4377(para) +msgid "Aliases: <function>arcsec</function>" +msgstr "Alias: <function>arcsec</function>" + +#: C/genius.xml:4378(para) +msgid "The inverse secant function." +msgstr "" + +#: C/genius.xml:4383(term) +msgid "<anchor id=\"gel-function-asech\"/>asech" +msgstr "<anchor id=\"gel-function-asech\"/>asech" + +#: C/genius.xml:4385(synopsis) +#, no-wrap +msgid "asech (x)" +msgstr "asech (x)" + +#: C/genius.xml:4386(para) +msgid "Aliases: <function>arcsech</function>" +msgstr "Alias: <function>arcsech</function>" + +#: C/genius.xml:4387(para) +msgid "The inverse hyperbolic secant function." +msgstr "" + +#: C/genius.xml:4392(term) +msgid "<anchor id=\"gel-function-asin\"/>asin" +msgstr "<anchor id=\"gel-function-asin\"/>asin" + +#: C/genius.xml:4394(synopsis) +#, no-wrap +msgid "asin (x)" +msgstr "asin (x)" + +#: C/genius.xml:4395(para) +msgid "Aliases: <function>arcsin</function>" +msgstr "Alias: <function>arcsin</function>" + +#: C/genius.xml:4396(para) +msgid "The arcsin (inverse sin) function." +msgstr "" + +#: C/genius.xml:4401(term) +msgid "<anchor id=\"gel-function-asinh\"/>asinh" +msgstr "<anchor id=\"gel-function-asinh\"/>asinh" + +#: C/genius.xml:4403(synopsis) +#, no-wrap +msgid "asinh (x)" +msgstr "asinh (x)" + +#: C/genius.xml:4404(para) +msgid "Aliases: <function>arcsinh</function>" +msgstr "Alias: <function>arcsinh</function>" + +#: C/genius.xml:4405(para) +msgid "The arcsinh (inverse sinh) function." +msgstr "" + +#: C/genius.xml:4410(term) +msgid "<anchor id=\"gel-function-atan\"/>atan" +msgstr "<anchor id=\"gel-function-atan\"/>atan" + +#: C/genius.xml:4412(synopsis) +#, no-wrap +msgid "atan (x)" +msgstr "atan (x)" + +#: C/genius.xml:4413(para) +msgid "Aliases: <function>arctan</function>" +msgstr "Alias: <function>arctan</function>" + +#: C/genius.xml:4414(para) +msgid "Calculates the arctan (inverse tan) function." +msgstr "" + +#: C/genius.xml:4415(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Arctangent\">Wikipedia</ulink> " +"or <ulink url=\"http://mathworld.wolfram.com/InverseTangent.html\">Mathworld</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:4424(term) +msgid "<anchor id=\"gel-function-atanh\"/>atanh" +msgstr "<anchor id=\"gel-function-atanh\"/>atanh" + +#: C/genius.xml:4426(synopsis) +#, no-wrap +msgid "atanh (x)" +msgstr "atanh (x)" + +#: C/genius.xml:4427(para) +msgid "Aliases: <function>arctanh</function>" +msgstr "Alias: <function>arctanh</function>" + +#: C/genius.xml:4428(para) +msgid "The arctanh (inverse tanh) function." +msgstr "" + +#: C/genius.xml:4433(term) +msgid "<anchor id=\"gel-function-atan2\"/>atan2" +msgstr "<anchor id=\"gel-function-atan2\"/>atan2" + +#: C/genius.xml:4435(synopsis) +#, no-wrap +msgid "atan2 (y, x)" +msgstr "atan2 (y, x)" + +#: C/genius.xml:4436(para) +msgid "Aliases: <function>arctan2</function>" +msgstr "Alias: <function>arctan2</function>" + +#: C/genius.xml:4437(para) +msgid "" +"Calculates the arctan2 function. If <userinput>x>0</userinput> then it " +"returns <userinput>atan(y/x)</userinput>. If <userinput>x<0</userinput> " +"then it returns <userinput>sign(y) * (pi - atan(|y/x|)</userinput>. When " +"<userinput>x=0</userinput> it returns <userinput>sign(y) *\n" +"\t pi/2</userinput>. <userinput>atan2(0,0)</userinput> returns 0 rather then " +"failing." +msgstr "" + +#: C/genius.xml:4445(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Atan2\">Wikipedia</ulink> or " +"<ulink url=\"http://mathworld.wolfram.com/InverseTangent.html\">Mathworld</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:4454(term) +msgid "<anchor id=\"gel-function-cos\"/>cos" +msgstr "<anchor id=\"gel-function-cos\"/>cos" + +#: C/genius.xml:4456(synopsis) +#, no-wrap +msgid "cos (x)" +msgstr "cos (x)" + +#: C/genius.xml:4457(para) +msgid "Calculates the cosine function." +msgstr "" + +#: C/genius.xml:4458(para) C/genius.xml:4482(para) C/genius.xml:4506(para) +#: C/genius.xml:4530(para) C/genius.xml:4554(para) C/genius.xml:4578(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/DefinitionsInTrigonometry." +"html\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:4466(term) +msgid "<anchor id=\"gel-function-cosh\"/>cosh" +msgstr "<anchor id=\"gel-function-cosh\"/>cosh" + +#: C/genius.xml:4468(synopsis) +#, no-wrap +msgid "cosh (x)" +msgstr "cosh (x)" + +#: C/genius.xml:4469(para) +msgid "Calculates the hyperbolic cosine function." +msgstr "" + +#: C/genius.xml:4470(para) C/genius.xml:4494(para) C/genius.xml:4518(para) +#: C/genius.xml:4542(para) C/genius.xml:4566(para) C/genius.xml:4590(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/HyperbolicFunctions.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:4478(term) +msgid "<anchor id=\"gel-function-cot\"/>cot" +msgstr "<anchor id=\"gel-function-cot\"/>cot" + +#: C/genius.xml:4480(synopsis) +#, no-wrap +msgid "cot (x)" +msgstr "cot (x)" + +#: C/genius.xml:4481(para) +msgid "The cotangent function." +msgstr "" + +#: C/genius.xml:4490(term) +msgid "<anchor id=\"gel-function-coth\"/>coth" +msgstr "<anchor id=\"gel-function-coth\"/>coth" + +#: C/genius.xml:4492(synopsis) +#, no-wrap +msgid "coth (x)" +msgstr "coth (x)" + +#: C/genius.xml:4493(para) +msgid "The hyperbolic cotangent function." +msgstr "" + +#: C/genius.xml:4502(term) +msgid "<anchor id=\"gel-function-csc\"/>csc" +msgstr "<anchor id=\"gel-function-csc\"/>csc" + +#: C/genius.xml:4504(synopsis) +#, no-wrap +msgid "csc (x)" +msgstr "csc (x)" + +#: C/genius.xml:4505(para) +msgid "The cosecant function." +msgstr "" + +#: C/genius.xml:4514(term) +msgid "<anchor id=\"gel-function-csch\"/>csch" +msgstr "<anchor id=\"gel-function-csch\"/>csch" + +#: C/genius.xml:4516(synopsis) +#, no-wrap +msgid "csch (x)" +msgstr "csch (x)" + +#: C/genius.xml:4517(para) +msgid "The hyperbolic cosecant function." +msgstr "" + +#: C/genius.xml:4526(term) +msgid "<anchor id=\"gel-function-sec\"/>sec" +msgstr "<anchor id=\"gel-function-sec\"/>sec" + +#: C/genius.xml:4528(synopsis) +#, no-wrap +msgid "sec (x)" +msgstr "sec (x)" + +#: C/genius.xml:4529(para) +msgid "The secant function." +msgstr "" + +#: C/genius.xml:4538(term) +msgid "<anchor id=\"gel-function-sech\"/>sech" +msgstr "<anchor id=\"gel-function-sech\"/>sech" + +#: C/genius.xml:4540(synopsis) +#, no-wrap +msgid "sech (x)" +msgstr "sech (x)" + +#: C/genius.xml:4541(para) +msgid "The hyperbolic secant function." +msgstr "" + +#: C/genius.xml:4550(term) +msgid "<anchor id=\"gel-function-sin\"/>sin" +msgstr "<anchor id=\"gel-function-sin\"/>sin" + +#: C/genius.xml:4552(synopsis) +#, no-wrap +msgid "sin (x)" +msgstr "sin (x)" + +#: C/genius.xml:4553(para) +msgid "Calculates the sine function." +msgstr "" + +#: C/genius.xml:4562(term) +msgid "<anchor id=\"gel-function-sinh\"/>sinh" +msgstr "<anchor id=\"gel-function-sinh\"/>sinh" + +#: C/genius.xml:4564(synopsis) +#, no-wrap +msgid "sinh (x)" +msgstr "sinh (x)" + +#: C/genius.xml:4565(para) +msgid "Calculates the hyperbolic sine function." +msgstr "" + +#: C/genius.xml:4574(term) +msgid "<anchor id=\"gel-function-tan\"/>tan" +msgstr "<anchor id=\"gel-function-tan\"/>tan" + +#: C/genius.xml:4576(synopsis) +#, no-wrap +msgid "tan (x)" +msgstr "tan (x)" + +#: C/genius.xml:4577(para) +msgid "Calculates the tan function." +msgstr "" + +#: C/genius.xml:4586(term) +msgid "<anchor id=\"gel-function-tanh\"/>tanh" +msgstr "<anchor id=\"gel-function-tanh\"/>tanh" + +#: C/genius.xml:4588(synopsis) +#, no-wrap +msgid "tanh (x)" +msgstr "tanh (x)" + +#: C/genius.xml:4589(para) +msgid "The hyperbolic tangent function." +msgstr "" + +#: C/genius.xml:4601(title) +msgid "Number Theory" +msgstr "" + +#: C/genius.xml:4604(term) +msgid "<anchor id=\"gel-function-AreRelativelyPrime\"/>AreRelativelyPrime" +msgstr "<anchor id=\"gel-function-AreRelativelyPrime\"/>AreRelativelyPrime" + +#: C/genius.xml:4606(synopsis) +#, no-wrap +msgid "AreRelativelyPrime (a,b)" +msgstr "AreRelativelyPrime (a,b)" + +#: C/genius.xml:4607(para) +msgid "" +"Are the real integers <varname>a</varname> and <varname>b</varname> relatively " +"prime? Returns <constant>true</constant> or <constant>false</constant>." +msgstr "" + +#: C/genius.xml:4611(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/RelativelyPrime.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"RelativelyPrime.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4620(term) +msgid "<anchor id=\"gel-function-BernoulliNumber\"/>BernoulliNumber" +msgstr "<anchor id=\"gel-function-BernoulliNumber\"/>BernoulliNumber" + +#: C/genius.xml:4622(synopsis) +#, no-wrap +msgid "BernoulliNumber (n)" +msgstr "BernoulliNumber (n)" + +#: C/genius.xml:4623(para) +msgid "Return the <varname>n</varname>th Bernoulli number." +msgstr "" + +#: C/genius.xml:4624(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Bernoulli_number\">Wikipedia</" +"ulink> or <ulink url=\"http://mathworld.wolfram.com/BernoulliNumber.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4633(term) +msgid "<anchor id=\"gel-function-ChineseRemainder\"/>ChineseRemainder" +msgstr "<anchor id=\"gel-function-ChineseRemainder\"/>ChineseRemainder" + +#: C/genius.xml:4635(synopsis) +#, no-wrap +msgid "ChineseRemainder (a,m)" +msgstr "ChineseRemainder (a,m)" + +#: C/genius.xml:4636(para) +msgid "Aliases: <function>CRT</function>" +msgstr "Alias: <function>CRT</function>" + +#: C/genius.xml:4637(para) +msgid "" +"Find the <varname>x</varname> that solves the system given by the vector " +"<varname>a</varname> and modulo the elements of <varname>m</varname>, using " +"the Chinese Remainder Theorem." +msgstr "" + +#: C/genius.xml:4641(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Chinese_remainder_theorem" +"\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/encyclopedia/" +"ChineseRemainderTheorem.html\">Planetmath</ulink> or <ulink url=\"http://" +"mathworld.wolfram.com/ChineseRemainderTheorem.html\">Mathworld</ulink> for " +"more information." +msgstr "" + +#: C/genius.xml:4651(term) +msgid "<anchor id=\"gel-function-CombineFactorizations\"/>CombineFactorizations" +msgstr "<anchor id=\"gel-function-CombineFactorizations\"/>CombineFactorizations" + +#: C/genius.xml:4653(synopsis) +#, no-wrap +msgid "CombineFactorizations (a,b)" +msgstr "CombineFactorizations (a,b)" + +#: C/genius.xml:4654(para) +msgid "Given two factorizations, give the factorization of the product." +msgstr "" + +#: C/genius.xml:4656(para) +msgid "See <link linkend=\"gel-function-Factorize\">Factorize</link>." +msgstr "" + +#: C/genius.xml:4661(term) +msgid "<anchor id=\"gel-function-ConvertFromBase\"/>ConvertFromBase" +msgstr "<anchor id=\"gel-function-ConvertFromBase\"/>ConvertFromBase" + +#: C/genius.xml:4663(synopsis) +#, no-wrap +msgid "ConvertFromBase (v,b)" +msgstr "ConvertFromBase (v,b)" + +#: C/genius.xml:4664(para) +msgid "Convert a vector of values indicating powers of b to a number." +msgstr "" + +#: C/genius.xml:4669(term) +msgid "<anchor id=\"gel-function-ConvertToBase\"/>ConvertToBase" +msgstr "<anchor id=\"gel-function-ConvertToBase\"/>ConvertToBase" + +#: C/genius.xml:4671(synopsis) +#, no-wrap +msgid "ConvertToBase (n,b)" +msgstr "ConvertToBase (n,b)" + +#: C/genius.xml:4672(para) +msgid "" +"Convert a number to a vector of powers for elements in base <varname>b</" +"varname>." +msgstr "" + +#: C/genius.xml:4677(term) +msgid "<anchor id=\"gel-function-DiscreteLog\"/>DiscreteLog" +msgstr "<anchor id=\"gel-function-DiscreteLog\"/>DiscreteLog" + +#: C/genius.xml:4679(synopsis) +#, no-wrap +msgid "DiscreteLog (n,b,q)" +msgstr "DiscreteLog (n,b,q)" + +#: C/genius.xml:4680(para) +msgid "" +"Find discrete log of <varname>n</varname> base <varname>b</varname> in " +"F<subscript>q</subscript>, the finite field of order <varname>q</varname>, " +"where <varname>q</varname> is a prime, using the Silver-Pohlig-Hellman " +"algorithm." +msgstr "" + +#: C/genius.xml:4683(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Discrete_logarithm\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/DiscreteLogarithm." +"html\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"DiscreteLogarithm.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4693(term) +msgid "<anchor id=\"gel-function-Divides\"/>Divides" +msgstr "<anchor id=\"gel-function-Divides\"/>Divides" + +#: C/genius.xml:4695(synopsis) +#, no-wrap +msgid "Divides (m,n)" +msgstr "Divides (m,n)" + +#: C/genius.xml:4696(para) +msgid "" +"Checks divisibility (if <varname>m</varname> divides <varname>n</varname>)." +msgstr "" + +#: C/genius.xml:4701(term) +msgid "<anchor id=\"gel-function-EulerPhi\"/>EulerPhi" +msgstr "<anchor id=\"gel-function-EulerPhi\"/>EulerPhi" + +#: C/genius.xml:4703(synopsis) +#, no-wrap +msgid "EulerPhi (n)" +msgstr "EulerPhi (n)" + +#: C/genius.xml:4704(para) +msgid "" +"Compute the Euler phi function for <varname>n</varname>, that is the number of " +"integers between 1 and <varname>n</varname> relatively prime to <varname>n</" +"varname>." +msgstr "" + +#: C/genius.xml:4709(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Euler_phi\">Wikipedia</ulink> or " +"<ulink url=\"http://planetmath.org/encyclopedia/EulerPhifunction.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"TotientFunction.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4719(term) +msgid "<anchor id=\"gel-function-ExactDivision\"/>ExactDivision" +msgstr "<anchor id=\"gel-function-ExactDivision\"/>ExactDivision" + +#: C/genius.xml:4721(synopsis) +#, no-wrap +msgid "ExactDivision (n,d)" +msgstr "ExactDivision (n,d)" + +#: C/genius.xml:4722(para) +msgid "" +"Return <userinput>n/d</userinput> but only if <varname>d</varname> divides " +"<varname>n</varname>. If <varname>d</varname> does not divide <varname>n</" +"varname> then this function returns garbage. This is a lot faster for very " +"large numbers than the operation <userinput>n/d</userinput>, but of course " +"only useful if you know that the division is exact." +msgstr "" + +#: C/genius.xml:4734(term) +msgid "<anchor id=\"gel-function-Factorize\"/>Factorize" +msgstr "<anchor id=\"gel-function-Factorize\"/>Factorize" + +#: C/genius.xml:4736(synopsis) +#, no-wrap +msgid "Factorize (n)" +msgstr "Factorize (n)" + +#: C/genius.xml:4737(para) +msgid "" +"Return factorization of a number as a matrix. The first row is the primes in " +"the factorization (including 1) and the second row are the powers. So for " +"example: <screen><prompt>genius></prompt> <userinput>Factorize(11*11*13)</" +"userinput>\n" +"=\n" +"[1 11 13\n" +" 1 2 1]</screen>" +msgstr "" + +#: C/genius.xml:4746(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Factorization\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:4754(term) +msgid "<anchor id=\"gel-function-Factors\"/>Factors" +msgstr "<anchor id=\"gel-function-Factors\"/>Factors" + +#: C/genius.xml:4756(synopsis) +#, no-wrap +msgid "Factors (n)" +msgstr "Factors (n)" + +#: C/genius.xml:4763(programlisting) +#, no-wrap +msgid "" +"for n=1 to 1000 do (\n" +" if MatrixSum (Factors(n)) == 2*n then\n" +" print(n)\n" +")\n" +msgstr "" +"for n=1 to 1000 do (\n" +" if MatrixSum (Factors(n)) == 2*n then\n" +" print(n)\n" +")\n" + +#: C/genius.xml:4757(para) +msgid "" +"Return all factors of <varname>n</varname> in a vector. This includes all the " +"non-prime factors as well. It includes 1 and the number itself. So for example " +"to print all the perfect numbers (those that are sums of their factors) up to " +"the number 1000 you could do (this is of course very inefficient) " +"<placeholder-1/>" +msgstr "" + +#: C/genius.xml:4773(term) +msgid "<anchor id=\"gel-function-FermatFactorization\"/>FermatFactorization" +msgstr "<anchor id=\"gel-function-FermatFactorization\"/>FermatFactorization" + +#: C/genius.xml:4775(synopsis) +#, no-wrap +msgid "FermatFactorization (n,tries)" +msgstr "" + +#: C/genius.xml:4776(para) +msgid "" +"Attempt Fermat factorization of <varname>n</varname> into <userinput>(t-s)*(t" +"+s)</userinput>, returns <varname>t</varname> and <varname>s</varname> as a " +"vector if possible, <constant>null</constant> otherwise. <varname>tries</" +"varname> specifies the number of tries before giving up." +msgstr "" + +#: C/genius.xml:4783(para) +msgid "" +"This is a fairly good factorization if your number is the product of two " +"factors that are very close to each other." +msgstr "" + +#: C/genius.xml:4787(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Fermat_factorization" +"\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:4795(term) +msgid "" +"<anchor id=\"gel-function-FindPrimitiveElementMod\"/>FindPrimitiveElementMod" +msgstr "" +"<anchor id=\"gel-function-FindPrimitiveElementMod\"/>FindPrimitiveElementMod" + +#: C/genius.xml:4797(synopsis) +#, no-wrap +msgid "FindPrimitiveElementMod (q)" +msgstr "FindPrimitiveElementMod (q)" + +#: C/genius.xml:4798(para) +msgid "" +"Find the first primitive element in F<subscript>q</subscript>, the finite " +"group of order <varname>q</varname>. Of course <varname>q</varname> must be a " +"prime." +msgstr "" + +#: C/genius.xml:4804(term) +msgid "" +"<anchor id=\"gel-function-FindRandomPrimitiveElementMod\"/" +">FindRandomPrimitiveElementMod" +msgstr "" +"<anchor id=\"gel-function-FindRandomPrimitiveElementMod\"/" +">FindRandomPrimitiveElementMod" + +#: C/genius.xml:4806(synopsis) +#, no-wrap +msgid "FindRandomPrimitiveElementMod (q)" +msgstr "FindRandomPrimitiveElementMod (q)" + +#: C/genius.xml:4807(para) +msgid "" +"Find a random primitive element in F<subscript>q</subscript>, the finite group " +"of order <varname>q</varname> (q must be a prime)." +msgstr "" + +#: C/genius.xml:4813(term) +msgid "<anchor id=\"gel-function-IndexCalculus\"/>IndexCalculus" +msgstr "<anchor id=\"gel-function-IndexCalculus\"/>IndexCalculus" + +#: C/genius.xml:4815(synopsis) +#, no-wrap +msgid "IndexCalculus (n,b,q,S)" +msgstr "IndexCalculus (n,b,q,S)" + +#: C/genius.xml:4816(para) +msgid "" +"Compute discrete log base <varname>b</varname> of n in F<subscript>q</" +"subscript>, the finite group of order <varname>q</varname> (<varname>q</" +"varname> a prime), using the factor base <varname>S</varname>. <varname>S</" +"varname> should be a column of primes possibly with second column " +"precalculated by <link linkend=\"gel-function-IndexCalculusPrecalculation" +"\"><function>IndexCalculusPrecalculation</function></link>." +msgstr "" + +#: C/genius.xml:4825(term) +msgid "" +"<anchor id=\"gel-function-IndexCalculusPrecalculation\"/" +">IndexCalculusPrecalculation" +msgstr "" +"<anchor id=\"gel-function-IndexCalculusPrecalculation\"/" +">IndexCalculusPrecalculation" + +#: C/genius.xml:4827(synopsis) +#, no-wrap +msgid "IndexCalculusPrecalculation (b,q,S)" +msgstr "IndexCalculusPrecalculation (b,q,S)" + +#: C/genius.xml:4828(para) +msgid "" +"Run the precalculation step of <link linkend=\"gel-function-IndexCalculus" +"\"><function>IndexCalculus</function></link> for logarithms base <varname>b</" +"varname> in F<subscript>q</subscript>, the finite group of order <varname>q</" +"varname> (<varname>q</varname> a prime), for the factor base <varname>S</" +"varname> (where <varname>S</varname> is a column vector of primes). The logs " +"will be precalculated and returned in the second column." +msgstr "" + +#: C/genius.xml:4838(term) +msgid "<anchor id=\"gel-function-IsEven\"/>IsEven" +msgstr "<anchor id=\"gel-function-IsEven\"/>IsEven" + +#: C/genius.xml:4840(synopsis) +#, no-wrap +msgid "IsEven (n)" +msgstr "IsEven (n)" + +#: C/genius.xml:4841(para) +msgid "Tests if an integer is even." +msgstr "" + +#: C/genius.xml:4846(term) +msgid "" +"<anchor id=\"gel-function-IsMersennePrimeExponent\"/>IsMersennePrimeExponent" +msgstr "" +"<anchor id=\"gel-function-IsMersennePrimeExponent\"/>IsMersennePrimeExponent" + +#: C/genius.xml:4848(synopsis) +#, no-wrap +msgid "IsMersennePrimeExponent (p)" +msgstr "IsMersennePrimeExponent (p)" + +#: C/genius.xml:4849(para) +msgid "" +"Tests if a positive integer <varname>p</varname> is a Mersenne prime exponent. " +"That is if 2<superscript>p</superscript>-1 is a prime. It does this by looking " +"it up in a table of known values, which is relatively short. See also <link " +"linkend=\"gel-function-MersennePrimeExponents\">MersennePrimeExponents</link> " +"and <link linkend=\"gel-function-LucasLehmer\">LucasLehmer</link>." +msgstr "" + +#: C/genius.xml:4860(para) C/genius.xml:5076(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Mersenne_prime\">Wikipedia</" +"ulink>, <ulink url=\"http://planetmath.org/encyclopedia/MersenneNumbers.html" +"\">Planetmath</ulink>, <ulink url=\"http://mathworld.wolfram.com/MersennePrime." +"html\">Mathworld</ulink> or <ulink url=\"http://www.mersenne.org/\">GIMPS</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:4872(term) +msgid "<anchor id=\"gel-function-IsNthPower\"/>IsNthPower" +msgstr "<anchor id=\"gel-function-IsNthPower\"/>IsNthPower" + +#: C/genius.xml:4874(synopsis) +#, no-wrap +msgid "IsNthPower (m,n)" +msgstr "IsNthPower (m,n)" + +#: C/genius.xml:4875(para) +msgid "" +"Tests if a rational number <varname>m</varname> is a perfect <varname>n</" +"varname>th power. See also <link linkend=\"gel-function-IsPerfectPower" +"\">IsPerfectPower</link> and <link linkend=\"gel-function-IsPerfectSquare" +"\">IsPerfectSquare</link>." +msgstr "" + +#: C/genius.xml:4886(term) +msgid "<anchor id=\"gel-function-IsOdd\"/>IsOdd" +msgstr "<anchor id=\"gel-function-IsOdd\"/>IsOdd" + +#: C/genius.xml:4888(synopsis) +#, no-wrap +msgid "IsOdd (n)" +msgstr "IsOdd (n)" + +#: C/genius.xml:4889(para) +msgid "Tests if an integer is odd." +msgstr "" + +#: C/genius.xml:4894(term) +msgid "<anchor id=\"gel-function-IsPerfectPower\"/>IsPerfectPower" +msgstr "<anchor id=\"gel-function-IsPerfectPower\"/>IsPerfectPower" + +#: C/genius.xml:4896(synopsis) +#, no-wrap +msgid "IsPerfectPower (n)" +msgstr "IsPerfectPower (n)" + +#: C/genius.xml:4897(para) +msgid "Check an integer is any perfect power, a<superscript>b</superscript>." +msgstr "" + +#: C/genius.xml:4902(term) +msgid "<anchor id=\"gel-function-IsPerfectSquare\"/>IsPerfectSquare" +msgstr "<anchor id=\"gel-function-IsPerfectSquare\"/>IsPerfectSquare" + +#: C/genius.xml:4904(synopsis) +#, no-wrap +msgid "IsPerfectSquare (n)" +msgstr "IsPerfectSquare (n)" + +#: C/genius.xml:4905(para) +msgid "" +"Check an integer for being a perfect square of an integer. The number must be " +"a real integer. Negative integers are of course never perfect squares of real " +"integers." +msgstr "" + +#: C/genius.xml:4914(term) +msgid "<anchor id=\"gel-function-IsPrime\"/>IsPrime" +msgstr "<anchor id=\"gel-function-IsPrime\"/>IsPrime" + +#: C/genius.xml:4916(synopsis) +#, no-wrap +msgid "IsPrime (n)" +msgstr "IsPrime (n)" + +#: C/genius.xml:4917(para) +msgid "" +"Tests primality of integers, for numbers less than 2.5e10 the answer is " +"deterministic (if Riemann hypothesis is true). For numbers larger, the " +"probability of a false positive depends on <link linkend=\"gel-function-" +"IsPrimeMillerRabinReps\"><function>IsPrimeMillerRabinReps</function></link>. " +"That is the probability of false positive is 1/4 to the power " +"<function>IsPrimeMillerRabinReps</function>. The default value of 22 yields a " +"probability of about 5.7e-14." +msgstr "" + +#: C/genius.xml:4928(para) +msgid "" +"If <constant>false</constant> is returned, you can be sure that the number is " +"a composite. If you want to be absolutely sure that you have a prime you can " +"use <link linkend=\"gel-function-MillerRabinTestSure" +"\"><function>MillerRabinTestSure</function></link> but it may take a lot " +"longer." +msgstr "" + +#: C/genius.xml:4936(para) C/genius.xml:5174(para) C/genius.xml:5214(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/PrimeNumber.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/PrimeNumber." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:4945(term) +msgid "<anchor id=\"gel-function-IsPrimitiveMod\"/>IsPrimitiveMod" +msgstr "<anchor id=\"gel-function-IsPrimitiveMod\"/>IsPrimitiveMod" + +#: C/genius.xml:4947(synopsis) +#, no-wrap +msgid "IsPrimitiveMod (g,q)" +msgstr "IsPrimitiveMod (g,q)" + +#: C/genius.xml:4948(para) +msgid "" +"Check if <varname>g</varname> is primitive in F<subscript>q</subscript>, the " +"finite group of order <varname>q</varname>, where <varname>q</varname> is a " +"prime. If <varname>q</varname> is not prime results are bogus." +msgstr "" + +#: C/genius.xml:4954(term) +msgid "" +"<anchor id=\"gel-function-IsPrimitiveModWithPrimeFactors\"/" +">IsPrimitiveModWithPrimeFactors" +msgstr "" +"<anchor id=\"gel-function-IsPrimitiveModWithPrimeFactors\"/" +">IsPrimitiveModWithPrimeFactors" + +#: C/genius.xml:4956(synopsis) +#, no-wrap +msgid "IsPrimitiveModWithPrimeFactors (g,q,f)" +msgstr "IsPrimitiveModWithPrimeFactors (g,q,f)" + +#: C/genius.xml:4957(para) +msgid "" +"Check if <varname>g</varname> is primitive in F<subscript>q</subscript>, the " +"finite group of order <varname>q</varname>, where <varname>q</varname> is a " +"prime and <varname>f</varname> is a vector of prime factors of <varname>q</" +"varname>-1. If <varname>q</varname> is not prime results are bogus." +msgstr "" + +#: C/genius.xml:4965(term) +msgid "<anchor id=\"gel-function-IsPseudoprime\"/>IsPseudoprime" +msgstr "<anchor id=\"gel-function-IsPseudoprime\"/>IsPseudoprime" + +#: C/genius.xml:4967(synopsis) +#, no-wrap +msgid "IsPseudoprime (n,b)" +msgstr "IsPseudoprime (n,b)" + +#: C/genius.xml:4968(para) +msgid "" +"If <varname>n</varname> is a pseudoprime base <varname>b</varname> but not a " +"prime, that is if <userinput>b^(n-1) == 1 mod n</userinput>. This calls the " +"<link linkend=\"gel-function-PseudoprimeTest\"><function>PseudoprimeTest</" +"function></link>" +msgstr "" + +#: C/genius.xml:4974(term) +msgid "<anchor id=\"gel-function-IsStrongPseudoprime\"/>IsStrongPseudoprime" +msgstr "<anchor id=\"gel-function-IsStrongPseudoprime\"/>IsStrongPseudoprime" + +#: C/genius.xml:4976(synopsis) +#, no-wrap +msgid "IsStrongPseudoprime (n,b)" +msgstr "IsStrongPseudoprime (n,b)" + +#: C/genius.xml:4977(para) +msgid "" +"Test if <varname>n</varname> is a strong pseudoprime to base <varname>b</" +"varname> but not a prime." +msgstr "" + +#: C/genius.xml:4982(term) +msgid "<anchor id=\"gel-function-Jacobi\"/>Jacobi" +msgstr "<anchor id=\"gel-function-Jacobi\"/>Jacobi" + +#: C/genius.xml:4984(synopsis) +#, no-wrap +msgid "Jacobi (a,b)" +msgstr "Jacobi (a,b)" + +#: C/genius.xml:4985(para) +msgid "Aliases: <function>JacobiSymbol</function>" +msgstr "Alias: <function>JacobiSymbol</function>" + +#: C/genius.xml:4986(para) +msgid "Calculate the Jacobi symbol (a/b) (b should be odd)." +msgstr "" + +#: C/genius.xml:4991(term) +msgid "<anchor id=\"gel-function-JacobiKronecker\"/>JacobiKronecker" +msgstr "<anchor id=\"gel-function-JacobiKronecker\"/>JacobiKronecker" + +#: C/genius.xml:4993(synopsis) +#, no-wrap +msgid "JacobiKronecker (a,b)" +msgstr "JacobiKronecker (a,b)" + +#: C/genius.xml:4994(para) +msgid "Aliases: <function>JacobiKroneckerSymbol</function>" +msgstr "Alias: <function>JacobiKroneckerSymbol</function>" + +#: C/genius.xml:4995(para) +msgid "" +"Calculate the Jacobi symbol (a/b) with the Kronecker extension (a/2)=(2/a) " +"when a odd, or (a/2)=0 when a even." +msgstr "" + +#: C/genius.xml:5000(term) +msgid "<anchor id=\"gel-function-LeastAbsoluteResidue\"/>LeastAbsoluteResidue" +msgstr "<anchor id=\"gel-function-LeastAbsoluteResidue\"/>LeastAbsoluteResidue" + +#: C/genius.xml:5002(synopsis) +#, no-wrap +msgid "LeastAbsoluteResidue (a,n)" +msgstr "LeastAbsoluteResidue (a,n)" + +#: C/genius.xml:5003(para) +msgid "" +"Return the residue of <varname>a</varname> mod <varname>n</varname> with the " +"least absolute value (in the interval -n/2 to n/2)." +msgstr "" + +#: C/genius.xml:5008(term) +msgid "<anchor id=\"gel-function-Legendre\"/>Legendre" +msgstr "<anchor id=\"gel-function-Legendre\"/>Legendre" + +#: C/genius.xml:5010(synopsis) +#, no-wrap +msgid "Legendre (a,p)" +msgstr "Legendre (a,p)" + +#: C/genius.xml:5011(para) +msgid "Aliases: <function>LegendreSymbol</function>" +msgstr "Alias: <function>LegendreSymbol</function>" + +#: C/genius.xml:5012(para) +msgid "Calculate the Legendre symbol (a/p)." +msgstr "" + +#: C/genius.xml:5013(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/LegendreSymbol.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"LegendreSymbol.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5022(term) +msgid "<anchor id=\"gel-function-LucasLehmer\"/>LucasLehmer" +msgstr "<anchor id=\"gel-function-LucasLehmer\"/>LucasLehmer" + +#: C/genius.xml:5024(synopsis) +#, no-wrap +msgid "LucasLehmer (p)" +msgstr "LucasLehmer (p)" + +#: C/genius.xml:5025(para) +msgid "" +"Test if 2<superscript>p</superscript>-1 is a Mersenne prime using the Lucas-" +"Lehmer test. See also <link linkend=\"gel-function-MersennePrimeExponents" +"\">MersennePrimeExponents</link> and <link linkend=\"gel-function-" +"IsMersennePrimeExponent\">IsMersennePrimeExponent</link>." +msgstr "" + +#: C/genius.xml:5031(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Lucas" +"%E2%80%93Lehmer_primality_test\">Wikipedia</ulink> or <ulink url=\"http://" +"planetmath.org/encyclopedia/LucasLhemer.html\">Planetmath</ulink> or <ulink " +"url=\"http://mathworld.wolfram.com/Lucas-LehmerTest.html\">Mathworld</ulink> " +"for more information." +msgstr "" + +#: C/genius.xml:5041(term) +msgid "<anchor id=\"gel-function-LucasNumber\"/>LucasNumber" +msgstr "<anchor id=\"gel-function-LucasNumber\"/>LucasNumber" + +#: C/genius.xml:5043(synopsis) +#, no-wrap +msgid "LucasNumber (n)" +msgstr "LucasNumber (n)" + +#: C/genius.xml:5044(para) +msgid "Returns the <varname>n</varname>th Lucas number." +msgstr "" + +#: C/genius.xml:5045(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Lucas_number\">Wikipedia</ulink> " +"or <ulink url=\"http://planetmath.org/encyclopedia/LucasNumbers.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/LucasNumber." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5055(term) +msgid "" +"<anchor id=\"gel-function-MaximalPrimePowerFactors\"/>MaximalPrimePowerFactors" +msgstr "" +"<anchor id=\"gel-function-MaximalPrimePowerFactors\"/>MaximalPrimePowerFactors" + +#: C/genius.xml:5057(synopsis) +#, no-wrap +msgid "MaximalPrimePowerFactors (n)" +msgstr "MaximalPrimePowerFactors (n)" + +#: C/genius.xml:5058(para) +msgid "Return all maximal prime power factors of a number." +msgstr "" + +#: C/genius.xml:5063(term) +msgid "" +"<anchor id=\"gel-function-MersennePrimeExponents\"/>MersennePrimeExponents" +msgstr "" +"<anchor id=\"gel-function-MersennePrimeExponents\"/>MersennePrimeExponents" + +#: C/genius.xml:5065(synopsis) +#, no-wrap +msgid "MersennePrimeExponents" +msgstr "MersennePrimeExponents" + +#: C/genius.xml:5066(para) +msgid "" +"A vector of known Mersenne prime exponents, that is a list of positive " +"integers <varname>p</varname> such that 2<superscript>p</superscript>-1 is a " +"prime. See also <link linkend=\"gel-function-IsMersennePrimeExponent" +"\">IsMersennePrimeExponent</link> and <link linkend=\"gel-function-LucasLehmer" +"\">LucasLehmer</link>." +msgstr "" + +#: C/genius.xml:5088(term) +msgid "<anchor id=\"gel-function-MillerRabinTest\"/>MillerRabinTest" +msgstr "<anchor id=\"gel-function-MillerRabinTest\"/>MillerRabinTest" + +#: C/genius.xml:5090(synopsis) +#, no-wrap +msgid "MillerRabinTest (n,reps)" +msgstr "" + +#: C/genius.xml:5091(para) +msgid "" +"Use the Miller-Rabin primality test on <varname>n</varname>, <varname>reps</" +"varname> number of times. The probability of false positive is " +"<userinput>(1/4)^reps</userinput>. It is probably usually better to use <link " +"linkend=\"gel-function-IsPrime\"><function>IsPrime</function></link> since " +"that is faster and better on smaller integers." +msgstr "" + +#: C/genius.xml:5100(para) C/genius.xml:5118(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Miller" +"%E2%80%93Rabin_primality_test\">Wikipedia</ulink> or <ulink url=\"http://" +"planetmath.org/encyclopedia/MillerRabinPrimeTest.html\">Planetmath</ulink> or " +"<ulink url=\"http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5110(term) +msgid "<anchor id=\"gel-function-MillerRabinTestSure\"/>MillerRabinTestSure" +msgstr "<anchor id=\"gel-function-MillerRabinTestSure\"/>MillerRabinTestSure" + +#: C/genius.xml:5112(synopsis) +#, no-wrap +msgid "MillerRabinTestSure (n)" +msgstr "MillerRabinTestSure (n)" + +#: C/genius.xml:5113(para) +msgid "" +"Use the Miller-Rabin primality test on <varname>n</varname> with enough bases " +"that assuming the Generalized Riemann Hypothesis the result is deterministic." +msgstr "" + +#: C/genius.xml:5128(term) +msgid "<anchor id=\"gel-function-ModInvert\"/>ModInvert" +msgstr "<anchor id=\"gel-function-ModInvert\"/>ModInvert" + +#: C/genius.xml:5130(synopsis) +#, no-wrap +msgid "ModInvert (n,m)" +msgstr "ModInvert (n,m)" + +#: C/genius.xml:5131(para) +msgid "Returns inverse of n mod m." +msgstr "" + +#: C/genius.xml:5132(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/ModularInverse.html\">Mathworld</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:5140(term) +msgid "<anchor id=\"gel-function-MoebiusMu\"/>MoebiusMu" +msgstr "<anchor id=\"gel-function-MoebiusMu\"/>MoebiusMu" + +#: C/genius.xml:5142(synopsis) +#, no-wrap +msgid "MoebiusMu (n)" +msgstr "MoebiusMu (n)" + +#: C/genius.xml:5143(para) +msgid "" +"Return the Moebius mu function evaluated in <varname>n</varname>. That is, it " +"returns 0 if <varname>n</varname> is not a product of distinct primes and " +"<userinput>(-1)^k</userinput> if it is a product of <varname>k</varname> " +"distinct primes." +msgstr "" + +#: C/genius.xml:5149(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/MoebiusFunction.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"MoebiusFunction.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5158(term) +msgid "<anchor id=\"gel-function-NextPrime\"/>NextPrime" +msgstr "<anchor id=\"gel-function-NextPrime\"/>NextPrime" + +#: C/genius.xml:5160(synopsis) +#, no-wrap +msgid "NextPrime (n)" +msgstr "NextPrime (n)" + +#: C/genius.xml:5161(para) +msgid "" +"Returns the least prime greater than <varname>n</varname>. Negatives of primes " +"are considered prime and so to get the previous prime you can use <userinput>-" +"NextPrime(-n)</userinput>." +msgstr "" + +#: C/genius.xml:5166(para) +msgid "" +"This function uses the GMPs <function>mpz_nextprime</function>, which in turn " +"uses the probabilistic Miller-Rabin test (See also <link linkend=\"gel-" +"function-MillerRabinTest\"><function>MillerRabinTest</function></link>). The " +"probability of false positive is not tunable, but is low enough for all " +"practical purposes." +msgstr "" + +#: C/genius.xml:5183(term) +msgid "<anchor id=\"gel-function-PadicValuation\"/>PadicValuation" +msgstr "<anchor id=\"gel-function-PadicValuation\"/>PadicValuation" + +#: C/genius.xml:5185(synopsis) +#, no-wrap +msgid "PadicValuation (n,p)" +msgstr "PadicValuation (n,p)" + +#: C/genius.xml:5186(para) +msgid "" +"Returns the p-adic valuation (number of trailing zeros in base <varname>p</" +"varname>)." +msgstr "" + +#: C/genius.xml:5187(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/PAdicValuation.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:5195(term) +msgid "<anchor id=\"gel-function-PowerMod\"/>PowerMod" +msgstr "<anchor id=\"gel-function-PowerMod\"/>PowerMod" + +#: C/genius.xml:5197(synopsis) +#, no-wrap +msgid "PowerMod (a,b,m)" +msgstr "PowerMod (a,b,m)" + +#: C/genius.xml:5198(para) +msgid "" +"Compute <userinput>a^b mod m</userinput>. The <varname>b</varname>'s power of " +"<varname>a</varname> modulo <varname>m</varname>. It is not necessary to use " +"this function as it is automatically used in modulo mode. Hence <userinput>a^b " +"mod m</userinput> is just as fast." +msgstr "" + +#: C/genius.xml:5209(term) +msgid "<anchor id=\"gel-function-Prime\"/>Prime" +msgstr "<anchor id=\"gel-function-Prime\"/>Prime" + +#: C/genius.xml:5211(synopsis) +#, no-wrap +msgid "Prime (n)" +msgstr "Prime (n)" + +#: C/genius.xml:5212(para) +msgid "Aliases: <function>prime</function>" +msgstr "Alias: <function>prime</function>" + +#: C/genius.xml:5213(para) +msgid "Return the <varname>n</varname>th prime (up to a limit)." +msgstr "" + +#: C/genius.xml:5223(term) +msgid "<anchor id=\"gel-function-PrimeFactors\"/>PrimeFactors" +msgstr "<anchor id=\"gel-function-PrimeFactors\"/>PrimeFactors" + +#: C/genius.xml:5225(synopsis) +#, no-wrap +msgid "PrimeFactors (n)" +msgstr "PrimeFactors (n)" + +#: C/genius.xml:5226(para) +msgid "Return all prime factors of a number as a vector." +msgstr "" + +#: C/genius.xml:5227(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/PrimeFactor.html\">Mathworld</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:5235(term) +msgid "<anchor id=\"gel-function-PseudoprimeTest\"/>PseudoprimeTest" +msgstr "<anchor id=\"gel-function-PseudoprimeTest\"/>PseudoprimeTest" + +#: C/genius.xml:5237(synopsis) +#, no-wrap +msgid "PseudoprimeTest (n,b)" +msgstr "PseudoprimeTest (n,b)" + +#: C/genius.xml:5238(para) +msgid "" +"Pseudoprime test, returns <constant>true</constant> if and only if " +"<userinput>b^(n-1) == 1 mod n</userinput>" +msgstr "" + +#: C/genius.xml:5240(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Pseudoprime.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/Pseudoprime." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5249(term) +msgid "<anchor id=\"gel-function-RemoveFactor\"/>RemoveFactor" +msgstr "<anchor id=\"gel-function-RemoveFactor\"/>RemoveFactor" + +#: C/genius.xml:5251(synopsis) +#, no-wrap +msgid "RemoveFactor (n,m)" +msgstr "RemoveFactor (n,m)" + +#: C/genius.xml:5252(para) +msgid "" +"Removes all instances of the factor <varname>m</varname> from the number " +"<varname>n</varname>. That is divides by the largest power of <varname>m</" +"varname>, that divides <varname>n</varname>." +msgstr "" + +#: C/genius.xml:5253(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Divisibility.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/Factor.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5262(term) +msgid "" +"<anchor id=\"gel-function-SilverPohligHellmanWithFactorization\"/" +">SilverPohligHellmanWithFactorization" +msgstr "" +"<anchor id=\"gel-function-SilverPohligHellmanWithFactorization\"/" +">SilverPohligHellmanWithFactorization" + +#: C/genius.xml:5264(synopsis) +#, no-wrap +msgid "SilverPohligHellmanWithFactorization (n,b,q,f)" +msgstr "SilverPohligHellmanWithFactorization (n,b,q,f)" + +#: C/genius.xml:5265(para) +msgid "" +"Find discrete log of <varname>n</varname> base <varname>b</varname> in " +"F<subscript>q</subscript>, the finite group of order <varname>q</varname>, " +"where <varname>q</varname> is a prime using the Silver-Pohlig-Hellman " +"algorithm, given <varname>f</varname> being the factorization of <varname>q</" +"varname>-1." +msgstr "" + +#: C/genius.xml:5270(term) +msgid "<anchor id=\"gel-function-SqrtModPrime\"/>SqrtModPrime" +msgstr "<anchor id=\"gel-function-SqrtModPrime\"/>SqrtModPrime" + +#: C/genius.xml:5272(synopsis) +#, no-wrap +msgid "SqrtModPrime (n,p)" +msgstr "SqrtModPrime (n,p)" + +#: C/genius.xml:5273(para) +msgid "" +"Find square root of <varname>n</varname> modulo <varname>p</varname> (where " +"<varname>p</varname> is a prime). Null is returned if not a quadratic residue." +msgstr "" + +#: C/genius.xml:5274(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/QuadraticResidue.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"QuadraticResidue.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5283(term) +msgid "<anchor id=\"gel-function-StrongPseudoprimeTest\"/>StrongPseudoprimeTest" +msgstr "<anchor id=\"gel-function-StrongPseudoprimeTest\"/>StrongPseudoprimeTest" + +#: C/genius.xml:5285(synopsis) +#, no-wrap +msgid "StrongPseudoprimeTest (n,b)" +msgstr "StrongPseudoprimeTest (n,b)" + +#: C/genius.xml:5286(para) +msgid "" +"Run the strong pseudoprime test base <varname>b</varname> on <varname>n</" +"varname>." +msgstr "" + +#: C/genius.xml:5287(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/StrongPseudoprime.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"StrongPseudoprime.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5296(term) +msgid "<anchor id=\"gel-function-gcd\"/>gcd" +msgstr "<anchor id=\"gel-function-gcd\"/>gcd" + +#: C/genius.xml:5298(synopsis) +#, no-wrap +msgid "gcd (a,args...)" +msgstr "" + +#: C/genius.xml:5299(para) +msgid "Aliases: <function>GCD</function>" +msgstr "Alias: <function>GCD</function>" + +#: C/genius.xml:5300(para) +msgid "" +"Greatest common divisor of integers. You can enter as many integers in the " +"argument list, or you can give a vector or a matrix of integers. If you give " +"more than one matrix of the same size then GCD is done element by element." +msgstr "" + +#: C/genius.xml:5306(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/GreatestCommonDivisor.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"GreatestCommonDivisor.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5315(term) +msgid "<anchor id=\"gel-function-lcm\"/>lcm" +msgstr "<anchor id=\"gel-function-lcm\"/>lcm" + +#: C/genius.xml:5317(synopsis) +#, no-wrap +msgid "lcm (a,args...)" +msgstr "" + +#: C/genius.xml:5318(para) +msgid "Aliases: <function>LCM</function>" +msgstr "Alias: <function>LCM</function>" + +#: C/genius.xml:5319(para) +msgid "" +"Least common multiplier of integers. You can enter as many integers in the " +"argument list, or you can give a vector or a matrix of integers. If you give " +"more than one matrix of the same size then LCM is done element by element." +msgstr "" + +#: C/genius.xml:5325(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/LeastCommonMultiple.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"LeastCommonMultiple.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5337(title) +msgid "Matrix Manipulation" +msgstr "" + +#: C/genius.xml:5340(term) +msgid "<anchor id=\"gel-function-ApplyOverMatrix\"/>ApplyOverMatrix" +msgstr "<anchor id=\"gel-function-ApplyOverMatrix\"/>ApplyOverMatrix" + +#: C/genius.xml:5342(synopsis) +#, no-wrap +msgid "ApplyOverMatrix (a,func)" +msgstr "" + +#: C/genius.xml:5343(para) +msgid "" +"Apply a function over all entries of a matrix and return a matrix of the " +"results." +msgstr "" + +#: C/genius.xml:5348(term) +msgid "<anchor id=\"gel-function-ApplyOverMatrix2\"/>ApplyOverMatrix2" +msgstr "<anchor id=\"gel-function-ApplyOverMatrix2\"/>ApplyOverMatrix2" + +#: C/genius.xml:5350(synopsis) +#, no-wrap +msgid "ApplyOverMatrix2 (a,b,func)" +msgstr "" + +#: C/genius.xml:5351(para) +msgid "" +"Apply a function over all entries of 2 matrices (or 1 value and 1 matrix) and " +"return a matrix of the results." +msgstr "" + +#: C/genius.xml:5356(term) +msgid "<anchor id=\"gel-function-ColumnsOf\"/>ColumnsOf" +msgstr "<anchor id=\"gel-function-ColumnsOf\"/>ColumnsOf" + +#: C/genius.xml:5358(synopsis) +#, no-wrap +msgid "ColumnsOf (M)" +msgstr "ColumnsOf (M)" + +#: C/genius.xml:5359(para) +msgid "Gets the columns of a matrix as a horizontal vector." +msgstr "" + +#: C/genius.xml:5364(term) +msgid "<anchor id=\"gel-function-ComplementSubmatrix\"/>ComplementSubmatrix" +msgstr "<anchor id=\"gel-function-ComplementSubmatrix\"/>ComplementSubmatrix" + +#: C/genius.xml:5366(synopsis) +#, no-wrap +msgid "ComplementSubmatrix (m,r,c)" +msgstr "ComplementSubmatrix (m,r,c)" + +#: C/genius.xml:5367(para) +msgid "Remove column(s) and row(s) from a matrix." +msgstr "" + +#: C/genius.xml:5372(term) +msgid "<anchor id=\"gel-function-CompoundMatrix\"/>CompoundMatrix" +msgstr "<anchor id=\"gel-function-CompoundMatrix\"/>CompoundMatrix" + +#: C/genius.xml:5374(synopsis) +#, no-wrap +msgid "CompoundMatrix (k,A)" +msgstr "CompoundMatrix (k,A)" + +#: C/genius.xml:5375(para) +msgid "Calculate the kth compound matrix of A." +msgstr "" + +#: C/genius.xml:5380(term) +msgid "<anchor id=\"gel-function-CountZeroColumns\"/>CountZeroColumns" +msgstr "<anchor id=\"gel-function-CountZeroColumns\"/>CountZeroColumns" + +#: C/genius.xml:5382(synopsis) +#, no-wrap +msgid "CountZeroColumns (M)" +msgstr "CountZeroColumns (M)" + +#: C/genius.xml:5383(para) +msgid "" +"Count the number of zero columns in a matrix. For example once your column " +"reduce a matrix you can use this to find the nullity. See <link linkend=\"gel-" +"function-cref\"><function>cref</function></link> and <link linkend=\"gel-" +"function-Nullity\"><function>Nullity</function></link>." +msgstr "" + +#: C/genius.xml:5393(term) +msgid "<anchor id=\"gel-function-DeleteColumn\"/>DeleteColumn" +msgstr "<anchor id=\"gel-function-DeleteColumn\"/>DeleteColumn" + +#: C/genius.xml:5395(synopsis) +#, no-wrap +msgid "DeleteColumn (M,col)" +msgstr "" + +#: C/genius.xml:5396(para) +msgid "Delete a column of a matrix." +msgstr "" + +#: C/genius.xml:5401(term) +msgid "<anchor id=\"gel-function-DeleteRow\"/>DeleteRow" +msgstr "<anchor id=\"gel-function-DeleteRow\"/>DeleteRow" + +#: C/genius.xml:5403(synopsis) +#, no-wrap +msgid "DeleteRow (M,row)" +msgstr "" + +#: C/genius.xml:5404(para) +msgid "Delete a row of a matrix." +msgstr "" + +#: C/genius.xml:5409(term) +msgid "<anchor id=\"gel-function-DiagonalOf\"/>DiagonalOf" +msgstr "<anchor id=\"gel-function-DiagonalOf\"/>DiagonalOf" + +#: C/genius.xml:5411(synopsis) +#, no-wrap +msgid "DiagonalOf (M)" +msgstr "DiagonalOf (M)" + +#: C/genius.xml:5412(para) +msgid "Gets the diagonal entries of a matrix as a column vector." +msgstr "" + +#: C/genius.xml:5413(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Diagonal_of_a_matrix#Matrices" +"\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:5421(term) +msgid "<anchor id=\"gel-function-DotProduct\"/>DotProduct" +msgstr "<anchor id=\"gel-function-DotProduct\"/>DotProduct" + +#: C/genius.xml:5423(synopsis) +#, no-wrap +msgid "DotProduct (u,v)" +msgstr "DotProduct (u,v)" + +#: C/genius.xml:5424(para) +msgid "" +"Get the dot product of two vectors. The vectors must be of the same size. No " +"conjugates are taken so this is a bilinear form even if working over the " +"complex numbers." +msgstr "" + +#: C/genius.xml:5426(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/DotProduct.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:5434(term) +msgid "<anchor id=\"gel-function-ExpandMatrix\"/>ExpandMatrix" +msgstr "<anchor id=\"gel-function-ExpandMatrix\"/>ExpandMatrix" + +#: C/genius.xml:5436(synopsis) +#, no-wrap +msgid "ExpandMatrix (M)" +msgstr "ExpandMatrix (M)" + +#: C/genius.xml:5437(para) +msgid "" +"Expands a matrix just like we do on unquoted matrix input. That is we expand " +"any internal matrices as blocks. This is a way to construct matrices out of " +"smaller ones and this is normally done automatically on input unless the " +"matrix is quoted." +msgstr "" + +#: C/genius.xml:5447(term) +msgid "<anchor id=\"gel-function-HermitianProduct\"/>HermitianProduct" +msgstr "<anchor id=\"gel-function-HermitianProduct\"/>HermitianProduct" + +#: C/genius.xml:5449(synopsis) +#, no-wrap +msgid "HermitianProduct (u,v)" +msgstr "HermitianProduct (u,v)" + +#: C/genius.xml:5450(para) +msgid "Aliases: <function>InnerProduct</function>" +msgstr "Alias: <function>InnerProduct</function>" + +#: C/genius.xml:5451(para) +msgid "" +"Get the Hermitian product of two vectors. The vectors must be of the same " +"size. This is a sesquilinear form using the identity matrix." +msgstr "" + +#: C/genius.xml:5452(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/HermitianInnerProduct.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:5460(term) +msgid "<anchor id=\"gel-function-I\"/>I" +msgstr "<anchor id=\"gel-function-I\"/>I" + +#: C/genius.xml:5462(synopsis) +#, no-wrap +msgid "I (n)" +msgstr "I (n)" + +#: C/genius.xml:5463(para) +msgid "Aliases: <function>eye</function>" +msgstr "Alias: <function>eye</function>" + +#: C/genius.xml:5464(para) +msgid "" +"Return an identity matrix of a given size, that is <varname>n</varname> by " +"<varname>n</varname>. If <varname>n</varname> is zero, returns <constant>null</" +"constant>." +msgstr "" + +#: C/genius.xml:5465(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/IdentityMatrix.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:5473(term) +msgid "<anchor id=\"gel-function-IndexComplement\"/>IndexComplement" +msgstr "<anchor id=\"gel-function-IndexComplement\"/>IndexComplement" + +#: C/genius.xml:5475(synopsis) +#, no-wrap +msgid "IndexComplement (vec,msize)" +msgstr "" + +#: C/genius.xml:5476(para) +msgid "" +"Return the index complement of a vector of indexes. Everything is one based. " +"For example for vector <userinput>[2,3]</userinput> and size <userinput>5</" +"userinput>, we return <userinput>[1,4,5]</userinput>. If <varname>msize</" +"varname> is 0, we always return <constant>null</constant>." +msgstr "" + +#: C/genius.xml:5483(term) +msgid "<anchor id=\"gel-function-IsDiagonal\"/>IsDiagonal" +msgstr "<anchor id=\"gel-function-IsDiagonal\"/>IsDiagonal" + +#: C/genius.xml:5485(synopsis) +#, no-wrap +msgid "IsDiagonal (M)" +msgstr "IsDiagonal (M)" + +#: C/genius.xml:5486(para) +msgid "Is a matrix diagonal." +msgstr "" + +#: C/genius.xml:5487(para) C/genius.xml:5637(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Diagonal_matrix\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/DiagonalMatrix.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:5496(term) +msgid "<anchor id=\"gel-function-IsIdentity\"/>IsIdentity" +msgstr "<anchor id=\"gel-function-IsIdentity\"/>IsIdentity" + +#: C/genius.xml:5498(synopsis) +#, no-wrap +msgid "IsIdentity (x)" +msgstr "IsIdentity (x)" + +#: C/genius.xml:5499(para) +msgid "" +"Check if a matrix is the identity matrix. Automatically returns " +"<constant>false</constant> if the matrix is not square. Also works on numbers, " +"in which case it is equivalent to <userinput>x==1</userinput>. When " +"<varname>x</varname> is <constant>null</constant> (we could think of that as a " +"0 by 0 matrix), no error is generated and <constant>false</constant> is " +"returned." +msgstr "" + +#: C/genius.xml:5508(term) +msgid "<anchor id=\"gel-function-IsLowerTriangular\"/>IsLowerTriangular" +msgstr "<anchor id=\"gel-function-IsLowerTriangular\"/>IsLowerTriangular" + +#: C/genius.xml:5510(synopsis) +#, no-wrap +msgid "IsLowerTriangular (M)" +msgstr "IsLowerTriangular (M)" + +#: C/genius.xml:5511(para) +msgid "" +"Is a matrix lower triangular. That is, are all the entries above the diagonal " +"zero." +msgstr "" + +#: C/genius.xml:5516(term) +msgid "<anchor id=\"gel-function-IsMatrixInteger\"/>IsMatrixInteger" +msgstr "<anchor id=\"gel-function-IsMatrixInteger\"/>IsMatrixInteger" + +#: C/genius.xml:5518(synopsis) +#, no-wrap +msgid "IsMatrixInteger (M)" +msgstr "IsMatrixInteger (M)" + +#: C/genius.xml:5519(para) +msgid "Check if a matrix is a matrix of an integers (non-complex)." +msgstr "" + +#: C/genius.xml:5524(term) +msgid "<anchor id=\"gel-function-IsMatrixNonnegative\"/>IsMatrixNonnegative" +msgstr "<anchor id=\"gel-function-IsMatrixNonnegative\"/>IsMatrixNonnegative" + +#: C/genius.xml:5526(synopsis) +#, no-wrap +msgid "IsMatrixNonnegative (M)" +msgstr "IsMatrixNonnegative (M)" + +#: C/genius.xml:5527(para) +msgid "" +"Check if a matrix is non-negative, that is if each element is non-negative. Do " +"not confuse positive matrices with positive semi-definite matrices." +msgstr "" + +#: C/genius.xml:5529(para) C/genius.xml:5543(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Positive_matrix\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:5537(term) +msgid "<anchor id=\"gel-function-IsMatrixPositive\"/>IsMatrixPositive" +msgstr "<anchor id=\"gel-function-IsMatrixPositive\"/>IsMatrixPositive" + +#: C/genius.xml:5539(synopsis) +#, no-wrap +msgid "IsMatrixPositive (M)" +msgstr "IsMatrixPositive (M)" + +#: C/genius.xml:5540(para) +msgid "" +"Check if a matrix is positive, that is if each element is positive (and hence " +"real). In particular, no element is 0. Do not confuse positive matrices with " +"positive definite matrices." +msgstr "" + +#: C/genius.xml:5551(term) +msgid "<anchor id=\"gel-function-IsMatrixRational\"/>IsMatrixRational" +msgstr "<anchor id=\"gel-function-IsMatrixRational\"/>IsMatrixRational" + +#: C/genius.xml:5553(synopsis) +#, no-wrap +msgid "IsMatrixRational (M)" +msgstr "IsMatrixRational (M)" + +#: C/genius.xml:5554(para) +msgid "Check if a matrix is a matrix of rational (non-complex) numbers." +msgstr "" + +#: C/genius.xml:5560(term) +msgid "<anchor id=\"gel-function-IsMatrixReal\"/>IsMatrixReal" +msgstr "<anchor id=\"gel-function-IsMatrixReal\"/>IsMatrixReal" + +#: C/genius.xml:5562(synopsis) +#, no-wrap +msgid "IsMatrixReal (M)" +msgstr "IsMatrixReal (M)" + +#: C/genius.xml:5563(para) +msgid "Check if a matrix is a matrix of real (non-complex) numbers." +msgstr "" + +#: C/genius.xml:5568(term) +msgid "<anchor id=\"gel-function-IsMatrixSquare\"/>IsMatrixSquare" +msgstr "<anchor id=\"gel-function-IsMatrixSquare\"/>IsMatrixSquare" + +#: C/genius.xml:5570(synopsis) +#, no-wrap +msgid "IsMatrixSquare (M)" +msgstr "IsMatrixSquare (M)" + +#: C/genius.xml:5571(para) +msgid "Check if a matrix is square, that is its width is equal to its height." +msgstr "" + +#: C/genius.xml:5579(term) +msgid "<anchor id=\"gel-function-IsUpperTriangular\"/>IsUpperTriangular" +msgstr "<anchor id=\"gel-function-IsUpperTriangular\"/>IsUpperTriangular" + +#: C/genius.xml:5581(synopsis) +#, no-wrap +msgid "IsUpperTriangular (M)" +msgstr "IsUpperTriangular (M)" + +#: C/genius.xml:5582(para) +msgid "" +"Is a matrix upper triangular? That is, a matrix is upper triangular if all the " +"entries below the diagonal are zero." +msgstr "" + +#: C/genius.xml:5587(term) +msgid "<anchor id=\"gel-function-IsValueOnly\"/>IsValueOnly" +msgstr "<anchor id=\"gel-function-IsValueOnly\"/>IsValueOnly" + +#: C/genius.xml:5589(synopsis) +#, no-wrap +msgid "IsValueOnly (M)" +msgstr "IsValueOnly (M)" + +#: C/genius.xml:5590(para) +msgid "" +"Check if a matrix is a matrix of numbers only. Many internal functions make " +"this check. Values can be any number including complex numbers." +msgstr "" + +#: C/genius.xml:5596(term) +msgid "<anchor id=\"gel-function-IsVector\"/>IsVector" +msgstr "<anchor id=\"gel-function-IsVector\"/>IsVector" + +#: C/genius.xml:5598(synopsis) +#, no-wrap +msgid "IsVector (v)" +msgstr "IsVector (v)" + +#: C/genius.xml:5599(para) +msgid "" +"Is argument a horizontal or a vertical vector. Genius does not distinguish " +"between a matrix and a vector and a vector is just a 1 by <varname>n</varname> " +"or <varname>n</varname> by 1 matrix." +msgstr "" + +#: C/genius.xml:5608(term) +msgid "<anchor id=\"gel-function-IsZero\"/>IsZero" +msgstr "<anchor id=\"gel-function-IsZero\"/>IsZero" + +#: C/genius.xml:5610(synopsis) +#, no-wrap +msgid "IsZero (x)" +msgstr "IsZero (x)" + +#: C/genius.xml:5611(para) +msgid "" +"Check if a matrix is composed of all zeros. Also works on numbers, in which " +"case it is equivalent to <userinput>x==0</userinput>. When <varname>x</" +"varname> is <constant>null</constant> (we could think of that as a 0 by 0 " +"matrix), no error is generated and <constant>true</constant> is returned as " +"the condition is vacuous." +msgstr "" + +#: C/genius.xml:5621(term) +msgid "<anchor id=\"gel-function-LowerTriangular\"/>LowerTriangular" +msgstr "<anchor id=\"gel-function-LowerTriangular\"/>LowerTriangular" + +#: C/genius.xml:5623(synopsis) +#, no-wrap +msgid "LowerTriangular (M)" +msgstr "LowerTriangular (M)" + +#: C/genius.xml:5624(para) +msgid "" +"Returns a copy of the matrix <varname>M</varname> with all the entries above " +"the diagonal set to zero." +msgstr "" + +#: C/genius.xml:5629(term) +msgid "<anchor id=\"gel-function-MakeDiagonal\"/>MakeDiagonal" +msgstr "<anchor id=\"gel-function-MakeDiagonal\"/>MakeDiagonal" + +#: C/genius.xml:5631(synopsis) +#, no-wrap +msgid "MakeDiagonal (v,arg...)" +msgstr "MakeDiagonal (v,arg...)" + +#: C/genius.xml:5632(para) +msgid "Aliases: <function>diag</function>" +msgstr "Alias: <function>diag</function>" + +#: C/genius.xml:5633(para) +msgid "" +"Make diagonal matrix from a vector. Alternatively you can pass in the values " +"to put on the diagonal as arguments. So <userinput>MakeDiagonal([1,2,3])</" +"userinput> is the same as <userinput>MakeDiagonal(1,2,3)</userinput>." +msgstr "" + +#: C/genius.xml:5646(term) +msgid "<anchor id=\"gel-function-MakeVector\"/>MakeVector" +msgstr "<anchor id=\"gel-function-MakeVector\"/>MakeVector" + +#: C/genius.xml:5648(synopsis) +#, no-wrap +msgid "MakeVector (A)" +msgstr "MakeVector (A)" + +#: C/genius.xml:5649(para) +msgid "" +"Make column vector out of matrix by putting columns above each other. Returns " +"<constant>null</constant> when given <constant>null</constant>." +msgstr "" + +#: C/genius.xml:5655(term) +msgid "<anchor id=\"gel-function-MatrixProduct\"/>MatrixProduct" +msgstr "<anchor id=\"gel-function-MatrixProduct\"/>MatrixProduct" + +#: C/genius.xml:5657(synopsis) +#, no-wrap +msgid "MatrixProduct (A)" +msgstr "MatrixProduct (A)" + +#: C/genius.xml:5658(para) +msgid "" +"Calculate the product of all elements in a matrix or vector. That is we " +"multiply all the elements and return a number that is the product of all the " +"elements." +msgstr "" + +#: C/genius.xml:5667(term) +msgid "<anchor id=\"gel-function-MatrixSum\"/>MatrixSum" +msgstr "<anchor id=\"gel-function-MatrixSum\"/>MatrixSum" + +#: C/genius.xml:5669(synopsis) +#, no-wrap +msgid "MatrixSum (A)" +msgstr "MatrixSum (A)" + +#: C/genius.xml:5670(para) +msgid "" +"Calculate the sum of all elements in a matrix or vector. That is we add all " +"the elements and return a number that is the sum of all the elements." +msgstr "" + +#: C/genius.xml:5679(term) +msgid "<anchor id=\"gel-function-MatrixSumSquares\"/>MatrixSumSquares" +msgstr "<anchor id=\"gel-function-MatrixSumSquares\"/>MatrixSumSquares" + +#: C/genius.xml:5681(synopsis) +#, no-wrap +msgid "MatrixSumSquares (A)" +msgstr "MatrixSumSquares (A)" + +#: C/genius.xml:5682(para) +msgid "Calculate the sum of squares of all elements in a matrix or vector." +msgstr "" + +#: C/genius.xml:5688(term) +msgid "<anchor id=\"gel-function-NonzeroColumns\"/>NonzeroColumns" +msgstr "<anchor id=\"gel-function-NonzeroColumns\"/>NonzeroColumns" + +#: C/genius.xml:5690(synopsis) +#, no-wrap +msgid "NonzeroColumns (M)" +msgstr "NonzeroColumns (M)" + +#: C/genius.xml:5691(para) +msgid "" +"Returns a row vector of the indices of nonzero columns in the matrix " +"<varname>M</varname>." +msgstr "" + +#: C/genius.xml:5697(term) +msgid "<anchor id=\"gel-function-NonzeroElements\"/>NonzeroElements" +msgstr "<anchor id=\"gel-function-NonzeroElements\"/>NonzeroElements" + +#: C/genius.xml:5699(synopsis) +#, no-wrap +msgid "NonzeroElements (v)" +msgstr "NonzeroElements (v)" + +#: C/genius.xml:5700(para) +msgid "" +"Returns a row vector of the indices of nonzero elements in the vector " +"<varname>v</varname>." +msgstr "" + +#: C/genius.xml:5706(term) +msgid "<anchor id=\"gel-function-OuterProduct\"/>OuterProduct" +msgstr "<anchor id=\"gel-function-OuterProduct\"/>OuterProduct" + +#: C/genius.xml:5708(synopsis) +#, no-wrap +msgid "OuterProduct (u,v)" +msgstr "OuterProduct (u,v)" + +#: C/genius.xml:5709(para) +msgid "" +"Get the outer product of two vectors. That is, suppose that <varname>u</" +"varname> and <varname>v</varname> are vertical vectors, then the outer product " +"is <userinput>v * u.'</userinput>." +msgstr "" + +#: C/genius.xml:5716(term) +msgid "<anchor id=\"gel-function-ReverseVector\"/>ReverseVector" +msgstr "<anchor id=\"gel-function-ReverseVector\"/>ReverseVector" + +#: C/genius.xml:5718(synopsis) +#, no-wrap +msgid "ReverseVector (v)" +msgstr "ReverseVector (v)" + +#: C/genius.xml:5719(para) +msgid "" +"Reverse elements in a vector. Return <constant>null</constant> if given " +"<constant>null</constant>" +msgstr "" + +#: C/genius.xml:5724(term) +msgid "<anchor id=\"gel-function-RowSum\"/>RowSum" +msgstr "<anchor id=\"gel-function-RowSum\"/>RowSum" + +#: C/genius.xml:5726(synopsis) +#, no-wrap +msgid "RowSum (m)" +msgstr "RowSum (m)" + +#: C/genius.xml:5727(para) +msgid "" +"Calculate sum of each row in a matrix and return a vertical vector with the " +"result." +msgstr "" + +#: C/genius.xml:5733(term) +msgid "<anchor id=\"gel-function-RowSumSquares\"/>RowSumSquares" +msgstr "<anchor id=\"gel-function-RowSumSquares\"/>RowSumSquares" + +#: C/genius.xml:5735(synopsis) +#, no-wrap +msgid "RowSumSquares (m)" +msgstr "RowSumSquares (m)" + +#: C/genius.xml:5736(para) +msgid "" +"Calculate sum of squares of each row in a matrix and return a vertical vector " +"with the results." +msgstr "" + +#: C/genius.xml:5741(term) +msgid "<anchor id=\"gel-function-RowsOf\"/>RowsOf" +msgstr "<anchor id=\"gel-function-RowsOf\"/>RowsOf" + +#: C/genius.xml:5743(synopsis) +#, no-wrap +msgid "RowsOf (M)" +msgstr "RowsOf (M)" + +#: C/genius.xml:5744(para) +msgid "" +"Gets the rows of a matrix as a vertical vector. Each element of the vector is " +"a horizontal vector that is the corresponding row of <varname>M</varname>. " +"This function is useful if you wish to loop over the rows of a matrix. For " +"example, as <userinput>for r in RowsOf(M) do\n" +"something(r)</userinput>." +msgstr "" + +#: C/genius.xml:5753(term) +msgid "<anchor id=\"gel-function-SetMatrixSize\"/>SetMatrixSize" +msgstr "<anchor id=\"gel-function-SetMatrixSize\"/>SetMatrixSize" + +#: C/genius.xml:5755(synopsis) +#, no-wrap +msgid "SetMatrixSize (M,rows,columns)" +msgstr "" + +#: C/genius.xml:5756(para) +msgid "" +"Make new matrix of given size from old one. That is, a new matrix will be " +"returned to which the old one is copied. Entries that don't fit are clipped " +"and extra space is filled with zeros. If <varname>rows</varname> or " +"<varname>columns</varname> are zero then <constant>null</constant> is returned." +msgstr "" + +#: C/genius.xml:5766(term) +msgid "<anchor id=\"gel-function-ShuffleVector\"/>ShuffleVector" +msgstr "<anchor id=\"gel-function-ShuffleVector\"/>ShuffleVector" + +#: C/genius.xml:5768(synopsis) +#, no-wrap +msgid "ShuffleVector (v)" +msgstr "ShuffleVector (v)" + +#: C/genius.xml:5769(para) +msgid "" +"Shuffle elements in a vector. Return <constant>null</constant> if given " +"<constant>null</constant>." +msgstr "" + +#: C/genius.xml:5770(para) +msgid "Version 1.0.13 onwards." +msgstr "Version 1.0.13 och framåt." + +#: C/genius.xml:5775(term) +msgid "<anchor id=\"gel-function-SortVector\"/>SortVector" +msgstr "<anchor id=\"gel-function-SortVector\"/>SortVector" + +#: C/genius.xml:5777(synopsis) +#, no-wrap +msgid "SortVector (v)" +msgstr "SortVector (v)" + +#: C/genius.xml:5778(para) +msgid "Sort vector elements in an increasing order." +msgstr "" + +#: C/genius.xml:5783(term) +msgid "<anchor id=\"gel-function-StripZeroColumns\"/>StripZeroColumns" +msgstr "<anchor id=\"gel-function-StripZeroColumns\"/>StripZeroColumns" + +#: C/genius.xml:5785(synopsis) +#, no-wrap +msgid "StripZeroColumns (M)" +msgstr "StripZeroColumns (M)" + +#: C/genius.xml:5786(para) +msgid "Removes any all-zero columns of <varname>M</varname>." +msgstr "" + +#: C/genius.xml:5791(term) +msgid "<anchor id=\"gel-function-StripZeroRows\"/>StripZeroRows" +msgstr "<anchor id=\"gel-function-StripZeroRows\"/>StripZeroRows" + +#: C/genius.xml:5793(synopsis) +#, no-wrap +msgid "StripZeroRows (M)" +msgstr "StripZeroRows (M)" + +#: C/genius.xml:5794(para) +msgid "Removes any all-zero rows of <varname>M</varname>." +msgstr "" + +#: C/genius.xml:5799(term) +msgid "<anchor id=\"gel-function-Submatrix\"/>Submatrix" +msgstr "<anchor id=\"gel-function-Submatrix\"/>Submatrix" + +#: C/genius.xml:5801(synopsis) +#, no-wrap +msgid "Submatrix (m,r,c)" +msgstr "Submatrix (m,r,c)" + +#: C/genius.xml:5802(para) +msgid "" +"Return column(s) and row(s) from a matrix. This is just equivalent to " +"<userinput>m@(r,c)</userinput>. <varname>r</varname> and <varname>c</varname> " +"should be vectors of rows and columns (or single numbers if only one row or " +"column is needed)." +msgstr "" + +#: C/genius.xml:5809(term) +msgid "<anchor id=\"gel-function-SwapRows\"/>SwapRows" +msgstr "<anchor id=\"gel-function-SwapRows\"/>SwapRows" + +#: C/genius.xml:5811(synopsis) +#, no-wrap +msgid "SwapRows (m,row1,row2)" +msgstr "" + +#: C/genius.xml:5812(para) +msgid "Swap two rows in a matrix." +msgstr "" + +#: C/genius.xml:5817(term) +msgid "<anchor id=\"gel-function-UpperTriangular\"/>UpperTriangular" +msgstr "<anchor id=\"gel-function-UpperTriangular\"/>UpperTriangular" + +#: C/genius.xml:5819(synopsis) +#, no-wrap +msgid "UpperTriangular (M)" +msgstr "UpperTriangular (M)" + +#: C/genius.xml:5820(para) +msgid "" +"Returns a copy of the matrix <varname>M</varname> with all the entries below " +"the diagonal set to zero." +msgstr "" + +#: C/genius.xml:5825(term) +msgid "<anchor id=\"gel-function-columns\"/>columns" +msgstr "<anchor id=\"gel-function-columns\"/>columns" + +#: C/genius.xml:5827(synopsis) +#, no-wrap +msgid "columns (M)" +msgstr "columns (M)" + +#: C/genius.xml:5828(para) +msgid "Get the number of columns of a matrix." +msgstr "" + +#: C/genius.xml:5833(term) +msgid "<anchor id=\"gel-function-elements\"/>elements" +msgstr "<anchor id=\"gel-function-elements\"/>elements" + +#: C/genius.xml:5835(synopsis) +#, no-wrap +msgid "elements (M)" +msgstr "elements (M)" + +#: C/genius.xml:5836(para) +msgid "" +"Get the total number of elements of a matrix. This is the number of columns " +"times the number of rows." +msgstr "" + +#: C/genius.xml:5842(term) +msgid "<anchor id=\"gel-function-ones\"/>ones" +msgstr "<anchor id=\"gel-function-ones\"/>ones" + +#: C/genius.xml:5844(synopsis) +#, no-wrap +msgid "ones (rows,columns...)" +msgstr "" + +#: C/genius.xml:5845(para) +msgid "" +"Make an matrix of all ones (or a row vector if only one argument is given). " +"Returns <constant>null</constant> if either rows or columns are zero." +msgstr "" + +#: C/genius.xml:5850(term) +msgid "<anchor id=\"gel-function-rows\"/>rows" +msgstr "<anchor id=\"gel-function-rows\"/>rows" + +#: C/genius.xml:5852(synopsis) +#, no-wrap +msgid "rows (M)" +msgstr "rows (M)" + +#: C/genius.xml:5853(para) +msgid "Get the number of rows of a matrix." +msgstr "" + +#: C/genius.xml:5858(term) +msgid "<anchor id=\"gel-function-zeros\"/>zeros" +msgstr "<anchor id=\"gel-function-zeros\"/>zeros" + +#: C/genius.xml:5860(synopsis) +#, no-wrap +msgid "zeros (rows,columns...)" +msgstr "" + +#: C/genius.xml:5861(para) +msgid "" +"Make a matrix of all zeros (or a row vector if only one argument is given). " +"Returns <constant>null</constant> if either rows or columns are zero." +msgstr "" + +#: C/genius.xml:5872(term) +msgid "<anchor id=\"gel-function-AuxiliaryUnitMatrix\"/>AuxiliaryUnitMatrix" +msgstr "<anchor id=\"gel-function-AuxiliaryUnitMatrix\"/>AuxiliaryUnitMatrix" + +#: C/genius.xml:5874(synopsis) +#, no-wrap +msgid "AuxiliaryUnitMatrix (n)" +msgstr "AuxiliaryUnitMatrix (n)" + +#: C/genius.xml:5875(para) +msgid "" +"Get the auxiliary unit matrix of size <varname>n</varname>. This is a square " +"matrix with that is all zero except the superdiagonal being all ones. It is " +"the Jordan block matrix of one zero eigenvalue." +msgstr "" + +#: C/genius.xml:5877(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/JordanCanonicalFormTheorem." +"html\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"JordanBlock.html\">Mathworld</ulink> for more information on Jordan Canonical " +"Form." +msgstr "" + +#: C/genius.xml:5886(term) +msgid "<anchor id=\"gel-function-BilinearForm\"/>BilinearForm" +msgstr "<anchor id=\"gel-function-BilinearForm\"/>BilinearForm" + +#: C/genius.xml:5888(synopsis) +#, no-wrap +msgid "BilinearForm (v,A,w)" +msgstr "BilinearForm (v,A,w)" + +#: C/genius.xml:5889(para) +msgid "Evaluate (v,w) with respect to the bilinear form given by the matrix A." +msgstr "" + +#: C/genius.xml:5894(term) +msgid "<anchor id=\"gel-function-BilinearFormFunction\"/>BilinearFormFunction" +msgstr "<anchor id=\"gel-function-BilinearFormFunction\"/>BilinearFormFunction" + +#: C/genius.xml:5896(synopsis) +#, no-wrap +msgid "BilinearFormFunction (A)" +msgstr "BilinearFormFunction (A)" + +#: C/genius.xml:5897(para) +msgid "" +"Return a function that evaluates two vectors with respect to the bilinear form " +"given by A." +msgstr "" + +#: C/genius.xml:5902(term) +msgid "" +"<anchor id=\"gel-function-CharacteristicPolynomial\"/>CharacteristicPolynomial" +msgstr "" +"<anchor id=\"gel-function-CharacteristicPolynomial\"/>CharacteristicPolynomial" + +#: C/genius.xml:5904(synopsis) +#, no-wrap +msgid "CharacteristicPolynomial (M)" +msgstr "CharacteristicPolynomial (M)" + +#: C/genius.xml:5905(para) +msgid "Aliases: <function>CharPoly</function>" +msgstr "Alias: <function>CharPoly</function>" + +#: C/genius.xml:5906(para) +msgid "" +"Get the characteristic polynomial as a vector. That is, return the " +"coefficients of the polynomial starting with the constant term. This is the " +"polynomial defined by <userinput>det(M-xI)</userinput>. The roots of this " +"polynomial are the eigenvalues of <varname>M</varname>. See also <link linkend=" +"\"gel-function-CharacteristicPolynomialFunction" +"\">CharacteristicPolynomialFunction</link>." +msgstr "" + +#: C/genius.xml:5912(para) C/genius.xml:5928(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/CharacteristicEquation.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:5920(term) +msgid "" +"<anchor id=\"gel-function-CharacteristicPolynomialFunction\"/" +">CharacteristicPolynomialFunction" +msgstr "" +"<anchor id=\"gel-function-CharacteristicPolynomialFunction\"/" +">CharacteristicPolynomialFunction" + +#: C/genius.xml:5922(synopsis) +#, no-wrap +msgid "CharacteristicPolynomialFunction (M)" +msgstr "CharacteristicPolynomialFunction (M)" + +#: C/genius.xml:5923(para) +msgid "" +"Get the characteristic polynomial as a function. This is the polynomial " +"defined by <userinput>det(M-xI)</userinput>. The roots of this polynomial are " +"the eigenvalues of <varname>M</varname>. See also <link linkend=\"gel-function-" +"CharacteristicPolynomial\">CharacteristicPolynomial</link>." +msgstr "" + +#: C/genius.xml:5936(term) +msgid "<anchor id=\"gel-function-ColumnSpace\"/>ColumnSpace" +msgstr "<anchor id=\"gel-function-ColumnSpace\"/>ColumnSpace" + +#: C/genius.xml:5938(synopsis) +#, no-wrap +msgid "ColumnSpace (M)" +msgstr "ColumnSpace (M)" + +#: C/genius.xml:5939(para) +msgid "" +"Get a basis matrix for the columnspace of a matrix. That is, return a matrix " +"whose columns are the basis for the column space of <varname>M</varname>. That " +"is the space spanned by the columns of <varname>M</varname>." +msgstr "" + +#: C/genius.xml:5947(term) +msgid "<anchor id=\"gel-function-CommutationMatrix\"/>CommutationMatrix" +msgstr "<anchor id=\"gel-function-CommutationMatrix\"/>CommutationMatrix" + +#: C/genius.xml:5949(synopsis) +#, no-wrap +msgid "CommutationMatrix (m, n)" +msgstr "CommutationMatrix (m, n)" + +#: C/genius.xml:5950(para) +msgid "" +"Return the commutation matrix <userinput>K(m,n)</userinput>, which is the " +"unique <userinput>m*n</userinput> by <userinput>m*n</userinput> matrix such " +"that <userinput>K(m,n) * MakeVector(A) = MakeVector(A.')</userinput> for all " +"<varname>m</varname> by <varname>n</varname> matrices <varname>A</varname>." +msgstr "" + +#: C/genius.xml:5957(term) +msgid "<anchor id=\"gel-function-CompanionMatrix\"/>CompanionMatrix" +msgstr "<anchor id=\"gel-function-CompanionMatrix\"/>CompanionMatrix" + +#: C/genius.xml:5959(synopsis) +#, no-wrap +msgid "CompanionMatrix (p)" +msgstr "CompanionMatrix (p)" + +#: C/genius.xml:5960(para) +msgid "Companion matrix of a polynomial (as vector)." +msgstr "" + +#: C/genius.xml:5965(term) +msgid "<anchor id=\"gel-function-ConjugateTranspose\"/>ConjugateTranspose" +msgstr "<anchor id=\"gel-function-ConjugateTranspose\"/>ConjugateTranspose" + +#: C/genius.xml:5967(synopsis) +#, no-wrap +msgid "ConjugateTranspose (M)" +msgstr "ConjugateTranspose (M)" + +#: C/genius.xml:5968(para) +msgid "" +"Conjugate transpose of a matrix (adjoint). This is the same as the " +"<userinput>'</userinput> operator." +msgstr "" + +#: C/genius.xml:5970(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/ConjugateTranspose.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:5978(term) +msgid "<anchor id=\"gel-function-Convolution\"/>Convolution" +msgstr "<anchor id=\"gel-function-Convolution\"/>Convolution" + +#: C/genius.xml:5980(synopsis) +#, no-wrap +msgid "Convolution (a,b)" +msgstr "Convolution (a,b)" + +#: C/genius.xml:5981(para) +msgid "Aliases: <function>convol</function>" +msgstr "Alias: <function>convol</function>" + +#: C/genius.xml:5982(para) +msgid "Calculate convolution of two horizontal vectors." +msgstr "" + +#: C/genius.xml:5987(term) +msgid "<anchor id=\"gel-function-ConvolutionVector\"/>ConvolutionVector" +msgstr "<anchor id=\"gel-function-ConvolutionVector\"/>ConvolutionVector" + +#: C/genius.xml:5989(synopsis) +#, no-wrap +msgid "ConvolutionVector (a,b)" +msgstr "ConvolutionVector (a,b)" + +#: C/genius.xml:5990(para) +msgid "" +"Calculate convolution of two horizontal vectors. Return result as a vector and " +"not added together." +msgstr "" + +#: C/genius.xml:5996(term) +msgid "<anchor id=\"gel-function-CrossProduct\"/>CrossProduct" +msgstr "<anchor id=\"gel-function-CrossProduct\"/>CrossProduct" + +#: C/genius.xml:5998(synopsis) +#, no-wrap +msgid "CrossProduct (v,w)" +msgstr "CrossProduct (v,w)" + +#: C/genius.xml:5999(para) +msgid "" +"CrossProduct of two vectors in R<superscript>3</superscript> as a column " +"vector." +msgstr "" + +#: C/genius.xml:6005(term) +msgid "" +"<anchor id=\"gel-function-DeterminantalDivisorsInteger\"/" +">DeterminantalDivisorsInteger" +msgstr "" +"<anchor id=\"gel-function-DeterminantalDivisorsInteger\"/" +">DeterminantalDivisorsInteger" + +#: C/genius.xml:6007(synopsis) +#, no-wrap +msgid "DeterminantalDivisorsInteger (M)" +msgstr "DeterminantalDivisorsInteger (M)" + +#: C/genius.xml:6008(para) +msgid "" +"Get the determinantal divisors of an integer matrix (not its characteristic)." +msgstr "" + +#: C/genius.xml:6013(term) +msgid "<anchor id=\"gel-function-DirectSum\"/>DirectSum" +msgstr "<anchor id=\"gel-function-DirectSum\"/>DirectSum" + +#: C/genius.xml:6015(synopsis) +#, no-wrap +msgid "DirectSum (M,N...)" +msgstr "DirectSum (M,N...)" + +#: C/genius.xml:6016(para) +msgid "Direct sum of matrices." +msgstr "" + +#: C/genius.xml:6021(term) +msgid "<anchor id=\"gel-function-DirectSumMatrixVector\"/>DirectSumMatrixVector" +msgstr "<anchor id=\"gel-function-DirectSumMatrixVector\"/>DirectSumMatrixVector" + +#: C/genius.xml:6023(synopsis) +#, no-wrap +msgid "DirectSumMatrixVector (v)" +msgstr "DirectSumMatrixVector (v)" + +#: C/genius.xml:6024(para) +msgid "Direct sum of a vector of matrices." +msgstr "" + +#: C/genius.xml:6029(term) +msgid "<anchor id=\"gel-function-Eigenvalues\"/>Eigenvalues" +msgstr "<anchor id=\"gel-function-Eigenvalues\"/>Eigenvalues" + +#: C/genius.xml:6031(synopsis) +#, no-wrap +msgid "Eigenvalues (M)" +msgstr "Eigenvalues (M)" + +#: C/genius.xml:6032(para) +msgid "Aliases: <function>eig</function>" +msgstr "Alias: <function>eig</function>" + +#: C/genius.xml:6033(para) +msgid "" +"Get the eigenvalues of a square matrix. Currently only works for matrices of " +"size up to 4 by 4, or for triangular matrices (for which the eigenvalues are " +"on the diagonal)." +msgstr "" + +#: C/genius.xml:6038(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Eigenvalue\">Wikipedia</ulink> " +"or <ulink url=\"http://planetmath.org/encyclopedia/Eigenvalue.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/Eigenvalue." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6048(term) +msgid "<anchor id=\"gel-function-Eigenvectors\"/>Eigenvectors" +msgstr "<anchor id=\"gel-function-Eigenvectors\"/>Eigenvectors" + +#: C/genius.xml:6050(synopsis) +#, no-wrap +msgid "Eigenvectors (M)" +msgstr "Eigenvectors (M)" + +#: C/genius.xml:6051(synopsis) +#, no-wrap +msgid "Eigenvectors (M, &eigenvalues)" +msgstr "" + +#: C/genius.xml:6052(synopsis) +#, no-wrap +msgid "Eigenvectors (M, &eigenvalues, &multiplicities)" +msgstr "" + +#: C/genius.xml:6053(para) +msgid "" +"Get the eigenvectors of a square matrix. Optionally get also the eigenvalues " +"and their algebraic multiplicities. Currently only works for matrices of size " +"up to 2 by 2." +msgstr "" + +#: C/genius.xml:6057(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Eigenvector\">Wikipedia</ulink> " +"or <ulink url=\"http://planetmath.org/encyclopedia/Eigenvector.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/Eigenvector." +"html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6067(term) +msgid "<anchor id=\"gel-function-GramSchmidt\"/>GramSchmidt" +msgstr "<anchor id=\"gel-function-GramSchmidt\"/>GramSchmidt" + +#: C/genius.xml:6069(synopsis) +#, no-wrap +msgid "GramSchmidt (v,B...)" +msgstr "GramSchmidt (v,B...)" + +#: C/genius.xml:6070(para) +msgid "" +"Apply the Gram-Schmidt process (to the columns) with respect to inner product " +"given by <varname>B</varname>. If <varname>B</varname> is not given then the " +"standard Hermitian product is used. <varname>B</varname> can either be a " +"sesquilinear function of two arguments or it can be a matrix giving a " +"sesquilinear form. The vectors will be made orthonormal with respect to " +"<varname>B</varname>." +msgstr "" + +#: C/genius.xml:6076(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/" +"GramSchmidtOrthogonalization.html\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6084(term) +msgid "<anchor id=\"gel-function-HankelMatrix\"/>HankelMatrix" +msgstr "<anchor id=\"gel-function-HankelMatrix\"/>HankelMatrix" + +#: C/genius.xml:6086(synopsis) +#, no-wrap +msgid "HankelMatrix (c,r)" +msgstr "HankelMatrix (c,r)" + +#: C/genius.xml:6087(para) +msgid "Hankel matrix." +msgstr "" + +#: C/genius.xml:6092(term) +msgid "<anchor id=\"gel-function-HilbertMatrix\"/>HilbertMatrix" +msgstr "<anchor id=\"gel-function-HilbertMatrix\"/>HilbertMatrix" + +#: C/genius.xml:6094(synopsis) +#, no-wrap +msgid "HilbertMatrix (n)" +msgstr "HilbertMatrix (n)" + +#: C/genius.xml:6095(para) +msgid "Hilbert matrix of order <varname>n</varname>." +msgstr "" + +#: C/genius.xml:6096(para) C/genius.xml:6132(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/HilbertMatrix.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6104(term) +msgid "<anchor id=\"gel-function-Image\"/>Image" +msgstr "<anchor id=\"gel-function-Image\"/>Image" + +#: C/genius.xml:6106(synopsis) +#, no-wrap +msgid "Image (T)" +msgstr "Image (T)" + +#: C/genius.xml:6107(para) +msgid "Get the image (columnspace) of a linear transform." +msgstr "" + +#: C/genius.xml:6112(term) +msgid "<anchor id=\"gel-function-InfNorm\"/>InfNorm" +msgstr "<anchor id=\"gel-function-InfNorm\"/>InfNorm" + +#: C/genius.xml:6114(synopsis) +#, no-wrap +msgid "InfNorm (v)" +msgstr "InfNorm (v)" + +#: C/genius.xml:6115(para) +msgid "" +"Get the Inf Norm of a vector, sometimes called the sup norm or the max norm." +msgstr "" + +#: C/genius.xml:6120(term) +msgid "" +"<anchor id=\"gel-function-InvariantFactorsInteger\"/>InvariantFactorsInteger" +msgstr "" +"<anchor id=\"gel-function-InvariantFactorsInteger\"/>InvariantFactorsInteger" + +#: C/genius.xml:6122(synopsis) +#, no-wrap +msgid "InvariantFactorsInteger (M)" +msgstr "InvariantFactorsInteger (M)" + +#: C/genius.xml:6123(para) +msgid "" +"Get the invariant factors of a square integer matrix (not its characteristic)." +msgstr "" + +#: C/genius.xml:6128(term) +msgid "<anchor id=\"gel-function-InverseHilbertMatrix\"/>InverseHilbertMatrix" +msgstr "<anchor id=\"gel-function-InverseHilbertMatrix\"/>InverseHilbertMatrix" + +#: C/genius.xml:6130(synopsis) +#, no-wrap +msgid "InverseHilbertMatrix (n)" +msgstr "InverseHilbertMatrix (n)" + +#: C/genius.xml:6131(para) +msgid "Inverse Hilbert matrix of order <varname>n</varname>." +msgstr "" + +#: C/genius.xml:6140(term) +msgid "<anchor id=\"gel-function-IsHermitian\"/>IsHermitian" +msgstr "<anchor id=\"gel-function-IsHermitian\"/>IsHermitian" + +#: C/genius.xml:6142(synopsis) +#, no-wrap +msgid "IsHermitian (M)" +msgstr "IsHermitian (M)" + +#: C/genius.xml:6143(para) +msgid "Is a matrix Hermitian. That is, is it equal to its conjugate transpose." +msgstr "" + +#: C/genius.xml:6144(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/HermitianMatrix.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6152(term) +msgid "<anchor id=\"gel-function-IsInSubspace\"/>IsInSubspace" +msgstr "<anchor id=\"gel-function-IsInSubspace\"/>IsInSubspace" + +#: C/genius.xml:6154(synopsis) +#, no-wrap +msgid "IsInSubspace (v,W)" +msgstr "IsInSubspace (v,W)" + +#: C/genius.xml:6155(para) +msgid "Test if a vector is in a subspace." +msgstr "" + +#: C/genius.xml:6160(term) +msgid "<anchor id=\"gel-function-IsInvertible\"/>IsInvertible" +msgstr "<anchor id=\"gel-function-IsInvertible\"/>IsInvertible" + +#: C/genius.xml:6162(synopsis) +#, no-wrap +msgid "IsInvertible (n)" +msgstr "IsInvertible (n)" + +#: C/genius.xml:6163(para) +msgid "" +"Is a matrix (or number) invertible (Integer matrix is invertible if and only " +"if it is invertible over the integers)." +msgstr "" + +#: C/genius.xml:6168(term) +msgid "<anchor id=\"gel-function-IsInvertibleField\"/>IsInvertibleField" +msgstr "<anchor id=\"gel-function-IsInvertibleField\"/>IsInvertibleField" + +#: C/genius.xml:6170(synopsis) +#, no-wrap +msgid "IsInvertibleField (n)" +msgstr "IsInvertibleField (n)" + +#: C/genius.xml:6171(para) +msgid "Is a matrix (or number) invertible over a field." +msgstr "" + +#: C/genius.xml:6176(term) +msgid "<anchor id=\"gel-function-IsNormal\"/>IsNormal" +msgstr "<anchor id=\"gel-function-IsNormal\"/>IsNormal" + +#: C/genius.xml:6178(synopsis) +#, no-wrap +msgid "IsNormal (M)" +msgstr "IsNormal (M)" + +#: C/genius.xml:6179(para) +msgid "" +"Is <varname>M</varname> a normal matrix. That is, does <userinput>M*M' == " +"M'*M</userinput>." +msgstr "" + +#: C/genius.xml:6181(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/NormalMatrix.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"NormalMatrix.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6190(term) +msgid "<anchor id=\"gel-function-IsPositiveDefinite\"/>IsPositiveDefinite" +msgstr "<anchor id=\"gel-function-IsPositiveDefinite\"/>IsPositiveDefinite" + +#: C/genius.xml:6192(synopsis) +#, no-wrap +msgid "IsPositiveDefinite (M)" +msgstr "IsPositiveDefinite (M)" + +#: C/genius.xml:6193(para) +msgid "" +"Is <varname>M</varname> a Hermitian positive definite matrix. That is if " +"<userinput>HermitianProduct(M*v,v)</userinput> is always strictly positive for " +"any vector <varname>v</varname>. <varname>M</varname> must be square and " +"Hermitian to be positive definite. The check that is performed is that every " +"principal submatrix has a non-negative determinant. (See <link linkend=\"gel-" +"function-HermitianProduct\">HermitianProduct</link>)" +msgstr "" + +#: C/genius.xml:6200(para) +msgid "" +"Note that some authors (for example Mathworld) do not require that <varname>M</" +"varname> be Hermitian, and then the condition is on the real part of the inner " +"product, but we do not take this view. If you wish to perform this check, just " +"check the Hermitian part of the matrix <varname>M</varname> as follows: " +"<userinput>IsPositiveDefinite(M+M')</userinput>." +msgstr "" + +#: C/genius.xml:6208(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/PositiveDefinite.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"PositiveDefiniteMatrix.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6217(term) +msgid "" +"<anchor id=\"gel-function-IsPositiveSemidefinite\"/>IsPositiveSemidefinite" +msgstr "" +"<anchor id=\"gel-function-IsPositiveSemidefinite\"/>IsPositiveSemidefinite" + +#: C/genius.xml:6219(synopsis) +#, no-wrap +msgid "IsPositiveSemidefinite (M)" +msgstr "IsPositiveSemidefinite (M)" + +#: C/genius.xml:6220(para) +msgid "" +"Is <varname>M</varname> a Hermitian positive semidefinite matrix. That is if " +"<userinput>HermitianProduct(M*v,v)</userinput> is always non-negative for any " +"vector <varname>v</varname>. <varname>M</varname> must be square and Hermitian " +"to be positive semidefinite. The check that is performed is that every " +"principal submatrix has a non-negative determinant. (See <link linkend=\"gel-" +"function-HermitianProduct\">HermitianProduct</link>)" +msgstr "" + +#: C/genius.xml:6227(para) +msgid "" +"Note that some authors do not require that <varname>M</varname> be Hermitian, " +"and then the condition is on the real part of the inner product, but we do not " +"take this view. If you wish to perform this check, just check the Hermitian " +"part of the matrix <varname>M</varname> as follows: " +"<userinput>IsPositiveSemidefinite(M+M')</userinput>." +msgstr "" + +#: C/genius.xml:6235(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/PositiveSemidefinite.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"PositiveSemidefiniteMatrix.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6244(term) +msgid "<anchor id=\"gel-function-IsSkewHermitian\"/>IsSkewHermitian" +msgstr "<anchor id=\"gel-function-IsSkewHermitian\"/>IsSkewHermitian" + +#: C/genius.xml:6246(synopsis) +#, no-wrap +msgid "IsSkewHermitian (M)" +msgstr "IsSkewHermitian (M)" + +#: C/genius.xml:6247(para) +msgid "" +"Is a matrix skew-Hermitian. That is, is the conjugate transpose equal to " +"negative of the matrix." +msgstr "" + +#: C/genius.xml:6248(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/SkewHermitianMatrix.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6256(term) +msgid "<anchor id=\"gel-function-IsUnitary\"/>IsUnitary" +msgstr "<anchor id=\"gel-function-IsUnitary\"/>IsUnitary" + +#: C/genius.xml:6258(synopsis) +#, no-wrap +msgid "IsUnitary (M)" +msgstr "IsUnitary (M)" + +#: C/genius.xml:6259(para) +msgid "" +"Is a matrix unitary? That is, does <userinput>M'*M</userinput> and " +"<userinput>M*M'</userinput> equal the identity." +msgstr "" + +#: C/genius.xml:6262(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/UnitaryTransformation.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"UnitaryMatrix.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6271(term) +msgid "<anchor id=\"gel-function-JordanBlock\"/>JordanBlock" +msgstr "<anchor id=\"gel-function-JordanBlock\"/>JordanBlock" + +#: C/genius.xml:6273(synopsis) +#, no-wrap +msgid "JordanBlock (n,lambda)" +msgstr "JordanBlock (n,lambda)" + +#: C/genius.xml:6274(para) +msgid "Aliases: <function>J</function>" +msgstr "Alias: <function>J</function>" + +#: C/genius.xml:6275(para) +msgid "" +"Get the Jordan block corresponding to the eigenvalue <varname>lambda</varname> " +"with multiplicity <varname>n</varname>." +msgstr "" + +#: C/genius.xml:6278(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/JordanCanonicalFormTheorem." +"html\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"JordanBlock.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6287(term) +msgid "<anchor id=\"gel-function-Kernel\"/>Kernel" +msgstr "<anchor id=\"gel-function-Kernel\"/>Kernel" + +#: C/genius.xml:6289(synopsis) +#, no-wrap +msgid "Kernel (T)" +msgstr "Kernel (T)" + +#: C/genius.xml:6290(para) +msgid "Get the kernel (nullspace) of a linear transform." +msgstr "" + +#: C/genius.xml:6291(para) +msgid "(See <link linkend=\"gel-function-NullSpace\">NullSpace</link>)" +msgstr "" + +#: C/genius.xml:6298(term) +msgid "<anchor id=\"gel-function-KroneckerProduct\"/>KroneckerProduct" +msgstr "<anchor id=\"gel-function-KroneckerProduct\"/>KroneckerProduct" + +#: C/genius.xml:6300(synopsis) +#, no-wrap +msgid "KroneckerProduct (M, N)" +msgstr "KroneckerProduct (M, N)" + +#: C/genius.xml:6301(para) +msgid "Aliases: <function>TensorProduct</function>" +msgstr "Alias: <function>TensorProduct</function>" + +#: C/genius.xml:6302(para) +msgid "" +"Compute the Kronecker product (tensor product in standard basis) of two " +"matrices." +msgstr "" + +#: C/genius.xml:6306(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Kronecker_product\">Wikipedia</" +"ulink>, <ulink url=\"http://planetmath.org/encyclopedia/KroneckerProduct.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"KroneckerProduct.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6318(term) +msgid "<anchor id=\"gel-function-LUDecomposition\"/>LUDecomposition" +msgstr "<anchor id=\"gel-function-LUDecomposition\"/>LUDecomposition" + +#: C/genius.xml:6320(synopsis) +#, no-wrap +msgid "LUDecomposition (A, L, U)" +msgstr "LUDecomposition (A, L, U)" + +#: C/genius.xml:6321(para) +msgid "" +"Get the LU decomposition of <varname>A</varname>, that is find a lower " +"triangular matrix and upper triangular matrix whose product is <varname>A</" +"varname> Store the result in the <varname>L</varname> and <varname>U</" +"varname>, which should be references. It returns <constant>true</constant> if " +"successful. For example suppose that A is a square matrix, then after running: " +"<screen><prompt>genius></prompt> <userinput>LUDecomposition(A,&L,&" +"U)</userinput>\n" +"</screen> You will have the lower matrix stored in a variable called " +"<varname>L</varname> and the upper matrix in a variable called <varname>U</" +"varname>." +msgstr "" + +#: C/genius.xml:6335(para) +msgid "" +"This is the LU decomposition of a matrix aka Crout and/or Cholesky reduction. " +"(ISBN 0-201-11577-8 pp.99-103) The upper triangular matrix features a diagonal " +"of values 1 (one). This is not Doolittle's Method, which features the 1's " +"diagonal on the lower matrix." +msgstr "" + +#: C/genius.xml:6343(para) +msgid "" +"Not all matrices have LU decompositions, for example <userinput>[0,1;1,0]</" +"userinput> does not and this function returns <constant>false</constant> in " +"this case and sets <varname>L</varname> and <varname>U</varname> to " +"<constant>null</constant>." +msgstr "" + +#: C/genius.xml:6349(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/LU_decomposition\">Wikipedia</" +"ulink>, <ulink url=\"http://planetmath.org/encyclopedia/LUDecomposition.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"LUDecomposition.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6359(term) +msgid "<anchor id=\"gel-function-Minor\"/>Minor" +msgstr "<anchor id=\"gel-function-Minor\"/>Minor" + +#: C/genius.xml:6361(synopsis) +#, no-wrap +msgid "Minor (M,i,j)" +msgstr "Minor (M,i,j)" + +#: C/genius.xml:6362(para) +msgid "Get the <varname>i</varname>-<varname>j</varname> minor of a matrix." +msgstr "" + +#: C/genius.xml:6363(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Minor.html\">Planetmath</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:6371(term) +msgid "<anchor id=\"gel-function-NonPivotColumns\"/>NonPivotColumns" +msgstr "<anchor id=\"gel-function-NonPivotColumns\"/>NonPivotColumns" + +#: C/genius.xml:6373(synopsis) +#, no-wrap +msgid "NonPivotColumns (M)" +msgstr "NonPivotColumns (M)" + +#: C/genius.xml:6374(para) +msgid "Return the columns that are not the pivot columns of a matrix." +msgstr "" + +#: C/genius.xml:6379(term) +msgid "<anchor id=\"gel-function-Norm\"/>Norm" +msgstr "<anchor id=\"gel-function-Norm\"/>Norm" + +#: C/genius.xml:6381(synopsis) +#, no-wrap +msgid "Norm (v,p...)" +msgstr "Norm (v,p...)" + +#: C/genius.xml:6382(para) +msgid "Aliases: <function>norm</function>" +msgstr "Alias: <function>norm</function>" + +#: C/genius.xml:6383(para) +msgid "Get the p Norm (or 2 Norm if no p is supplied) of a vector." +msgstr "" + +#: C/genius.xml:6388(term) +msgid "<anchor id=\"gel-function-NullSpace\"/>NullSpace" +msgstr "<anchor id=\"gel-function-NullSpace\"/>NullSpace" + +#: C/genius.xml:6390(synopsis) +#, no-wrap +msgid "NullSpace (T)" +msgstr "NullSpace (T)" + +#: C/genius.xml:6391(para) +msgid "" +"Get the nullspace of a matrix. That is the kernel of the linear mapping that " +"the matrix represents. This is returned as a matrix whose column space is the " +"nullspace of <varname>T</varname>." +msgstr "" + +#: C/genius.xml:6395(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Nullspace.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6403(term) +msgid "<anchor id=\"gel-function-Nullity\"/>Nullity" +msgstr "<anchor id=\"gel-function-Nullity\"/>Nullity" + +#: C/genius.xml:6405(synopsis) +#, no-wrap +msgid "Nullity (M)" +msgstr "Nullity (M)" + +#: C/genius.xml:6406(para) +msgid "Aliases: <function>nullity</function>" +msgstr "Alias: <function>nullity</function>" + +#: C/genius.xml:6407(para) +msgid "" +"Get the nullity of a matrix. That is, return the dimension of the nullspace; " +"the dimension of the kernel of <varname>M</varname>." +msgstr "" + +#: C/genius.xml:6409(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Nullity.html\">Planetmath</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:6417(term) +msgid "<anchor id=\"gel-function-OrthogonalComplement\"/>OrthogonalComplement" +msgstr "<anchor id=\"gel-function-OrthogonalComplement\"/>OrthogonalComplement" + +#: C/genius.xml:6419(synopsis) +#, no-wrap +msgid "OrthogonalComplement (M)" +msgstr "OrthogonalComplement (M)" + +#: C/genius.xml:6420(para) +msgid "Get the orthogonal complement of the columnspace." +msgstr "" + +#: C/genius.xml:6425(term) +msgid "<anchor id=\"gel-function-PivotColumns\"/>PivotColumns" +msgstr "<anchor id=\"gel-function-PivotColumns\"/>PivotColumns" + +#: C/genius.xml:6427(synopsis) +#, no-wrap +msgid "PivotColumns (M)" +msgstr "PivotColumns (M)" + +#: C/genius.xml:6428(para) +msgid "" +"Return pivot columns of a matrix, that is columns that have a leading 1 in row " +"reduced form. Also returns the row where they occur." +msgstr "" + +#: C/genius.xml:6433(term) +msgid "<anchor id=\"gel-function-Projection\"/>Projection" +msgstr "<anchor id=\"gel-function-Projection\"/>Projection" + +#: C/genius.xml:6435(synopsis) +#, no-wrap +msgid "Projection (v,W,B...)" +msgstr "Projection (v,W,B...)" + +#: C/genius.xml:6436(para) +msgid "" +"Projection of vector <varname>v</varname> onto subspace <varname>W</varname> " +"with respect to inner product given by <varname>B</varname>. If <varname>B</" +"varname> is not given then the standard Hermitian product is used. <varname>B</" +"varname> can either be a sesquilinear function of two arguments or it can be a " +"matrix giving a sesquilinear form." +msgstr "" + +#: C/genius.xml:6446(term) +msgid "<anchor id=\"gel-function-QRDecomposition\"/>QRDecomposition" +msgstr "<anchor id=\"gel-function-QRDecomposition\"/>QRDecomposition" + +#: C/genius.xml:6448(synopsis) +#, no-wrap +msgid "QRDecomposition (A, Q)" +msgstr "QRDecomposition (A, Q)" + +#: C/genius.xml:6449(para) +msgid "" +"Get the QR decomposition of a square matrix <varname>A</varname>, returns the " +"upper triangular matrix <varname>R</varname> and sets <varname>Q</varname> to " +"the orthogonal (unitary) matrix. <varname>Q</varname> should be a reference or " +"<constant>null</constant> if you don't want any return. For example: " +"<screen><prompt>genius></prompt> <userinput>R = QRDecomposition(A,&Q)</" +"userinput>\n" +"</screen> You will have the upper triangular matrix stored in a variable " +"called <varname>R</varname> and the orthogonal (unitary) matrix stored in " +"<varname>Q</varname>." +msgstr "" + +#: C/genius.xml:6463(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/QR_decomposition\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/QRDecomposition.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"QRDecomposition.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6473(term) +msgid "<anchor id=\"gel-function-RayleighQuotient\"/>RayleighQuotient" +msgstr "<anchor id=\"gel-function-RayleighQuotient\"/>RayleighQuotient" + +#: C/genius.xml:6475(synopsis) +#, no-wrap +msgid "RayleighQuotient (A,x)" +msgstr "RayleighQuotient (A,x)" + +#: C/genius.xml:6476(para) +msgid "" +"Return the Rayleigh quotient (also called the Rayleigh-Ritz quotient or ratio) " +"of a matrix and a vector." +msgstr "" + +#: C/genius.xml:6477(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/RayleighQuotient.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6485(term) +msgid "" +"<anchor id=\"gel-function-RayleighQuotientIteration\"/" +">RayleighQuotientIteration" +msgstr "" +"<anchor id=\"gel-function-RayleighQuotientIteration\"/" +">RayleighQuotientIteration" + +#: C/genius.xml:6487(synopsis) +#, no-wrap +msgid "RayleighQuotientIteration (A,x,epsilon,maxiter,vecref)" +msgstr "" + +#: C/genius.xml:6488(para) +msgid "" +"Find eigenvalues of <varname>A</varname> using the Rayleigh quotient iteration " +"method. <varname>x</varname> is a guess at a eigenvector and could be random. " +"It should have nonzero imaginary part if it will have any chance at finding " +"complex eigenvalues. The code will run at most <varname>maxiter</varname> " +"iterations and return <constant>null</constant> if we cannot get within an " +"error of <varname>epsilon</varname>. <varname>vecref</varname> should either " +"be <constant>null</constant> or a reference to a variable where the " +"eigenvector should be stored." +msgstr "" + +#: C/genius.xml:6498(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/RayleighQuotient.html" +"\">Planetmath</ulink> for more information on Rayleigh quotient." +msgstr "" + +#: C/genius.xml:6506(term) +msgid "<anchor id=\"gel-function-Rank\"/>Rank" +msgstr "<anchor id=\"gel-function-Rank\"/>Rank" + +#: C/genius.xml:6508(synopsis) +#, no-wrap +msgid "Rank (M)" +msgstr "Rank (M)" + +#: C/genius.xml:6509(para) +msgid "Aliases: <function>rank</function>" +msgstr "Alias: <function>rank</function>" + +#: C/genius.xml:6510(para) +msgid "Get the rank of a matrix." +msgstr "" + +#: C/genius.xml:6511(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/SylvestersLaw.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6519(term) +msgid "<anchor id=\"gel-function-RosserMatrix\"/>RosserMatrix" +msgstr "<anchor id=\"gel-function-RosserMatrix\"/>RosserMatrix" + +#: C/genius.xml:6521(synopsis) +#, no-wrap +msgid "RosserMatrix ()" +msgstr "RosserMatrix ()" + +#: C/genius.xml:6522(para) +msgid "" +"Returns the Rosser matrix, which is a classic symmetric eigenvalue test " +"problem." +msgstr "" + +#: C/genius.xml:6527(term) +msgid "<anchor id=\"gel-function-Rotation2D\"/>Rotation2D" +msgstr "<anchor id=\"gel-function-Rotation2D\"/>Rotation2D" + +#: C/genius.xml:6529(synopsis) +#, no-wrap +msgid "Rotation2D (angle)" +msgstr "Rotation2D (vinkel)" + +#: C/genius.xml:6530(para) +msgid "Aliases: <function>RotationMatrix</function>" +msgstr "Alias: <function>RotationMatrix</function>" + +#: C/genius.xml:6531(para) +msgid "" +"Return the matrix corresponding to rotation around origin in R<superscript>2</" +"superscript>." +msgstr "" + +#: C/genius.xml:6536(term) +msgid "<anchor id=\"gel-function-Rotation3DX\"/>Rotation3DX" +msgstr "<anchor id=\"gel-function-Rotation3DX\"/>Rotation3DX" + +#: C/genius.xml:6538(synopsis) +#, no-wrap +msgid "Rotation3DX (angle)" +msgstr "Rotation3DX (vinkel)" + +#: C/genius.xml:6539(para) +msgid "" +"Return the matrix corresponding to rotation around origin in R<superscript>3</" +"superscript> about the x-axis." +msgstr "" + +#: C/genius.xml:6544(term) +msgid "<anchor id=\"gel-function-Rotation3DY\"/>Rotation3DY" +msgstr "<anchor id=\"gel-function-Rotation3DY\"/>Rotation3DY" + +#: C/genius.xml:6546(synopsis) +#, no-wrap +msgid "Rotation3DY (angle)" +msgstr "Rotation3DY (vinkel)" + +#: C/genius.xml:6547(para) +msgid "" +"Return the matrix corresponding to rotation around origin in R<superscript>3</" +"superscript> about the y-axis." +msgstr "" + +#: C/genius.xml:6552(term) +msgid "<anchor id=\"gel-function-Rotation3DZ\"/>Rotation3DZ" +msgstr "<anchor id=\"gel-function-Rotation3DZ\"/>Rotation3DZ" + +#: C/genius.xml:6554(synopsis) +#, no-wrap +msgid "Rotation3DZ (angle)" +msgstr "Rotation3DZ (vinkel)" + +#: C/genius.xml:6555(para) +msgid "" +"Return the matrix corresponding to rotation around origin in R<superscript>3</" +"superscript> about the z-axis." +msgstr "" + +#: C/genius.xml:6560(term) +msgid "<anchor id=\"gel-function-RowSpace\"/>RowSpace" +msgstr "<anchor id=\"gel-function-RowSpace\"/>RowSpace" + +#: C/genius.xml:6562(synopsis) +#, no-wrap +msgid "RowSpace (M)" +msgstr "RowSpace (M)" + +#: C/genius.xml:6563(para) +msgid "Get a basis matrix for the rowspace of a matrix." +msgstr "" + +#: C/genius.xml:6568(term) +msgid "<anchor id=\"gel-function-SesquilinearForm\"/>SesquilinearForm" +msgstr "<anchor id=\"gel-function-SesquilinearForm\"/>SesquilinearForm" + +#: C/genius.xml:6570(synopsis) +#, no-wrap +msgid "SesquilinearForm (v,A,w)" +msgstr "SesquilinearForm (v,A,w)" + +#: C/genius.xml:6571(para) +msgid "" +"Evaluate (v,w) with respect to the sesquilinear form given by the matrix A." +msgstr "" + +#: C/genius.xml:6576(term) +msgid "" +"<anchor id=\"gel-function-SesquilinearFormFunction\"/>SesquilinearFormFunction" +msgstr "" +"<anchor id=\"gel-function-SesquilinearFormFunction\"/>SesquilinearFormFunction" + +#: C/genius.xml:6578(synopsis) +#, no-wrap +msgid "SesquilinearFormFunction (A)" +msgstr "SesquilinearFormFunction (A)" + +#: C/genius.xml:6579(para) +msgid "" +"Return a function that evaluates two vectors with respect to the sesquilinear " +"form given by A." +msgstr "" + +#: C/genius.xml:6584(term) +msgid "<anchor id=\"gel-function-SmithNormalFormField\"/>SmithNormalFormField" +msgstr "<anchor id=\"gel-function-SmithNormalFormField\"/>SmithNormalFormField" + +#: C/genius.xml:6586(synopsis) +#, no-wrap +msgid "SmithNormalFormField (A)" +msgstr "SmithNormalFormField (A)" + +#: C/genius.xml:6587(para) +msgid "" +"Returns the Smith normal form of a matrix over fields (will end up with 1's on " +"the diagonal)." +msgstr "" + +#: C/genius.xml:6588(para) C/genius.xml:6600(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Smith_normal_form\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:6596(term) +msgid "" +"<anchor id=\"gel-function-SmithNormalFormInteger\"/>SmithNormalFormInteger" +msgstr "" +"<anchor id=\"gel-function-SmithNormalFormInteger\"/>SmithNormalFormInteger" + +#: C/genius.xml:6598(synopsis) +#, no-wrap +msgid "SmithNormalFormInteger (M)" +msgstr "SmithNormalFormInteger (M)" + +#: C/genius.xml:6599(para) +msgid "" +"Return the Smith normal form for square integer matrices over integers (not " +"its characteristic)." +msgstr "" + +#: C/genius.xml:6608(term) +msgid "<anchor id=\"gel-function-SolveLinearSystem\"/>SolveLinearSystem" +msgstr "<anchor id=\"gel-function-SolveLinearSystem\"/>SolveLinearSystem" + +#: C/genius.xml:6610(synopsis) +#, no-wrap +msgid "SolveLinearSystem (M,V,args...)" +msgstr "" + +#: C/genius.xml:6611(para) +msgid "" +"Solve linear system Mx=V, return solution V if there is a unique solution, " +"<constant>null</constant> otherwise. Extra two reference parameters can " +"optionally be used to get the reduced M and V." +msgstr "" + +#: C/genius.xml:6616(term) +msgid "<anchor id=\"gel-function-ToeplitzMatrix\"/>ToeplitzMatrix" +msgstr "<anchor id=\"gel-function-ToeplitzMatrix\"/>ToeplitzMatrix" + +#: C/genius.xml:6618(synopsis) +#, no-wrap +msgid "ToeplitzMatrix (c, r...)" +msgstr "" + +#: C/genius.xml:6619(para) +msgid "" +"Return the Toeplitz matrix constructed given the first column c and " +"(optionally) the first row r. If only the column c is given then it is " +"conjugated and the nonconjugated version is used for the first row to give a " +"Hermitian matrix (if the first element is real of course)." +msgstr "" + +#: C/genius.xml:6623(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Toeplitz_matrix\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/ToeplitzMatrix.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6632(term) +msgid "<anchor id=\"gel-function-Trace\"/>Trace" +msgstr "<anchor id=\"gel-function-Trace\"/>Trace" + +#: C/genius.xml:6634(synopsis) +#, no-wrap +msgid "Trace (M)" +msgstr "Trace (M)" + +#: C/genius.xml:6635(para) +msgid "Aliases: <function>trace</function>" +msgstr "Alias: <function>trace</function>" + +#: C/genius.xml:6636(para) +msgid "" +"Calculate the trace of a matrix. That is the sum of the diagonal elements." +msgstr "" + +#: C/genius.xml:6637(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/" +"Trace_(linear_algebra)\">Wikipedia</ulink> or <ulink url=\"http://planetmath." +"org/encyclopedia/Trace.html\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6646(term) +msgid "<anchor id=\"gel-function-Transpose\"/>Transpose" +msgstr "<anchor id=\"gel-function-Transpose\"/>Transpose" + +#: C/genius.xml:6648(synopsis) +#, no-wrap +msgid "Transpose (M)" +msgstr "Transpose (M)" + +#: C/genius.xml:6649(para) +msgid "" +"Transpose of a matrix. This is the same as the <userinput>.'</userinput> " +"operator." +msgstr "" + +#: C/genius.xml:6651(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Transpose\">Wikipedia</ulink> or " +"<ulink url=\"http://planetmath.org/encyclopedia/Transpose.html\">Planetmath</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:6660(term) +msgid "<anchor id=\"gel-function-VandermondeMatrix\"/>VandermondeMatrix" +msgstr "<anchor id=\"gel-function-VandermondeMatrix\"/>VandermondeMatrix" + +#: C/genius.xml:6662(synopsis) +#, no-wrap +msgid "VandermondeMatrix (v)" +msgstr "VandermondeMatrix (v)" + +#: C/genius.xml:6663(para) +msgid "Aliases: <function>vander</function>" +msgstr "Alias: <function>vander</function>" + +#: C/genius.xml:6664(para) +msgid "Return the Vandermonde matrix." +msgstr "" + +#: C/genius.xml:6665(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Vandermonde_matrix\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:6673(term) +msgid "<anchor id=\"gel-function-VectorAngle\"/>VectorAngle" +msgstr "<anchor id=\"gel-function-VectorAngle\"/>VectorAngle" + +#: C/genius.xml:6675(synopsis) +#, no-wrap +msgid "VectorAngle (v,w,B...)" +msgstr "VectorAngle (v,w,B...)" + +#: C/genius.xml:6676(para) +msgid "" +"The angle of two vectors with respect to inner product given by <varname>B</" +"varname>. If <varname>B</varname> is not given then the standard Hermitian " +"product is used. <varname>B</varname> can either be a sesquilinear function of " +"two arguments or it can be a matrix giving a sesquilinear form." +msgstr "" + +#: C/genius.xml:6685(term) +msgid "<anchor id=\"gel-function-VectorSpaceDirectSum\"/>VectorSpaceDirectSum" +msgstr "<anchor id=\"gel-function-VectorSpaceDirectSum\"/>VectorSpaceDirectSum" + +#: C/genius.xml:6687(synopsis) +#, no-wrap +msgid "VectorSpaceDirectSum (M,N)" +msgstr "VectorSpaceDirectSum (M,N)" + +#: C/genius.xml:6688(para) +msgid "The direct sum of the vector spaces M and N." +msgstr "" + +#: C/genius.xml:6693(term) +msgid "" +"<anchor id=\"gel-function-VectorSubspaceIntersection\"/" +">VectorSubspaceIntersection" +msgstr "" +"<anchor id=\"gel-function-VectorSubspaceIntersection\"/" +">VectorSubspaceIntersection" + +#: C/genius.xml:6695(synopsis) +#, no-wrap +msgid "VectorSubspaceIntersection (M,N)" +msgstr "VectorSubspaceIntersection (M,N)" + +#: C/genius.xml:6696(para) +msgid "Intersection of the subspaces given by M and N." +msgstr "" + +#: C/genius.xml:6701(term) +msgid "<anchor id=\"gel-function-VectorSubspaceSum\"/>VectorSubspaceSum" +msgstr "<anchor id=\"gel-function-VectorSubspaceSum\"/>VectorSubspaceSum" + +#: C/genius.xml:6703(synopsis) +#, no-wrap +msgid "VectorSubspaceSum (M,N)" +msgstr "VectorSubspaceSum (M,N)" + +#: C/genius.xml:6704(para) +msgid "" +"The sum of the vector spaces M and N, that is {w | w=m+n, m in M, n in N}." +msgstr "" + +#: C/genius.xml:6709(term) +msgid "<anchor id=\"gel-function-adj\"/>adj" +msgstr "<anchor id=\"gel-function-adj\"/>adj" + +#: C/genius.xml:6711(synopsis) +#, no-wrap +msgid "adj (m)" +msgstr "adj (m)" + +#: C/genius.xml:6712(para) +msgid "Aliases: <function>Adjugate</function>" +msgstr "Alias: <function>Adjugate</function>" + +#: C/genius.xml:6713(para) +msgid "Get the classical adjoint (adjugate) of a matrix." +msgstr "" + +#: C/genius.xml:6718(term) +msgid "<anchor id=\"gel-function-cref\"/>cref" +msgstr "<anchor id=\"gel-function-cref\"/>cref" + +#: C/genius.xml:6720(synopsis) +#, no-wrap +msgid "cref (M)" +msgstr "cref (M)" + +#: C/genius.xml:6721(para) +msgid "" +"Aliases: <function>CREF</function><function>ColumnReducedEchelonForm</function>" +msgstr "" +"Alias: <function>CREF</function><function>ColumnReducedEchelonForm</function>" + +#: C/genius.xml:6722(para) +msgid "Compute the Column Reduced Echelon Form." +msgstr "" + +#: C/genius.xml:6727(term) +msgid "<anchor id=\"gel-function-det\"/>det" +msgstr "<anchor id=\"gel-function-det\"/>det" + +#: C/genius.xml:6729(synopsis) +#, no-wrap +msgid "det (M)" +msgstr "det (M)" + +#: C/genius.xml:6730(para) +msgid "Aliases: <function>Determinant</function>" +msgstr "Alias: <function>Determinant</function>" + +#: C/genius.xml:6731(para) +msgid "Get the determinant of a matrix." +msgstr "" + +#: C/genius.xml:6732(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Determinant\">Wikipedia</ulink> " +"or <ulink url=\"http://planetmath.org/encyclopedia/Determinant2.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6741(term) +msgid "<anchor id=\"gel-function-ref\"/>ref" +msgstr "<anchor id=\"gel-function-ref\"/>ref" + +#: C/genius.xml:6743(synopsis) +#, no-wrap +msgid "ref (M)" +msgstr "ref (M)" + +#: C/genius.xml:6744(para) +msgid "Aliases: <function>REF</function><function>RowEchelonForm</function>" +msgstr "Alias: <function>REF</function><function>RowEchelonForm</function>" + +#: C/genius.xml:6745(para) +msgid "" +"Get the row echelon form of a matrix. That is, apply gaussian elimination but " +"not backaddition to <varname>M</varname>. The pivot rows are divided to make " +"all pivots 1." +msgstr "" + +#: C/genius.xml:6748(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Row_echelon_form\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/RowEchelonForm.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6757(term) +msgid "<anchor id=\"gel-function-rref\"/>rref" +msgstr "<anchor id=\"gel-function-rref\"/>rref" + +#: C/genius.xml:6759(synopsis) +#, no-wrap +msgid "rref (M)" +msgstr "rref (M)" + +#: C/genius.xml:6760(para) +msgid "" +"Aliases: <function>RREF</function><function>ReducedRowEchelonForm</function>" +msgstr "" +"Alias: <function>RREF</function><function>ReducedRowEchelonForm</function>" + +#: C/genius.xml:6761(para) +msgid "" +"Get the reduced row echelon form of a matrix. That is, apply gaussian " +"elimination together with backaddition to <varname>M</varname>." +msgstr "" + +#: C/genius.xml:6762(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Reduced_row_echelon_form" +"\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/encyclopedia/" +"ReducedRowEchelonForm.html\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6774(title) +msgid "Combinatorics" +msgstr "" + +#: C/genius.xml:6777(term) +msgid "<anchor id=\"gel-function-Catalan\"/>Catalan" +msgstr "<anchor id=\"gel-function-Catalan\"/>Catalan" + +#: C/genius.xml:6779(synopsis) +#, no-wrap +msgid "Catalan (n)" +msgstr "Catalan (n)" + +#: C/genius.xml:6780(para) +msgid "Get <varname>n</varname>th Catalan number." +msgstr "" + +#: C/genius.xml:6781(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/CatalanNumbers.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6789(term) +msgid "<anchor id=\"gel-function-Combinations\"/>Combinations" +msgstr "<anchor id=\"gel-function-Combinations\"/>Combinations" + +#: C/genius.xml:6791(synopsis) +#, no-wrap +msgid "Combinations (k,n)" +msgstr "Combinations (k,n)" + +#: C/genius.xml:6792(para) +msgid "" +"Get all combinations of k numbers from 1 to n as a vector of vectors. (See " +"also <link linkend=\"gel-function-NextCombination\">NextCombination</link>)" +msgstr "" + +#: C/genius.xml:6799(term) +msgid "<anchor id=\"gel-function-DoubleFactorial\"/>DoubleFactorial" +msgstr "<anchor id=\"gel-function-DoubleFactorial\"/>DoubleFactorial" + +#: C/genius.xml:6801(synopsis) +#, no-wrap +msgid "DoubleFactorial (n)" +msgstr "DoubleFactorial (n)" + +#: C/genius.xml:6802(para) +msgid "Double factorial: <userinput>n(n-2)(n-4)...</userinput>" +msgstr "" + +#: C/genius.xml:6803(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/DoubleFactorial.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6811(term) +msgid "<anchor id=\"gel-function-Factorial\"/>Factorial" +msgstr "<anchor id=\"gel-function-Factorial\"/>Factorial" + +#: C/genius.xml:6813(synopsis) +#, no-wrap +msgid "Factorial (n)" +msgstr "Factorial (n)" + +#: C/genius.xml:6814(para) +msgid "Factorial: <userinput>n(n-1)(n-2)...</userinput>" +msgstr "" + +#: C/genius.xml:6815(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Factorial.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6823(term) +msgid "<anchor id=\"gel-function-FallingFactorial\"/>FallingFactorial" +msgstr "<anchor id=\"gel-function-FallingFactorial\"/>FallingFactorial" + +#: C/genius.xml:6825(synopsis) +#, no-wrap +msgid "FallingFactorial (n,k)" +msgstr "FallingFactorial (n,k)" + +#: C/genius.xml:6826(para) +msgid "Falling factorial: <userinput>(n)_k = n(n-1)...(n-(k-1))</userinput>" +msgstr "" + +#: C/genius.xml:6827(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/FallingFactorial.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6835(term) +msgid "<anchor id=\"gel-function-Fibonacci\"/>Fibonacci" +msgstr "<anchor id=\"gel-function-Fibonacci\"/>Fibonacci" + +#: C/genius.xml:6837(synopsis) +#, no-wrap +msgid "Fibonacci (x)" +msgstr "Fibonacci (x)" + +#: C/genius.xml:6838(para) +msgid "Aliases: <function>fib</function>" +msgstr "Alias: <function>fib</function>" + +#: C/genius.xml:6839(para) +msgid "" +"Calculate <varname>n</varname>th Fibonacci number. That is the number defined " +"recursively by <userinput>Fibonacci(n) = Fibonacci(n-1) + Fibonacci(n-2)</" +"userinput> and <userinput>Fibonacci(1) = Fibonacci(2) = 1</userinput>." +msgstr "" + +#: C/genius.xml:6846(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Fibonacci_number\">Wikipedia</" +"ulink> or <ulink url=\"http://planetmath.org/encyclopedia/FibonacciSequence." +"html\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"FibonacciNumber.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6856(term) +msgid "<anchor id=\"gel-function-FrobeniusNumber\"/>FrobeniusNumber" +msgstr "<anchor id=\"gel-function-FrobeniusNumber\"/>FrobeniusNumber" + +#: C/genius.xml:6858(synopsis) +#, no-wrap +msgid "FrobeniusNumber (v,arg...)" +msgstr "FrobeniusNumber (v,arg...)" + +#: C/genius.xml:6859(para) +msgid "" +"Calculate the Frobenius number. That is calculate smallest number that cannot " +"be given as a non-negative integer linear combination of a given vector of non-" +"negative integers. The vector can be given as separate numbers or a single " +"vector. All the numbers given should have GCD of 1." +msgstr "" + +#: C/genius.xml:6866(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/FrobeniusNumber.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6874(term) +msgid "<anchor id=\"gel-function-GaloisMatrix\"/>GaloisMatrix" +msgstr "<anchor id=\"gel-function-GaloisMatrix\"/>GaloisMatrix" + +#: C/genius.xml:6876(synopsis) +#, no-wrap +msgid "GaloisMatrix (combining_rule)" +msgstr "" + +#: C/genius.xml:6877(para) +msgid "" +"Galois matrix given a linear combining rule (a_1*x_1+...+a_n*x_n=x_(n+1))." +msgstr "" + +#: C/genius.xml:6882(term) +msgid "<anchor id=\"gel-function-GreedyAlgorithm\"/>GreedyAlgorithm" +msgstr "<anchor id=\"gel-function-GreedyAlgorithm\"/>GreedyAlgorithm" + +# TODO: error?? Should be GreedyAlgorithm? +#: C/genius.xml:6884(synopsis) +#, no-wrap +msgid "FrobeniusNumber (n,v)" +msgstr "" + +#: C/genius.xml:6885(para) +msgid "" +"Find the vector <varname>c</varname> of non-negative integers such that taking " +"the dot product with <varname>v</varname> is equal to n. If not possible " +"returns <constant>null</constant>. <varname>v</varname> should be given sorted " +"in increasing order and should consist of non-negative integers." +msgstr "" + +#: C/genius.xml:6892(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/GreedyAlgorithm.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:6900(term) +msgid "<anchor id=\"gel-function-HarmonicNumber\"/>HarmonicNumber" +msgstr "<anchor id=\"gel-function-HarmonicNumber\"/>HarmonicNumber" + +#: C/genius.xml:6902(synopsis) +#, no-wrap +msgid "HarmonicNumber (n,r)" +msgstr "HarmonicNumber (n,r)" + +#: C/genius.xml:6903(para) +msgid "Aliases: <function>HarmonicH</function>" +msgstr "Alias: <function>HarmonicH</function>" + +#: C/genius.xml:6904(para) +msgid "" +"Harmonic Number, the <varname>n</varname>th harmonic number of order " +"<varname>r</varname>." +msgstr "" + +#: C/genius.xml:6909(term) +msgid "<anchor id=\"gel-function-Hofstadter\"/>Hofstadter" +msgstr "<anchor id=\"gel-function-Hofstadter\"/>Hofstadter" + +#: C/genius.xml:6911(synopsis) +#, no-wrap +msgid "Hofstadter (n)" +msgstr "Hofstadter (n)" + +#: C/genius.xml:6912(para) +msgid "" +"Hofstadter's function q(n) defined by q(1)=1, q(2)=1, q(n)=q(n-q(n-1))+q(n-" +"q(n-2))." +msgstr "" + +#: C/genius.xml:6917(term) +msgid "" +"<anchor id=\"gel-function-LinearRecursiveSequence\"/>LinearRecursiveSequence" +msgstr "" +"<anchor id=\"gel-function-LinearRecursiveSequence\"/>LinearRecursiveSequence" + +#: C/genius.xml:6919(synopsis) +#, no-wrap +msgid "LinearRecursiveSequence (seed_values,combining_rule,n)" +msgstr "" + +#: C/genius.xml:6920(para) +msgid "Compute linear recursive sequence using Galois stepping." +msgstr "" + +#: C/genius.xml:6925(term) +msgid "<anchor id=\"gel-function-Multinomial\"/>Multinomial" +msgstr "<anchor id=\"gel-function-Multinomial\"/>Multinomial" + +#: C/genius.xml:6927(synopsis) +#, no-wrap +msgid "Multinomial (v,arg...)" +msgstr "Multinomial (v,arg...)" + +#: C/genius.xml:6928(para) +msgid "" +"Calculate multinomial coefficients. Takes a vector of <varname>k</varname> non-" +"negative integers and computes the multinomial coefficient. This corresponds " +"to the coefficient in the homogeneous polynomial in <varname>k</varname> " +"variables with the corresponding powers." +msgstr "" + +#: C/genius.xml:6937(programlisting) +#, no-wrap +msgid "(a+b+c)! / (a!b!c!)\n" +msgstr "(a+b+c)! / (a!b!c!)\n" + +#: C/genius.xml:6934(para) +msgid "" +"The formula for <userinput>Multinomial(a,b,c)</userinput> can be written as: " +"<placeholder-1/> In other words, if we would have only two elements, then " +"<userinput>Multinomial(a,b)</userinput> is the same thing as " +"<userinput>Binomial(a+b,a)</userinput> or <userinput>Binomial(a+b,b)</" +"userinput>." +msgstr "" + +#: C/genius.xml:6944(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/MultinomialTheorem.html" +"\">Planetmath</ulink>, <ulink url=\"http://mathworld.wolfram.com/" +"MultinomialCoefficient.html\">Mathworld</ulink>, or <ulink url=\"http://en." +"wikipedia.org/wiki/Multinomial_theorem\">Wikipedia</ulink> for more " +"information." +msgstr "" + +#: C/genius.xml:6954(term) +msgid "<anchor id=\"gel-function-NextCombination\"/>NextCombination" +msgstr "<anchor id=\"gel-function-NextCombination\"/>NextCombination" + +#: C/genius.xml:6956(synopsis) +#, no-wrap +msgid "NextCombination (v,n)" +msgstr "NextCombination (v,n)" + +#: C/genius.xml:6957(para) +msgid "" +"Get combination that would come after v in call to combinations, first " +"combination should be <userinput>[1:k]</userinput>. This function is useful if " +"you have many combinations to go through and you don't want to waste memory to " +"store them all." +msgstr "" + +#: C/genius.xml:6962(para) +msgid "" +"For example with Combination you would normally write a loop like: " +"<screen><userinput>for n in Combinations (4,6) do (\n" +" SomeFunction (n)\n" +");</userinput>\n" +"</screen> But with NextCombination you would write something like: " +"<screen><userinput>n:=[1:4];\n" +"do (\n" +" SomeFunction (n)\n" +") while not IsNull(n:=NextCombination(n,6));</userinput>\n" +"</screen> See also <link linkend=\"gel-function-Combinations\">Combinations</" +"link>." +msgstr "" + +#: C/genius.xml:6980(term) +msgid "<anchor id=\"gel-function-Pascal\"/>Pascal" +msgstr "<anchor id=\"gel-function-Pascal\"/>Pascal" + +#: C/genius.xml:6982(synopsis) +#, no-wrap +msgid "Pascal (i)" +msgstr "Pascal (i)" + +#: C/genius.xml:6983(para) +msgid "" +"Get the Pascal's triangle as a matrix. This will return an <varname>i</varname>" +"+1 by <varname>i</varname>+1 lower diagonal matrix that is the Pascal's " +"triangle after <varname>i</varname> iterations." +msgstr "" + +#: C/genius.xml:6987(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/PascalsTriangle.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:6995(term) +msgid "<anchor id=\"gel-function-Permutations\"/>Permutations" +msgstr "<anchor id=\"gel-function-Permutations\"/>Permutations" + +#: C/genius.xml:6997(synopsis) +#, no-wrap +msgid "Permutations (k,n)" +msgstr "Permutations (k,n)" + +#: C/genius.xml:6998(para) +msgid "" +"Get all permutations of <varname>k</varname> numbers from 1 to <varname>n</" +"varname> as a vector of vectors." +msgstr "" + +#: C/genius.xml:6999(para) C/genius.xml:7088(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/Permutation.html\">Mathworld</" +"ulink> or <ulink url=\"http://en.wikipedia.org/wiki/Permutation\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:7008(term) +msgid "<anchor id=\"gel-function-RisingFactorial\"/>RisingFactorial" +msgstr "<anchor id=\"gel-function-RisingFactorial\"/>RisingFactorial" + +#: C/genius.xml:7010(synopsis) +#, no-wrap +msgid "RisingFactorial (n,k)" +msgstr "RisingFactorial (n,k)" + +#: C/genius.xml:7011(para) +msgid "Aliases: <function>Pochhammer</function>" +msgstr "Alias: <function>Pochhammer</function>" + +#: C/genius.xml:7012(para) +msgid "(Pochhammer) Rising factorial: (n)_k = n(n+1)...(n+(k-1))." +msgstr "" + +#: C/genius.xml:7013(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/RisingFactorial.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:7021(term) +msgid "<anchor id=\"gel-function-StirlingNumberFirst\"/>StirlingNumberFirst" +msgstr "<anchor id=\"gel-function-StirlingNumberFirst\"/>StirlingNumberFirst" + +#: C/genius.xml:7023(synopsis) +#, no-wrap +msgid "StirlingNumberFirst (n,m)" +msgstr "StirlingNumberFirst (n,m)" + +#: C/genius.xml:7024(para) +msgid "Aliases: <function>StirlingS1</function>" +msgstr "Alias: <function>StirlingS1</function>" + +#: C/genius.xml:7025(para) +msgid "Stirling number of the first kind." +msgstr "" + +#: C/genius.xml:7026(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/" +"StirlingNumbersOfTheFirstKind.html\">Planetmath</ulink> or <ulink url=\"http://" +"mathworld.wolfram.com/StirlingNumberoftheFirstKind.html\">Mathworld</ulink> " +"for more information." +msgstr "" + +#: C/genius.xml:7035(term) +msgid "<anchor id=\"gel-function-StirlingNumberSecond\"/>StirlingNumberSecond" +msgstr "<anchor id=\"gel-function-StirlingNumberSecond\"/>StirlingNumberSecond" + +#: C/genius.xml:7037(synopsis) +#, no-wrap +msgid "StirlingNumberSecond (n,m)" +msgstr "StirlingNumberSecond (n,m)" + +#: C/genius.xml:7038(para) +msgid "Aliases: <function>StirlingS2</function>" +msgstr "Alias: <function>StirlingS2</function>" + +#: C/genius.xml:7039(para) +msgid "Stirling number of the second kind." +msgstr "" + +#: C/genius.xml:7040(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/StirlingNumbersSecondKind." +"html\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"StirlingNumberoftheSecondKind.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:7049(term) +msgid "<anchor id=\"gel-function-Subfactorial\"/>Subfactorial" +msgstr "<anchor id=\"gel-function-Subfactorial\"/>Subfactorial" + +#: C/genius.xml:7051(synopsis) +#, no-wrap +msgid "Subfactorial (n)" +msgstr "Subfactorial (n)" + +#: C/genius.xml:7052(para) +msgid "Subfactorial: n! times sum_{k=0}^n (-1)^k/k!." +msgstr "" + +#: C/genius.xml:7057(term) +msgid "<anchor id=\"gel-function-Triangular\"/>Triangular" +msgstr "<anchor id=\"gel-function-Triangular\"/>Triangular" + +#: C/genius.xml:7059(synopsis) +#, no-wrap +msgid "Triangular (nth)" +msgstr "" + +#: C/genius.xml:7060(para) +msgid "Calculate the <varname>n</varname>th triangular number." +msgstr "" + +#: C/genius.xml:7061(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/TriangularNumbers.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:7069(term) +msgid "<anchor id=\"gel-function-nCr\"/>nCr" +msgstr "<anchor id=\"gel-function-nCr\"/>nCr" + +#: C/genius.xml:7071(synopsis) +#, no-wrap +msgid "nCr (n,r)" +msgstr "nCr (n,r)" + +#: C/genius.xml:7072(para) +msgid "Aliases: <function>Binomial</function>" +msgstr "Alias: <function>Binomial</function>" + +#: C/genius.xml:7073(para) +msgid "" +"Calculate combinations, that is, the binomial coefficient. <varname>n</" +"varname> can be any real number." +msgstr "" + +#: C/genius.xml:7075(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/Choose.html\">Planetmath</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:7083(term) +msgid "<anchor id=\"gel-function-nPr\"/>nPr" +msgstr "<anchor id=\"gel-function-nPr\"/>nPr" + +#: C/genius.xml:7085(synopsis) +#, no-wrap +msgid "nPr (n,r)" +msgstr "nPr (n,r)" + +#: C/genius.xml:7086(para) +msgid "" +"Calculate the number of permutations of size <varname>r</varname>of numbers " +"from 1 to <varname>n</varname>." +msgstr "" + +#: C/genius.xml:7100(title) +msgid "Calculus" +msgstr "" + +#: C/genius.xml:7103(term) +msgid "<anchor id=\"gel-function-CompositeSimpsonsRule\"/>CompositeSimpsonsRule" +msgstr "<anchor id=\"gel-function-CompositeSimpsonsRule\"/>CompositeSimpsonsRule" + +#: C/genius.xml:7105(synopsis) +#, no-wrap +msgid "CompositeSimpsonsRule (f,a,b,n)" +msgstr "CompositeSimpsonsRule (f,a,b,n)" + +#: C/genius.xml:7106(para) +msgid "" +"Integration of f by Composite Simpson's Rule on the interval [a,b] with n " +"subintervals with error of max(f'''')*h^4*(b-a)/180, note that n should be " +"even." +msgstr "" + +#: C/genius.xml:7107(para) C/genius.xml:7119(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/SimpsonsRule.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:7115(term) +msgid "" +"<anchor id=\"gel-function-CompositeSimpsonsRuleTolerance\"/" +">CompositeSimpsonsRuleTolerance" +msgstr "" +"<anchor id=\"gel-function-CompositeSimpsonsRuleTolerance\"/" +">CompositeSimpsonsRuleTolerance" + +#: C/genius.xml:7117(synopsis) +#, no-wrap +msgid "CompositeSimpsonsRuleTolerance (f,a,b,FourthDerivativeBound,Tolerance)" +msgstr "" + +#: C/genius.xml:7118(para) +msgid "" +"Integration of f by Composite Simpson's Rule on the interval [a,b] with the " +"number of steps calculated by the fourth derivative bound and the desired " +"tolerance." +msgstr "" + +#: C/genius.xml:7127(term) +msgid "<anchor id=\"gel-function-Derivative\"/>Derivative" +msgstr "<anchor id=\"gel-function-Derivative\"/>Derivative" + +#: C/genius.xml:7129(synopsis) +#, no-wrap +msgid "Derivative (f,x0)" +msgstr "Derivative (f,x0)" + +#: C/genius.xml:7130(para) +msgid "" +"Attempt to calculate derivative by trying first symbolically and then " +"numerically." +msgstr "" + +#: C/genius.xml:7135(term) +msgid "<anchor id=\"gel-function-EvenPeriodicExtension\"/>EvenPeriodicExtension" +msgstr "<anchor id=\"gel-function-EvenPeriodicExtension\"/>EvenPeriodicExtension" + +#: C/genius.xml:7137(synopsis) +#, no-wrap +msgid "EvenPeriodicExtension (f,L)" +msgstr "EvenPeriodicExtension (f,L)" + +#: C/genius.xml:7138(para) +msgid "" +"Return a function that is the even periodic extension of <function>f</" +"function> with half period <varname>L</varname>. That is a function defined on " +"the interval <userinput>[0,L]</userinput> extended to be even on <userinput>[-" +"L,L]</userinput> and then extended to be periodic with period <userinput>2*L</" +"userinput>." +msgstr "" + +#: C/genius.xml:7143(para) +msgid "" +"See also <link linkend=\"gel-function-OddPeriodicExtension" +"\">OddPeriodicExtension</link> and <link linkend=\"gel-function-" +"PeriodicExtension\">PeriodicExtension</link>." +msgstr "" + +#: C/genius.xml:7154(term) +msgid "<anchor id=\"gel-function-FourierSeriesFunction\"/>FourierSeriesFunction" +msgstr "<anchor id=\"gel-function-FourierSeriesFunction\"/>FourierSeriesFunction" + +#: C/genius.xml:7156(synopsis) +#, no-wrap +msgid "FourierSeriesFunction (a,b,L)" +msgstr "FourierSeriesFunction (a,b,L)" + +#: C/genius.xml:7157(para) +msgid "" +"Return a function that is a Fourier series with the coefficients given by the " +"vectors <varname>a</varname> (sines) and <varname>b</varname> (cosines). Note " +"that <userinput>a@(1)</userinput> is the constant coefficient! That is, " +"<userinput>a@(n)</userinput> refers to the term <userinput>cos(x*(n-1)*pi/L)</" +"userinput>, while <userinput>b@(n)</userinput> refers to the term " +"<userinput>sin(x*n*pi/L)</userinput>. Either <varname>a</varname> or " +"<varname>b</varname> can be <constant>null</constant>." +msgstr "" + +#: C/genius.xml:7165(para) C/genius.xml:7267(para) C/genius.xml:7287(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</" +"ulink> or <ulink url=\"http://mathworld.wolfram.com/FourierSeries.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:7174(term) +msgid "<anchor id=\"gel-function-InfiniteProduct\"/>InfiniteProduct" +msgstr "<anchor id=\"gel-function-InfiniteProduct\"/>InfiniteProduct" + +#: C/genius.xml:7176(synopsis) +#, no-wrap +msgid "InfiniteProduct (func,start,inc)" +msgstr "" + +#: C/genius.xml:7177(para) +msgid "Try to calculate an infinite product for a single parameter function." +msgstr "" + +#: C/genius.xml:7182(term) +msgid "<anchor id=\"gel-function-InfiniteProduct2\"/>InfiniteProduct2" +msgstr "<anchor id=\"gel-function-InfiniteProduct2\"/>InfiniteProduct2" + +#: C/genius.xml:7184(synopsis) +#, no-wrap +msgid "InfiniteProduct2 (func,arg,start,inc)" +msgstr "" + +#: C/genius.xml:7185(para) +msgid "" +"Try to calculate an infinite product for a double parameter function with " +"func(arg,n)." +msgstr "" + +#: C/genius.xml:7190(term) +msgid "<anchor id=\"gel-function-InfiniteSum\"/>InfiniteSum" +msgstr "<anchor id=\"gel-function-InfiniteSum\"/>InfiniteSum" + +#: C/genius.xml:7192(synopsis) +#, no-wrap +msgid "InfiniteSum (func,start,inc)" +msgstr "" + +#: C/genius.xml:7193(para) +msgid "Try to calculate an infinite sum for a single parameter function." +msgstr "" + +#: C/genius.xml:7198(term) +msgid "<anchor id=\"gel-function-InfiniteSum2\"/>InfiniteSum2" +msgstr "<anchor id=\"gel-function-InfiniteSum2\"/>InfiniteSum2" + +#: C/genius.xml:7200(synopsis) +#, no-wrap +msgid "InfiniteSum2 (func,arg,start,inc)" +msgstr "" + +#: C/genius.xml:7201(para) +msgid "" +"Try to calculate an infinite sum for a double parameter function with func(arg," +"n)." +msgstr "" + +#: C/genius.xml:7206(term) +msgid "<anchor id=\"gel-function-IsContinuous\"/>IsContinuous" +msgstr "<anchor id=\"gel-function-IsContinuous\"/>IsContinuous" + +#: C/genius.xml:7208(synopsis) +#, no-wrap +msgid "IsContinuous (f,x0)" +msgstr "IsContinuous (f,x0)" + +#: C/genius.xml:7209(para) +msgid "" +"Try and see if a real-valued function is continuous at x0 by calculating the " +"limit there." +msgstr "" + +#: C/genius.xml:7214(term) +msgid "<anchor id=\"gel-function-IsDifferentiable\"/>IsDifferentiable" +msgstr "<anchor id=\"gel-function-IsDifferentiable\"/>IsDifferentiable" + +#: C/genius.xml:7216(synopsis) +#, no-wrap +msgid "IsDifferentiable (f,x0)" +msgstr "IsDifferentiable (f,x0)" + +#: C/genius.xml:7217(para) +msgid "" +"Test for differentiability by approximating the left and right limits and " +"comparing." +msgstr "" + +#: C/genius.xml:7222(term) +msgid "<anchor id=\"gel-function-LeftLimit\"/>LeftLimit" +msgstr "<anchor id=\"gel-function-LeftLimit\"/>LeftLimit" + +#: C/genius.xml:7224(synopsis) +#, no-wrap +msgid "LeftLimit (f,x0)" +msgstr "LeftLimit (f,x0)" + +#: C/genius.xml:7225(para) +msgid "Calculate the left limit of a real-valued function at x0." +msgstr "" + +#: C/genius.xml:7230(term) +msgid "<anchor id=\"gel-function-Limit\"/>Limit" +msgstr "<anchor id=\"gel-function-Limit\"/>Limit" + +#: C/genius.xml:7232(synopsis) +#, no-wrap +msgid "Limit (f,x0)" +msgstr "Limit (f,x0)" + +#: C/genius.xml:7233(para) +msgid "" +"Calculate the limit of a real-valued function at x0. Tries to calculate both " +"left and right limits." +msgstr "" + +#: C/genius.xml:7238(term) +msgid "<anchor id=\"gel-function-MidpointRule\"/>MidpointRule" +msgstr "<anchor id=\"gel-function-MidpointRule\"/>MidpointRule" + +#: C/genius.xml:7240(synopsis) +#, no-wrap +msgid "MidpointRule (f,a,b,n)" +msgstr "MidpointRule (f,a,b,n)" + +#: C/genius.xml:7241(para) +msgid "Integration by midpoint rule." +msgstr "" + +#: C/genius.xml:7246(term) +msgid "<anchor id=\"gel-function-NumericalDerivative\"/>NumericalDerivative" +msgstr "<anchor id=\"gel-function-NumericalDerivative\"/>NumericalDerivative" + +#: C/genius.xml:7248(synopsis) +#, no-wrap +msgid "NumericalDerivative (f,x0)" +msgstr "NumericalDerivative (f,x0)" + +#: C/genius.xml:7249(para) +msgid "Aliases: <function>NDerivative</function>" +msgstr "Alias: <function>NDerivative</function>" + +#: C/genius.xml:7250(para) +msgid "Attempt to calculate numerical derivative." +msgstr "" + +#: C/genius.xml:7255(term) +msgid "" +"<anchor id=\"gel-function-NumericalFourierSeriesCoefficients\"/" +">NumericalFourierSeriesCoefficients" +msgstr "" +"<anchor id=\"gel-function-NumericalFourierSeriesCoefficients\"/" +">NumericalFourierSeriesCoefficients" + +#: C/genius.xml:7257(synopsis) +#, no-wrap +msgid "NumericalFourierSeriesCoefficients (f,L,N)" +msgstr "NumericalFourierSeriesCoefficients (f,L,N)" + +#: C/genius.xml:7258(para) +msgid "" +"Return a vector of vectors <userinput>[a,b]</userinput> where <varname>a</" +"varname> are the cosine coefficients and <varname>b</varname> are the sine " +"coefficients of the Fourier series of <function>f</function> with half-period " +"<varname>L</varname> (that is defined on <userinput>[-L,L]</userinput> and " +"extended periodically) with coefficients up to <varname>N</varname>th harmonic " +"computed numerically. The coefficients are computed by numerical integration " +"using <link linkend=\"gel-function-NumericalIntegral" +"\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:7277(term) +msgid "" +"<anchor id=\"gel-function-NumericalFourierSeriesFunction\"/" +">NumericalFourierSeriesFunction" +msgstr "" +"<anchor id=\"gel-function-NumericalFourierSeriesFunction\"/" +">NumericalFourierSeriesFunction" + +#: C/genius.xml:7279(synopsis) +#, no-wrap +msgid "NumericalFourierSeriesFunction (f,L,N)" +msgstr "NumericalFourierSeriesFunction (f,L,N)" + +#: C/genius.xml:7280(para) +msgid "" +"Return a function that is the Fourier series of <function>f</function> with " +"half-period <varname>L</varname> (that is defined on <userinput>[-L,L]</" +"userinput> and extended periodically) with coefficients up to <varname>N</" +"varname>th harmonic computed numerically. This is the trigonometric real " +"series composed of sines and cosines. The coefficients are computed by " +"numerical integration using <link linkend=\"gel-function-NumericalIntegral" +"\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:7297(term) +msgid "" +"<anchor id=\"gel-function-NumericalFourierCosineSeriesCoefficients\"/" +">NumericalFourierCosineSeriesCoefficients" +msgstr "" +"<anchor id=\"gel-function-NumericalFourierCosineSeriesCoefficients\"/" +">NumericalFourierCosineSeriesCoefficients" + +#: C/genius.xml:7299(synopsis) +#, no-wrap +msgid "NumericalFourierCosineSeriesCoefficients (f,L,N)" +msgstr "NumericalFourierCosineSeriesCoefficients (f,L,N)" + +#: C/genius.xml:7300(para) +msgid "" +"Return a vector of coefficients of the cosine Fourier series of <function>f</" +"function> with half-period <varname>L</varname>. That is, we take <function>f</" +"function> defined on <userinput>[0,L]</userinput> take the even periodic " +"extension and compute the Fourier series, which only has cosine terms. The " +"series is computed up to the <varname>N</varname>th harmonic. The coefficients " +"are computed by numerical integration using <link linkend=\"gel-function-" +"NumericalIntegral\"><function>NumericalIntegral</function></link>. Note that " +"<userinput>a@(1)</userinput> is the constant coefficient! That is, " +"<userinput>a@(n)</userinput> refers to the term <userinput>cos(x*(n-1)*pi/L)</" +"userinput>." +msgstr "" + +#: C/genius.xml:7312(para) C/genius.xml:7333(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</" +"ulink> or <ulink url=\"http://mathworld.wolfram.com/FourierCosineSeries.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:7322(term) +msgid "" +"<anchor id=\"gel-function-NumericalFourierCosineSeriesFunction\"/" +">NumericalFourierCosineSeriesFunction" +msgstr "" +"<anchor id=\"gel-function-NumericalFourierCosineSeriesFunction\"/" +">NumericalFourierCosineSeriesFunction" + +#: C/genius.xml:7324(synopsis) +#, no-wrap +msgid "NumericalFourierCosineSeriesFunction (f,L,N)" +msgstr "NumericalFourierCosineSeriesFunction (f,L,N)" + +#: C/genius.xml:7325(para) +msgid "" +"Return a function that is the cosine Fourier series of <function>f</function> " +"with half-period <varname>L</varname>. That is, we take <function>f</function> " +"defined on <userinput>[0,L]</userinput> take the even periodic extension and " +"compute the Fourier series, which only has cosine terms. The series is " +"computed up to the <varname>N</varname>th harmonic. The coefficients are " +"computed by numerical integration using <link linkend=\"gel-function-" +"NumericalIntegral\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:7343(term) +msgid "" +"<anchor id=\"gel-function-NumericalFourierSineSeriesCoefficients\"/" +">NumericalFourierSineSeriesCoefficients" +msgstr "" +"<anchor id=\"gel-function-NumericalFourierSineSeriesCoefficients\"/" +">NumericalFourierSineSeriesCoefficients" + +#: C/genius.xml:7345(synopsis) +#, no-wrap +msgid "NumericalFourierSineSeriesCoefficients (f,L,N)" +msgstr "NumericalFourierSineSeriesCoefficients (f,L,N)" + +#: C/genius.xml:7346(para) +msgid "" +"Return a vector of coefficients of the sine Fourier series of <function>f</" +"function> with half-period <varname>L</varname>. That is, we take <function>f</" +"function> defined on <userinput>[0,L]</userinput> take the odd periodic " +"extension and compute the Fourier series, which only has sine terms. The " +"series is computed up to the <varname>N</varname>th harmonic. The coefficients " +"are computed by numerical integration using <link linkend=\"gel-function-" +"NumericalIntegral\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:7355(para) C/genius.xml:7376(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</" +"ulink> or <ulink url=\"http://mathworld.wolfram.com/FourierSineSeries.html" +"\">Mathworld</ulink> for more information." +msgstr "" +"Se <ulink url=\"http://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</" +"ulink> eller <ulink url=\"http://mathworld.wolfram.com/FourierSineSeries.html" +"\">Mathworld</ulink> för mer information." + +#: C/genius.xml:7365(term) +msgid "" +"<anchor id=\"gel-function-NumericalFourierSineSeriesFunction\"/" +">NumericalFourierSineSeriesFunction" +msgstr "" +"<anchor id=\"gel-function-NumericalFourierSineSeriesFunction\"/" +">NumericalFourierSineSeriesFunction" + +#: C/genius.xml:7367(synopsis) +#, no-wrap +msgid "NumericalFourierSineSeriesFunction (f,L,N)" +msgstr "NumericalFourierSineSeriesFunction (f,L,N)" + +#: C/genius.xml:7368(para) +msgid "" +"Return a function that is the sine Fourier series of <function>f</function> " +"with half-period <varname>L</varname>. That is, we take <function>f</function> " +"defined on <userinput>[0,L]</userinput> take the odd periodic extension and " +"compute the Fourier series, which only has sine terms. The series is computed " +"up to the <varname>N</varname>th harmonic. The coefficients are computed by " +"numerical integration using <link linkend=\"gel-function-NumericalIntegral" +"\"><function>NumericalIntegral</function></link>." +msgstr "" + +#: C/genius.xml:7386(term) +msgid "<anchor id=\"gel-function-NumericalIntegral\"/>NumericalIntegral" +msgstr "<anchor id=\"gel-function-NumericalIntegral\"/>NumericalIntegral" + +#: C/genius.xml:7388(synopsis) +#, no-wrap +msgid "NumericalIntegral (f,a,b)" +msgstr "NumericalIntegral (f,a,b)" + +#: C/genius.xml:7389(para) +msgid "" +"Integration by rule set in NumericalIntegralFunction of f from a to b using " +"NumericalIntegralSteps steps." +msgstr "" + +#: C/genius.xml:7394(term) +msgid "" +"<anchor id=\"gel-function-NumericalLeftDerivative\"/>NumericalLeftDerivative" +msgstr "" +"<anchor id=\"gel-function-NumericalLeftDerivative\"/>NumericalLeftDerivative" + +#: C/genius.xml:7396(synopsis) +#, no-wrap +msgid "NumericalLeftDerivative (f,x0)" +msgstr "NumericalLeftDerivative (f,x0)" + +#: C/genius.xml:7397(para) +msgid "Attempt to calculate numerical left derivative." +msgstr "" + +#: C/genius.xml:7402(term) +msgid "" +"<anchor id=\"gel-function-NumericalLimitAtInfinity\"/>NumericalLimitAtInfinity" +msgstr "" +"<anchor id=\"gel-function-NumericalLimitAtInfinity\"/>NumericalLimitAtInfinity" + +#: C/genius.xml:7404(synopsis) +#, no-wrap +msgid "NumericalLimitAtInfinity (_f,step_fun,tolerance,successive_for_success,N)" +msgstr "" + +#: C/genius.xml:7405(para) +msgid "Attempt to calculate the limit of f(step_fun(i)) as i goes from 1 to N." +msgstr "" + +#: C/genius.xml:7410(term) +msgid "" +"<anchor id=\"gel-function-NumericalRightDerivative\"/>NumericalRightDerivative" +msgstr "" +"<anchor id=\"gel-function-NumericalRightDerivative\"/>NumericalRightDerivative" + +#: C/genius.xml:7412(synopsis) +#, no-wrap +msgid "NumericalRightDerivative (f,x0)" +msgstr "NumericalRightDerivative (f,x0)" + +#: C/genius.xml:7413(para) +msgid "Attempt to calculate numerical right derivative." +msgstr "" + +#: C/genius.xml:7418(term) +msgid "<anchor id=\"gel-function-OddPeriodicExtension\"/>OddPeriodicExtension" +msgstr "<anchor id=\"gel-function-OddPeriodicExtension\"/>OddPeriodicExtension" + +#: C/genius.xml:7420(synopsis) +#, no-wrap +msgid "OddPeriodicExtension (f,L)" +msgstr "OddPeriodicExtension (f,L)" + +#: C/genius.xml:7421(para) +msgid "" +"Return a function that is the odd periodic extension of <function>f</function> " +"with half period <varname>L</varname>. That is a function defined on the " +"interval <userinput>[0,L]</userinput> extended to be odd on <userinput>[-L,L]</" +"userinput> and then extended to be periodic with period <userinput>2*L</" +"userinput>." +msgstr "" + +#: C/genius.xml:7426(para) +msgid "" +"See also <link linkend=\"gel-function-EvenPeriodicExtension" +"\">EvenPeriodicExtension</link> and <link linkend=\"gel-function-" +"PeriodicExtension\">PeriodicExtension</link>." +msgstr "" + +#: C/genius.xml:7437(term) +msgid "" +"<anchor id=\"gel-function-OneSidedFivePointFormula\"/>OneSidedFivePointFormula" +msgstr "" +"<anchor id=\"gel-function-OneSidedFivePointFormula\"/>OneSidedFivePointFormula" + +#: C/genius.xml:7439(synopsis) +#, no-wrap +msgid "OneSidedFivePointFormula (f,x0,h)" +msgstr "OneSidedFivePointFormula (f,x0,h)" + +#: C/genius.xml:7440(para) +msgid "Compute one-sided derivative using five point formula." +msgstr "" + +#: C/genius.xml:7445(term) +msgid "" +"<anchor id=\"gel-function-OneSidedThreePointFormula\"/" +">OneSidedThreePointFormula" +msgstr "" +"<anchor id=\"gel-function-OneSidedThreePointFormula\"/" +">OneSidedThreePointFormula" + +#: C/genius.xml:7447(synopsis) +#, no-wrap +msgid "OneSidedThreePointFormula (f,x0,h)" +msgstr "OneSidedThreePointFormula (f,x0,h)" + +#: C/genius.xml:7448(para) +msgid "Compute one-sided derivative using three-point formula." +msgstr "" + +#: C/genius.xml:7453(term) +msgid "<anchor id=\"gel-function-PeriodicExtension\"/>PeriodicExtension" +msgstr "<anchor id=\"gel-function-PeriodicExtension\"/>PeriodicExtension" + +#: C/genius.xml:7455(synopsis) +#, no-wrap +msgid "PeriodicExtension (f,a,b)" +msgstr "PeriodicExtension (f,a,b)" + +#: C/genius.xml:7456(para) +msgid "" +"Return a function that is the periodic extension of <function>f</function> " +"defined on the interval <userinput>[a,b]</userinput> and has period " +"<userinput>b-a</userinput>." +msgstr "" + +#: C/genius.xml:7459(para) +msgid "" +"See also <link linkend=\"gel-function-OddPeriodicExtension" +"\">OddPeriodicExtension</link> and <link linkend=\"gel-function-" +"EvenPeriodicExtension\">EvenPeriodicExtension</link>." +msgstr "" + +#: C/genius.xml:7470(term) +msgid "<anchor id=\"gel-function-RightLimit\"/>RightLimit" +msgstr "<anchor id=\"gel-function-RightLimit\"/>RightLimit" + +#: C/genius.xml:7472(synopsis) +#, no-wrap +msgid "RightLimit (f,x0)" +msgstr "RightLimit (f,x0)" + +#: C/genius.xml:7473(para) +msgid "Calculate the right limit of a real-valued function at x0." +msgstr "" + +#: C/genius.xml:7478(term) +msgid "" +"<anchor id=\"gel-function-TwoSidedFivePointFormula\"/>TwoSidedFivePointFormula" +msgstr "" +"<anchor id=\"gel-function-TwoSidedFivePointFormula\"/>TwoSidedFivePointFormula" + +#: C/genius.xml:7480(synopsis) +#, no-wrap +msgid "TwoSidedFivePointFormula (f,x0,h)" +msgstr "TwoSidedFivePointFormula (f,x0,h)" + +#: C/genius.xml:7481(para) +msgid "Compute two-sided derivative using five-point formula." +msgstr "" + +#: C/genius.xml:7486(term) +msgid "" +"<anchor id=\"gel-function-TwoSidedThreePointFormula\"/" +">TwoSidedThreePointFormula" +msgstr "" +"<anchor id=\"gel-function-TwoSidedThreePointFormula\"/" +">TwoSidedThreePointFormula" + +#: C/genius.xml:7488(synopsis) +#, no-wrap +msgid "TwoSidedThreePointFormula (f,x0,h)" +msgstr "TwoSidedThreePointFormula (f,x0,h)" + +#: C/genius.xml:7489(para) +msgid "Compute two-sided derivative using three-point formula." +msgstr "" + +#: C/genius.xml:7497(title) +msgid "Functions" +msgstr "" + +#: C/genius.xml:7500(term) +msgid "<anchor id=\"gel-function-Argument\"/>Argument" +msgstr "<anchor id=\"gel-function-Argument\"/>Argument" + +#: C/genius.xml:7502(synopsis) +#, no-wrap +msgid "Argument (z)" +msgstr "Argument (z)" + +#: C/genius.xml:7503(para) +msgid "Aliases: <function>Arg</function><function>arg</function>" +msgstr "Alias: <function>Arg</function><function>arg</function>" + +#: C/genius.xml:7504(para) +msgid "argument (angle) of complex number." +msgstr "" + +#: C/genius.xml:7509(term) +msgid "<anchor id=\"gel-function-BesselJ0\"/>BesselJ0" +msgstr "<anchor id=\"gel-function-BesselJ0\"/>BesselJ0" + +#: C/genius.xml:7511(synopsis) +#, no-wrap +msgid "BesselJ0 (x)" +msgstr "BesselJ0 (x)" + +#: C/genius.xml:7512(para) +msgid "" +"Bessel function of the first kind of order 0. Only implemented for real " +"numbers." +msgstr "" + +#: C/genius.xml:7513(para) C/genius.xml:7526(para) C/genius.xml:7539(para) +#: C/genius.xml:7552(para) C/genius.xml:7565(para) C/genius.xml:7578(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Bessel_functions\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:7522(term) +msgid "<anchor id=\"gel-function-BesselJ1\"/>BesselJ1" +msgstr "<anchor id=\"gel-function-BesselJ1\"/>BesselJ1" + +#: C/genius.xml:7524(synopsis) +#, no-wrap +msgid "BesselJ1 (x)" +msgstr "BesselJ1 (x)" + +#: C/genius.xml:7525(para) +msgid "" +"Bessel function of the first kind of order 1. Only implemented for real " +"numbers." +msgstr "" + +#: C/genius.xml:7535(term) +msgid "<anchor id=\"gel-function-BesselJn\"/>BesselJn" +msgstr "<anchor id=\"gel-function-BesselJn\"/>BesselJn" + +#: C/genius.xml:7537(synopsis) +#, no-wrap +msgid "BesselJn (n,x)" +msgstr "BesselJn (n,x)" + +#: C/genius.xml:7538(para) +msgid "" +"Bessel function of the first kind of order <varname>n</varname>. Only " +"implemented for real numbers." +msgstr "" + +#: C/genius.xml:7548(term) +msgid "<anchor id=\"gel-function-BesselY0\"/>BesselY0" +msgstr "<anchor id=\"gel-function-BesselY0\"/>BesselY0" + +#: C/genius.xml:7550(synopsis) +#, no-wrap +msgid "BesselY0 (x)" +msgstr "BesselY0 (x)" + +#: C/genius.xml:7551(para) +msgid "" +"Bessel function of the second kind of order 0. Only implemented for real " +"numbers." +msgstr "" + +#: C/genius.xml:7561(term) +msgid "<anchor id=\"gel-function-BesselY1\"/>BesselY1" +msgstr "<anchor id=\"gel-function-BesselY1\"/>BesselY1" + +#: C/genius.xml:7563(synopsis) +#, no-wrap +msgid "BesselY1 (x)" +msgstr "BesselY1 (x)" + +#: C/genius.xml:7564(para) +msgid "" +"Bessel function of the second kind of order 1. Only implemented for real " +"numbers." +msgstr "" + +#: C/genius.xml:7574(term) +msgid "<anchor id=\"gel-function-BesselYn\"/>BesselYn" +msgstr "<anchor id=\"gel-function-BesselYn\"/>BesselYn" + +#: C/genius.xml:7576(synopsis) +#, no-wrap +msgid "BesselYn (n,x)" +msgstr "BesselYn (n,x)" + +#: C/genius.xml:7577(para) +msgid "" +"Bessel function of the second kind of order <varname>n</varname>. Only " +"implemented for real numbers." +msgstr "" + +#: C/genius.xml:7587(term) +msgid "<anchor id=\"gel-function-DirichletKernel\"/>DirichletKernel" +msgstr "<anchor id=\"gel-function-DirichletKernel\"/>DirichletKernel" + +#: C/genius.xml:7589(synopsis) +#, no-wrap +msgid "DirichletKernel (n,t)" +msgstr "DirichletKernel (n,t)" + +#: C/genius.xml:7590(para) +msgid "Dirichlet kernel of order n." +msgstr "" + +#: C/genius.xml:7595(term) +msgid "<anchor id=\"gel-function-DiscreteDelta\"/>DiscreteDelta" +msgstr "<anchor id=\"gel-function-DiscreteDelta\"/>DiscreteDelta" + +#: C/genius.xml:7597(synopsis) +#, no-wrap +msgid "DiscreteDelta (v)" +msgstr "DiscreteDelta (v)" + +#: C/genius.xml:7598(para) +msgid "Returns 1 if and only if all elements are zero." +msgstr "" + +#: C/genius.xml:7603(term) +msgid "<anchor id=\"gel-function-ErrorFunction\"/>ErrorFunction" +msgstr "<anchor id=\"gel-function-ErrorFunction\"/>ErrorFunction" + +#: C/genius.xml:7605(synopsis) +#, no-wrap +msgid "ErrorFunction (x)" +msgstr "ErrorFunction (x)" + +#: C/genius.xml:7606(para) +msgid "Aliases: <function>erf</function>" +msgstr "Alias: <function>erf</function>" + +#: C/genius.xml:7607(para) +msgid "The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt." +msgstr "" + +#: C/genius.xml:7608(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/ErrorFunction.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:7616(term) +msgid "<anchor id=\"gel-function-FejerKernel\"/>FejerKernel" +msgstr "<anchor id=\"gel-function-FejerKernel\"/>FejerKernel" + +#: C/genius.xml:7618(synopsis) +#, no-wrap +msgid "FejerKernel (n,t)" +msgstr "FejerKernel (n,t)" + +#: C/genius.xml:7619(para) +msgid "" +"Fejer kernel of order <varname>n</varname> evaluated at <varname>t</varname>" +msgstr "" + +#: C/genius.xml:7621(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/FejerKernel.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:7629(term) +msgid "<anchor id=\"gel-function-GammaFunction\"/>GammaFunction" +msgstr "<anchor id=\"gel-function-GammaFunction\"/>GammaFunction" + +#: C/genius.xml:7631(synopsis) +#, no-wrap +msgid "GammaFunction (x)" +msgstr "GammaFunction (x)" + +#: C/genius.xml:7632(para) +msgid "Aliases: <function>Gamma</function>" +msgstr "Alias: <function>Gamma</function>" + +#: C/genius.xml:7633(para) +msgid "The Gamma function. Currently only implemented for real values." +msgstr "" + +#: C/genius.xml:7634(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/GammaFunction.html" +"\">Planetmath</ulink> or <ulink url=\"http://en.wikipedia.org/wiki/" +"Gamma_function\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:7643(term) +msgid "<anchor id=\"gel-function-KroneckerDelta\"/>KroneckerDelta" +msgstr "<anchor id=\"gel-function-KroneckerDelta\"/>KroneckerDelta" + +#: C/genius.xml:7645(synopsis) +#, no-wrap +msgid "KroneckerDelta (v)" +msgstr "KroneckerDelta (v)" + +#: C/genius.xml:7646(para) +msgid "Returns 1 if and only if all elements are equal." +msgstr "" + +#: C/genius.xml:7651(term) +msgid "<anchor id=\"gel-function-LambertW\"/>LambertW" +msgstr "<anchor id=\"gel-function-LambertW\"/>LambertW" + +#: C/genius.xml:7653(synopsis) +#, no-wrap +msgid "LambertW (x)" +msgstr "LambertW (x)" + +#: C/genius.xml:7654(para) +msgid "" +"The principal branch of Lambert W function computed for only real values " +"greater than or equal to <userinput>-1/e</userinput>. That is, " +"<function>LambertW</function> is the inverse of the expression " +"<userinput>x*e^x</userinput>. Even for real <varname>x</varname> this " +"expression is not one to one and therefore has two branches over " +"<userinput>[-1/e,0)</userinput>. See <link linkend=\"gel-function-" +"LambertWm1\"><function>LambertWm1</function></link> for the other real branch." +msgstr "" + +#: C/genius.xml:7663(para) C/genius.xml:7683(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Lambert_W_function\">Wikipedia</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:7672(term) +msgid "<anchor id=\"gel-function-LambertWm1\"/>LambertWm1" +msgstr "<anchor id=\"gel-function-LambertWm1\"/>LambertWm1" + +#: C/genius.xml:7674(synopsis) +#, no-wrap +msgid "LambertWm1 (x)" +msgstr "LambertWm1 (x)" + +#: C/genius.xml:7675(para) +msgid "" +"The minus-one branch of Lambert W function computed for only real values " +"greater than or equal to <userinput>-1/e</userinput> and less than 0. That is, " +"<function>LambertWm1</function> is the second branch of the inverse of " +"<userinput>x*e^x</userinput>. See <link linkend=\"gel-function-LambertW" +"\"><function>LambertW</function></link> for the principal branch." +msgstr "" + +#: C/genius.xml:7691(term) +msgid "<anchor id=\"gel-function-MinimizeFunction\"/>MinimizeFunction" +msgstr "<anchor id=\"gel-function-MinimizeFunction\"/>MinimizeFunction" + +#: C/genius.xml:7693(synopsis) +#, no-wrap +msgid "MinimizeFunction (func,x,incr)" +msgstr "" + +#: C/genius.xml:7694(para) +msgid "Find the first value where f(x)=0." +msgstr "" + +#: C/genius.xml:7699(term) +msgid "<anchor id=\"gel-function-MoebiusDiskMapping\"/>MoebiusDiskMapping" +msgstr "<anchor id=\"gel-function-MoebiusDiskMapping\"/>MoebiusDiskMapping" + +#: C/genius.xml:7701(synopsis) +#, no-wrap +msgid "MoebiusDiskMapping (a,z)" +msgstr "MoebiusDiskMapping (a,z)" + +#: C/genius.xml:7702(para) +msgid "Moebius mapping of the disk to itself mapping a to 0." +msgstr "" + +#: C/genius.xml:7703(para) C/genius.xml:7715(para) C/genius.xml:7727(para) +#: C/genius.xml:7739(para) C/genius.xml:7751(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/MobiusTransformation.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:7711(term) +msgid "<anchor id=\"gel-function-MoebiusMapping\"/>MoebiusMapping" +msgstr "<anchor id=\"gel-function-MoebiusMapping\"/>MoebiusMapping" + +#: C/genius.xml:7713(synopsis) +#, no-wrap +msgid "MoebiusMapping (z,z2,z3,z4)" +msgstr "MoebiusMapping (z,z2,z3,z4)" + +#: C/genius.xml:7714(para) +msgid "" +"Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity " +"respectively." +msgstr "" + +#: C/genius.xml:7723(term) +msgid "" +"<anchor id=\"gel-function-MoebiusMappingInftyToInfty\"/" +">MoebiusMappingInftyToInfty" +msgstr "" +"<anchor id=\"gel-function-MoebiusMappingInftyToInfty\"/" +">MoebiusMappingInftyToInfty" + +#: C/genius.xml:7725(synopsis) +#, no-wrap +msgid "MoebiusMappingInftyToInfty (z,z2,z3)" +msgstr "MoebiusMappingInftyToInfty (z,z2,z3)" + +#: C/genius.xml:7726(para) +msgid "" +"Moebius mapping using the cross ratio taking infinity to infinity and z2,z3 to " +"1 and 0 respectively." +msgstr "" + +#: C/genius.xml:7735(term) +msgid "" +"<anchor id=\"gel-function-MoebiusMappingInftyToOne\"/>MoebiusMappingInftyToOne" +msgstr "" +"<anchor id=\"gel-function-MoebiusMappingInftyToOne\"/>MoebiusMappingInftyToOne" + +#: C/genius.xml:7737(synopsis) +#, no-wrap +msgid "MoebiusMappingInftyToOne (z,z3,z4)" +msgstr "MoebiusMappingInftyToOne (z,z3,z4)" + +#: C/genius.xml:7738(para) +msgid "" +"Moebius mapping using the cross ratio taking infinity to 1 and z3,z4 to 0 and " +"infinity respectively." +msgstr "" + +#: C/genius.xml:7747(term) +msgid "" +"<anchor id=\"gel-function-MoebiusMappingInftyToZero\"/" +">MoebiusMappingInftyToZero" +msgstr "" +"<anchor id=\"gel-function-MoebiusMappingInftyToZero\"/" +">MoebiusMappingInftyToZero" + +#: C/genius.xml:7749(synopsis) +#, no-wrap +msgid "MoebiusMappingInftyToZero (z,z2,z4)" +msgstr "MoebiusMappingInftyToZero (z,z2,z4)" + +#: C/genius.xml:7750(para) +msgid "" +"Moebius mapping using the cross ratio taking infinity to 0 and z2,z4 to 1 and " +"infinity respectively." +msgstr "" + +#: C/genius.xml:7759(term) +msgid "<anchor id=\"gel-function-PoissonKernel\"/>PoissonKernel" +msgstr "<anchor id=\"gel-function-PoissonKernel\"/>PoissonKernel" + +#: C/genius.xml:7761(synopsis) +#, no-wrap +msgid "PoissonKernel (r,sigma)" +msgstr "PoissonKernel (r,sigma)" + +#: C/genius.xml:7762(para) +msgid "" +"Poisson kernel on D(0,1) (not normalized to 1, that is integral of this is " +"2pi)." +msgstr "" + +#: C/genius.xml:7767(term) +msgid "<anchor id=\"gel-function-PoissonKernelRadius\"/>PoissonKernelRadius" +msgstr "<anchor id=\"gel-function-PoissonKernelRadius\"/>PoissonKernelRadius" + +#: C/genius.xml:7769(synopsis) +#, no-wrap +msgid "PoissonKernelRadius (r,sigma)" +msgstr "PoissonKernelRadius (r,sigma)" + +#: C/genius.xml:7770(para) +msgid "Poisson kernel on D(0,R) (not normalized to 1)." +msgstr "" + +#: C/genius.xml:7775(term) +msgid "<anchor id=\"gel-function-RiemannZeta\"/>RiemannZeta" +msgstr "<anchor id=\"gel-function-RiemannZeta\"/>RiemannZeta" + +#: C/genius.xml:7777(synopsis) +#, no-wrap +msgid "RiemannZeta (x)" +msgstr "RiemannZeta (x)" + +#: C/genius.xml:7778(para) +msgid "Aliases: <function>zeta</function>" +msgstr "Alias: <function>zeta</function>" + +#: C/genius.xml:7779(para) +msgid "The Riemann zeta function. Currently only implemented for real values." +msgstr "" + +#: C/genius.xml:7780(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/RiemannZetaFunction.html" +"\">Planetmath</ulink> or <ulink url=\"http://en.wikipedia.org/wiki/" +"Riemann_zeta_function\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:7789(term) +msgid "<anchor id=\"gel-function-UnitStep\"/>UnitStep" +msgstr "<anchor id=\"gel-function-UnitStep\"/>UnitStep" + +#: C/genius.xml:7791(synopsis) +#, no-wrap +msgid "UnitStep (x)" +msgstr "UnitStep (x)" + +#: C/genius.xml:7792(para) +msgid "" +"The unit step function is 0 for x<0, 1 otherwise. This is the integral of " +"the Dirac Delta function. Also called the Heaviside function." +msgstr "" + +#: C/genius.xml:7793(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Unit_step\">Wikipedia</ulink> " +"for more information." +msgstr "" +"Se <ulink url=\"http://en.wikipedia.org/wiki/Unit_step\">Wikipedia</ulink> för " +"mer information." + +#: C/genius.xml:7801(term) +msgid "<anchor id=\"gel-function-cis\"/>cis" +msgstr "<anchor id=\"gel-function-cis\"/>cis" + +#: C/genius.xml:7803(synopsis) +#, no-wrap +msgid "cis (x)" +msgstr "cis (x)" + +#: C/genius.xml:7804(para) +msgid "" +"The <function>cis</function> function, that is the same as " +"<userinput>cos(x)+1i*sin(x)</userinput>" +msgstr "" + +#: C/genius.xml:7812(term) +msgid "<anchor id=\"gel-function-deg2rad\"/>deg2rad" +msgstr "<anchor id=\"gel-function-deg2rad\"/>deg2rad" + +#: C/genius.xml:7814(synopsis) +#, no-wrap +msgid "deg2rad (x)" +msgstr "deg2rad (x)" + +#: C/genius.xml:7815(para) +msgid "Convert degrees to radians." +msgstr "" + +#: C/genius.xml:7820(term) +msgid "<anchor id=\"gel-function-rad2deg\"/>rad2deg" +msgstr "<anchor id=\"gel-function-rad2deg\"/>rad2deg" + +#: C/genius.xml:7822(synopsis) +#, no-wrap +msgid "rad2deg (x)" +msgstr "rad2deg (x)" + +#: C/genius.xml:7823(para) +msgid "Convert radians to degrees." +msgstr "" + +#: C/genius.xml:7828(term) +msgid "<anchor id=\"gel-function-sinc\"/>sinc" +msgstr "<anchor id=\"gel-function-sinc\"/>sinc" + +#: C/genius.xml:7830(synopsis) +#, no-wrap +msgid "sinc (x)" +msgstr "sinc (x)" + +#: C/genius.xml:7831(para) +msgid "" +"Calculates the unnormalized sinc function, that is <userinput>sin(x)/x</" +"userinput>. If you want the normalized function call <userinput>sinc(pi*x)</" +"userinput>." +msgstr "" + +#: C/genius.xml:7834(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Sinc\">Wikipedia</ulink> for " +"more information." +msgstr "" +"Se <ulink url=\"http://en.wikipedia.org/wiki/Sinc\">Wikipedia</ulink> för mer " +"information." + +#: C/genius.xml:7846(title) +msgid "Equation Solving" +msgstr "" + +#: C/genius.xml:7850(term) +msgid "<anchor id=\"gel-function-CubicFormula\"/>CubicFormula" +msgstr "<anchor id=\"gel-function-CubicFormula\"/>CubicFormula" + +#: C/genius.xml:7852(synopsis) +#, no-wrap +msgid "CubicFormula (p)" +msgstr "CubicFormula (p)" + +#: C/genius.xml:7853(para) +msgid "" +"Compute roots of a cubic (degree 3) polynomial using the cubic formula. The " +"polynomial should be given as a vector of coefficients. That is " +"<userinput>4*x^3 + 2*x + 1</userinput> corresponds to the vector " +"<userinput>[1,2,0,4]</userinput>. Returns a column vector of the three " +"solutions. The first solution is always the real one as a cubic always has one " +"real solution." +msgstr "" + +#: C/genius.xml:7862(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/CubicFormula.html" +"\">Planetmath</ulink>, <ulink url=\"http://mathworld.wolfram.com/CubicFormula." +"html\">Mathworld</ulink>, or <ulink url=\"http://en.wikipedia.org/wiki/" +"Cubic_equation\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:7872(term) +msgid "<anchor id=\"gel-function-EulersMethod\"/>EulersMethod" +msgstr "<anchor id=\"gel-function-EulersMethod\"/>EulersMethod" + +#: C/genius.xml:7874(synopsis) +#, no-wrap +msgid "EulersMethod (f,x0,y0,x1,n)" +msgstr "EulersMethod (f,x0,y0,x1,n)" + +#: C/genius.xml:7875(para) +msgid "" +"Use classical Euler's method to numerically solve y'=f(x,y) for initial " +"<varname>x0</varname>, <varname>y0</varname> going to <varname>x1</varname> " +"with <varname>n</varname> increments, returns <varname>y</varname> at " +"<varname>x1</varname>. Unless you explicitly want to use Euler's method, you " +"should really think about using <link linkend=\"gel-function-RungeKutta" +"\">RungeKutta</link> for solving ODE." +msgstr "" + +#: C/genius.xml:7885(para) C/genius.xml:7926(para) C/genius.xml:8130(para) +#: C/genius.xml:8168(para) +msgid "" +"Systems can be solved by just having <varname>y</varname> be a (column) vector " +"everywhere. That is, <varname>y0</varname> can be a vector in which case " +"<varname>f</varname> should take a number <varname>x</varname> and a vector of " +"the same size for the second argument and should return a vector of the same " +"size." +msgstr "" + +#: C/genius.xml:7892(para) C/genius.xml:7948(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/EulerForwardMethod.html" +"\">Mathworld</ulink>, or <ulink url=\"http://en.wikipedia.org/wiki/" +"Eulers_method\">Wikipedia</ulink> for more information." +msgstr "" +"Se <ulink url=\"http://mathworld.wolfram.com/EulerForwardMethod.html" +"\">Mathworld</ulink> ellerr <ulink url=\"http://en.wikipedia.org/wiki/" +"Eulers_method\">Wikipedia</ulink> för mer information." + +#: C/genius.xml:7901(term) +msgid "<anchor id=\"gel-function-EulersMethodFull\"/>EulersMethodFull" +msgstr "<anchor id=\"gel-function-EulersMethodFull\"/>EulersMethodFull" + +#: C/genius.xml:7903(synopsis) +#, no-wrap +msgid "EulersMethodFull (f,x0,y0,x1,n)" +msgstr "EulersMethodFull (f,x0,y0,x1,n)" + +#: C/genius.xml:7904(para) +msgid "" +"Use classical Euler's method to numerically solve y'=f(x,y) for initial " +"<varname>x0</varname>, <varname>y0</varname> going to <varname>x1</varname> " +"with <varname>n</varname> increments, returns a 2 by <userinput>n+1</" +"userinput> matrix with the <varname>x</varname> and <varname>y</varname> " +"values. Unless you explicitly want to use Euler's method, you should really " +"think about using <link linkend=\"gel-function-RungeKuttaFull" +"\">RungeKuttaFull</link> for solving ODE. Suitable for plugging into <link " +"linkend=\"gel-function-LinePlotDrawLine\">LinePlotDrawLine</link> or <link " +"linkend=\"gel-function-LinePlotDrawPoints\">LinePlotDrawPoints</link>." +msgstr "" + +#: C/genius.xml:7919(para) +msgid "" +"Example: <screen><prompt>genius></prompt> <userinput>LinePlotClear();</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>line = EulersMethodFull(`(x," +"y)=y,0,1.0,3.0,50);</userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine(line,\"window\",\"fit" +"\",\"color\",\"blue\",\"legend\",\"Exponential growth\");</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:7933(para) +msgid "" +"The output for a system is still a n by 2 matrix with the second entry being a " +"vector. If you wish to plot the line, make sure to use row vectors, and then " +"flatten the matrix with <link linkend=\"gel-function-ExpandMatrix" +"\">ExpandMatrix</link>, and pick out the right columns. Example: " +"<screen><prompt>genius></prompt> <userinput>LinePlotClear();</userinput>\n" +"<prompt>genius></prompt> <userinput>lines = EulersMethodFull(`(x,y)=[y@(2),-" +"y@(1)],0,[1.0,1.0],10.0,500);</userinput>\n" +"<prompt>genius></prompt> <userinput>lines = ExpandMatrix(lines);</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>firstline = lines@(,[1,2]);</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>secondline = lines@(,[1,3]);</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotWindow = [0,10,-2,2];</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine(firstline,\"color\"," +"\"blue\",\"legend\",\"First\");</userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawPoints(secondline,\"color\"," +"\"red\",\"thickness\",3,\"legend\",\"Second\");</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:7958(term) +msgid "<anchor id=\"gel-function-FindRootBisection\"/>FindRootBisection" +msgstr "<anchor id=\"gel-function-FindRootBisection\"/>FindRootBisection" + +#: C/genius.xml:7960(synopsis) +#, no-wrap +msgid "FindRootBisection (f,a,b,TOL,N)" +msgstr "FindRootBisection (f,a,b,TOL,N)" + +#: C/genius.xml:7961(para) +msgid "" +"Find root of a function using the bisection method. <varname>a</varname> and " +"<varname>b</varname> are the initial guess interval, <userinput>f(a)</" +"userinput> and <userinput>f(b)</userinput> should have opposite signs. " +"<varname>TOL</varname> is the desired tolerance and <varname>N</varname> is " +"the limit on the number of iterations to run, 0 means no limit. The function " +"returns a vector <userinput>[success,value,iteration]</userinput>, where " +"<varname>success</varname> is a boolean indicating success, <varname>value</" +"varname> is the last value computed, and <varname>iteration</varname> is the " +"number of iterations done." +msgstr "" + +#: C/genius.xml:7970(term) +msgid "<anchor id=\"gel-function-FindRootFalsePosition\"/>FindRootFalsePosition" +msgstr "<anchor id=\"gel-function-FindRootFalsePosition\"/>FindRootFalsePosition" + +#: C/genius.xml:7972(synopsis) +#, no-wrap +msgid "FindRootFalsePosition (f,a,b,TOL,N)" +msgstr "FindRootFalsePosition (f,a,b,TOL,N)" + +#: C/genius.xml:7973(para) +msgid "" +"Find root of a function using the method of false position. <varname>a</" +"varname> and <varname>b</varname> are the initial guess interval, " +"<userinput>f(a)</userinput> and <userinput>f(b)</userinput> should have " +"opposite signs. <varname>TOL</varname> is the desired tolerance and " +"<varname>N</varname> is the limit on the number of iterations to run, 0 means " +"no limit. The function returns a vector <userinput>[success,value,iteration]</" +"userinput>, where <varname>success</varname> is a boolean indicating success, " +"<varname>value</varname> is the last value computed, and <varname>iteration</" +"varname> is the number of iterations done." +msgstr "" + +#: C/genius.xml:7982(term) +msgid "<anchor id=\"gel-function-FindRootMullersMethod\"/>FindRootMullersMethod" +msgstr "<anchor id=\"gel-function-FindRootMullersMethod\"/>FindRootMullersMethod" + +#: C/genius.xml:7984(synopsis) +#, no-wrap +msgid "FindRootMullersMethod (f,x0,x1,x2,TOL,N)" +msgstr "FindRootMullersMethod (f,x0,x1,x2,TOL,N)" + +#: C/genius.xml:7985(para) +msgid "" +"Find root of a function using the Muller's method. <varname>TOL</varname> is " +"the desired tolerance and <varname>N</varname> is the limit on the number of " +"iterations to run, 0 means no limit. The function returns a vector " +"<userinput>[success,value,iteration]</userinput>, where <varname>success</" +"varname> is a boolean indicating success, <varname>value</varname> is the last " +"value computed, and <varname>iteration</varname> is the number of iterations " +"done." +msgstr "" + +#: C/genius.xml:7992(term) +msgid "<anchor id=\"gel-function-FindRootSecant\"/>FindRootSecant" +msgstr "<anchor id=\"gel-function-FindRootSecant\"/>FindRootSecant" + +#: C/genius.xml:7994(synopsis) +#, no-wrap +msgid "FindRootSecant (f,a,b,TOL,N)" +msgstr "FindRootSecant (f,a,b,TOL,N)" + +#: C/genius.xml:7995(para) +msgid "" +"Find root of a function using the secant method. <varname>a</varname> and " +"<varname>b</varname> are the initial guess interval, <userinput>f(a)</" +"userinput> and <userinput>f(b)</userinput> should have opposite signs. " +"<varname>TOL</varname> is the desired tolerance and <varname>N</varname> is " +"the limit on the number of iterations to run, 0 means no limit. The function " +"returns a vector <userinput>[success,value,iteration]</userinput>, where " +"<varname>success</varname> is a boolean indicating success, <varname>value</" +"varname> is the last value computed, and <varname>iteration</varname> is the " +"number of iterations done." +msgstr "" + +#: C/genius.xml:8004(term) +msgid "<anchor id=\"gel-function-HalleysMethod\"/>HalleysMethod" +msgstr "<anchor id=\"gel-function-HalleysMethod\"/>HalleysMethod" + +#: C/genius.xml:8006(synopsis) +#, no-wrap +msgid "HalleysMethod (f,df,ddf,guess,epsilon,maxn)" +msgstr "" + +#: C/genius.xml:8007(para) +msgid "" +"Find zeros using Halley's method. <varname>f</varname> is the function, " +"<varname>df</varname> is the derivative of <varname>f</varname>, and " +"<varname>ddf</varname> is the second derivative of <varname>f</varname>. " +"<varname>guess</varname> is the initial guess. The function returns after two " +"successive values are within <varname>epsilon</varname> of each other, or " +"after <varname>maxn</varname> tries, in which case the function returns " +"<constant>null</constant> indicating failure." +msgstr "" + +#: C/genius.xml:8014(para) +msgid "" +"See also <link linkend=\"gel-function-NewtonsMethod\"><function>NewtonsMethod</" +"function></link> and <link linkend=\"gel-function-SymbolicDerivative" +"\"><function>SymbolicDerivative</function></link>." +msgstr "" +"Se även <link linkend=\"gel-function-NewtonsMethod\"><function>NewtonsMethod</" +"function></link> och <link linkend=\"gel-function-SymbolicDerivative" +"\"><function>SymbolicDerivative</function></link>." + +#: C/genius.xml:8017(para) +msgid "" +"Example to find the square root of 10: <screen><prompt>genius></prompt> " +"<userinput>HalleysMethod(`(x)=x^2-10,`(x)=2*x,`(x)=2,3,10^-10,100)</" +"userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8022(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Halley%27s_method\">Wikipedia</" +"ulink> for more information." +msgstr "" +"Se <ulink url=\"http://en.wikipedia.org/wiki/Halley%27s_method\">Wikipedia</" +"ulink> för mer information." + +#: C/genius.xml:8031(term) +msgid "<anchor id=\"gel-function-NewtonsMethod\"/>NewtonsMethod" +msgstr "<anchor id=\"gel-function-NewtonsMethod\"/>NewtonsMethod" + +#: C/genius.xml:8033(synopsis) +#, no-wrap +msgid "NewtonsMethod (f,df,guess,epsilon,maxn)" +msgstr "" + +#: C/genius.xml:8034(para) +msgid "" +"Find zeros using Newton's method. <varname>f</varname> is the function and " +"<varname>df</varname> is the derivative of <varname>f</varname>. " +"<varname>guess</varname> is the initial guess. The function returns after two " +"successive values are within <varname>epsilon</varname> of each other, or " +"after <varname>maxn</varname> tries, in which case the function returns " +"<constant>null</constant> indicating failure." +msgstr "" + +#: C/genius.xml:8040(para) +msgid "" +"See also <link linkend=\"gel-function-NewtonsMethodPoly" +"\"><function>NewtonsMethodPoly</function></link> and <link linkend=\"gel-" +"function-SymbolicDerivative\"><function>SymbolicDerivative</function></link>." +msgstr "" + +#: C/genius.xml:8043(para) +msgid "" +"Example to find the square root of 10: <screen><prompt>genius></prompt> " +"<userinput>NewtonsMethod(`(x)=x^2-10,`(x)=2*x,3,10^-10,100)</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8048(para) C/genius.xml:8382(para) +msgid "" +"See <ulink url=\"http://en.wikipedia.org/wiki/Newtons_method\">Wikipedia</" +"ulink> for more information." +msgstr "" +"Se <ulink url=\"http://en.wikipedia.org/wiki/Newtons_method\">Wikipedia</" +"ulink> för mer information." + +#: C/genius.xml:8057(term) +msgid "<anchor id=\"gel-function-PolynomialRoots\"/>PolynomialRoots" +msgstr "<anchor id=\"gel-function-PolynomialRoots\"/>PolynomialRoots" + +#: C/genius.xml:8059(synopsis) +#, no-wrap +msgid "PolynomialRoots (p)" +msgstr "PolynomialRoots (p)" + +#: C/genius.xml:8060(para) +msgid "" +"Compute roots of a polynomial (degrees 1 through 4) using one of the formulas " +"for such polynomials. The polynomial should be given as a vector of " +"coefficients. That is <userinput>4*x^3 + 2*x + 1</userinput> corresponds to " +"the vector <userinput>[1,2,0,4]</userinput>. Returns a column vector of the " +"solutions." +msgstr "" + +#: C/genius.xml:8069(para) +msgid "" +"The function calls <link linkend=\"gel-function-QuadraticFormula" +"\">QuadraticFormula</link>, <link linkend=\"gel-function-CubicFormula" +"\">CubicFormula</link>, and <link linkend=\"gel-function-QuarticFormula" +"\">QuarticFormula</link>." +msgstr "" + +#: C/genius.xml:8079(term) +msgid "<anchor id=\"gel-function-QuadraticFormula\"/>QuadraticFormula" +msgstr "<anchor id=\"gel-function-QuadraticFormula\"/>QuadraticFormula" + +#: C/genius.xml:8081(synopsis) +#, no-wrap +msgid "QuadraticFormula (p)" +msgstr "QuadraticFormula (p)" + +#: C/genius.xml:8082(para) +msgid "" +"Compute roots of a quadratic (degree 2) polynomial using the quadratic " +"formula. The polynomial should be given as a vector of coefficients. That is " +"<userinput>3*x^2 + 2*x + 1</userinput> corresponds to the vector " +"<userinput>[1,2,3]</userinput>. Returns a column vector of the two solutions." +msgstr "" + +#: C/genius.xml:8090(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/QuadraticFormula.html" +"\">Planetmath</ulink> or <ulink url=\"http://mathworld.wolfram.com/" +"QuadraticFormula.html\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:8099(term) +msgid "<anchor id=\"gel-function-QuarticFormula\"/>QuarticFormula" +msgstr "<anchor id=\"gel-function-QuarticFormula\"/>QuarticFormula" + +#: C/genius.xml:8101(synopsis) +#, no-wrap +msgid "QuarticFormula (p)" +msgstr "QuarticFormula (p)" + +#: C/genius.xml:8102(para) +msgid "" +"Compute roots of a quartic (degree 4) polynomial using the quartic formula. " +"The polynomial should be given as a vector of coefficients. That is " +"<userinput>5*x^4 + 2*x + 1</userinput> corresponds to the vector " +"<userinput>[1,2,0,0,5]</userinput>. Returns a column vector of the four " +"solutions." +msgstr "" + +#: C/genius.xml:8110(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/QuarticFormula.html" +"\">Planetmath</ulink>, <ulink url=\"http://mathworld.wolfram.com/" +"QuarticEquation.html\">Mathworld</ulink>, or <ulink url=\"http://en.wikipedia." +"org/wiki/Quartic_equation\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:8120(term) +msgid "<anchor id=\"gel-function-RungeKutta\"/>RungeKutta" +msgstr "<anchor id=\"gel-function-RungeKutta\"/>RungeKutta" + +#: C/genius.xml:8122(synopsis) +#, no-wrap +msgid "RungeKutta (f,x0,y0,x1,n)" +msgstr "RungeKutta (f,x0,y0,x1,n)" + +#: C/genius.xml:8123(para) +msgid "" +"Use classical non-adaptive fourth order Runge-Kutta method to numerically " +"solve y'=f(x,y) for initial <varname>x0</varname>, <varname>y0</varname> going " +"to <varname>x1</varname> with <varname>n</varname> increments, returns " +"<varname>y</varname> at <varname>x1</varname>." +msgstr "" + +#: C/genius.xml:8137(para) C/genius.xml:8190(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/Runge-KuttaMethod.html" +"\">Mathworld</ulink>, or <ulink url=\"http://en.wikipedia.org/wiki/Runge-" +"Kutta_methods\">Wikipedia</ulink> for more information." +msgstr "" + +#: C/genius.xml:8146(term) +msgid "<anchor id=\"gel-function-RungeKuttaFull\"/>RungeKuttaFull" +msgstr "<anchor id=\"gel-function-RungeKuttaFull\"/>RungeKuttaFull" + +#: C/genius.xml:8148(synopsis) +#, no-wrap +msgid "RungeKuttaFull (f,x0,y0,x1,n)" +msgstr "RungeKuttaFull (f,x0,y0,x1,n)" + +#: C/genius.xml:8149(para) +msgid "" +"Use classical non-adaptive fourth order Runge-Kutta method to numerically " +"solve y'=f(x,y) for initial <varname>x0</varname>, <varname>y0</varname> going " +"to <varname>x1</varname> with <varname>n</varname> increments, returns a 2 by " +"<userinput>n+1</userinput> matrix with the <varname>x</varname> and " +"<varname>y</varname> values. Suitable for plugging into <link linkend=\"gel-" +"function-LinePlotDrawLine\">LinePlotDrawLine</link> or <link linkend=\"gel-" +"function-LinePlotDrawPoints\">LinePlotDrawPoints</link>." +msgstr "" + +#: C/genius.xml:8161(para) +msgid "" +"Example: <screen><prompt>genius></prompt> <userinput>LinePlotClear();</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>line = RungeKuttaFull(`(x," +"y)=y,0,1.0,3.0,50);</userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine(line,\"window\",\"fit" +"\",\"color\",\"blue\",\"legend\",\"Exponential growth\");</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8175(para) +msgid "" +"The output for a system is still a n by 2 matrix with the second entry being a " +"vector. If you wish to plot the line, make sure to use row vectors, and then " +"flatten the matrix with <link linkend=\"gel-function-ExpandMatrix" +"\">ExpandMatrix</link>, and pick out the right columns. Example: " +"<screen><prompt>genius></prompt> <userinput>LinePlotClear();</userinput>\n" +"<prompt>genius></prompt> <userinput>lines = RungeKuttaFull(`(x,y)=[y@(2),-" +"y@(1)],0,[1.0,1.0],10.0,100);</userinput>\n" +"<prompt>genius></prompt> <userinput>lines = ExpandMatrix(lines);</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>firstline = lines@(,[1,2]);</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>secondline = lines@(,[1,3]);</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotWindow = [0,10,-2,2];</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine(firstline,\"color\"," +"\"blue\",\"legend\",\"First\");</userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawPoints(secondline,\"color\"," +"\"red\",\"thickness\",3,\"legend\",\"Second\");</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8204(title) +msgid "Statistics" +msgstr "" + +#: C/genius.xml:8207(term) +msgid "<anchor id=\"gel-function-Average\"/>Average" +msgstr "<anchor id=\"gel-function-Average\"/>Average" + +#: C/genius.xml:8209(synopsis) +#, no-wrap +msgid "Average (m)" +msgstr "Average (m)" + +#: C/genius.xml:8210(para) +msgid "" +"Aliases: <function>average</function><function>Mean</function><function>mean</" +"function>" +msgstr "" +"Alias: <function>average</function><function>Mean</function><function>mean</" +"function>" + +#: C/genius.xml:8211(para) +msgid "Calculate average of an entire matrix." +msgstr "" + +#: C/genius.xml:8212(para) C/genius.xml:8272(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/ArithmeticMean.html\">Mathworld</" +"ulink> for more information." +msgstr "" + +#: C/genius.xml:8220(term) +msgid "<anchor id=\"gel-function-GaussDistribution\"/>GaussDistribution" +msgstr "<anchor id=\"gel-function-GaussDistribution\"/>GaussDistribution" + +#: C/genius.xml:8222(synopsis) +#, no-wrap +msgid "GaussDistribution (x,sigma)" +msgstr "GaussDistribution (x,sigma)" + +#: C/genius.xml:8223(para) +msgid "" +"Integral of the GaussFunction from 0 to <varname>x</varname> (area under the " +"normal curve)." +msgstr "" + +#: C/genius.xml:8224(para) C/genius.xml:8236(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/NormalDistribution.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:8232(term) +msgid "<anchor id=\"gel-function-GaussFunction\"/>GaussFunction" +msgstr "<anchor id=\"gel-function-GaussFunction\"/>GaussFunction" + +#: C/genius.xml:8234(synopsis) +#, no-wrap +msgid "GaussFunction (x,sigma)" +msgstr "GaussFunction (x,sigma)" + +#: C/genius.xml:8235(para) +msgid "The normalized Gauss distribution function (the normal curve)." +msgstr "" + +#: C/genius.xml:8245(term) +msgid "<anchor id=\"gel-function-Median\"/>Median" +msgstr "<anchor id=\"gel-function-Median\"/>Median" + +#: C/genius.xml:8247(synopsis) +#, no-wrap +msgid "Median (m)" +msgstr "Median (m)" + +#: C/genius.xml:8248(para) +msgid "Aliases: <function>median</function>" +msgstr "Alias: <function>median</function>" + +#: C/genius.xml:8249(para) +msgid "Calculate median of an entire matrix." +msgstr "" + +#: C/genius.xml:8250(para) C/genius.xml:8285(para) +msgid "" +"See <ulink url=\"http://mathworld.wolfram.com/StatisticalMedian.html" +"\">Mathworld</ulink> for more information." +msgstr "" + +#: C/genius.xml:8258(term) +msgid "" +"<anchor id=\"gel-function-PopulationStandardDeviation\"/" +">PopulationStandardDeviation" +msgstr "" +"<anchor id=\"gel-function-PopulationStandardDeviation\"/" +">PopulationStandardDeviation" + +#: C/genius.xml:8260(synopsis) +#, no-wrap +msgid "PopulationStandardDeviation (m)" +msgstr "PopulationStandardDeviation (m)" + +#: C/genius.xml:8261(para) +msgid "Aliases: <function>stdevp</function>" +msgstr "Alias: <function>stdevp</function>" + +#: C/genius.xml:8262(para) +msgid "Calculate the population standard deviation of a whole matrix." +msgstr "" + +#: C/genius.xml:8267(term) +msgid "<anchor id=\"gel-function-RowAverage\"/>RowAverage" +msgstr "<anchor id=\"gel-function-RowAverage\"/>RowAverage" + +#: C/genius.xml:8269(synopsis) +#, no-wrap +msgid "RowAverage (m)" +msgstr "RowAverage (m)" + +#: C/genius.xml:8270(para) +msgid "Aliases: <function>RowMean</function>" +msgstr "Alias: <function>RowMean</function>" + +#: C/genius.xml:8271(para) +msgid "Calculate average of each row in a matrix." +msgstr "" + +#: C/genius.xml:8280(term) +msgid "<anchor id=\"gel-function-RowMedian\"/>RowMedian" +msgstr "<anchor id=\"gel-function-RowMedian\"/>RowMedian" + +#: C/genius.xml:8282(synopsis) +#, no-wrap +msgid "RowMedian (m)" +msgstr "RowMedian (m)" + +#: C/genius.xml:8283(para) +msgid "" +"Calculate median of each row in a matrix and return a column vector of the " +"medians." +msgstr "" + +#: C/genius.xml:8293(term) +msgid "" +"<anchor id=\"gel-function-RowPopulationStandardDeviation\"/" +">RowPopulationStandardDeviation" +msgstr "" +"<anchor id=\"gel-function-RowPopulationStandardDeviation\"/" +">RowPopulationStandardDeviation" + +#: C/genius.xml:8295(synopsis) +#, no-wrap +msgid "RowPopulationStandardDeviation (m)" +msgstr "RowPopulationStandardDeviation (m)" + +#: C/genius.xml:8296(para) +msgid "Aliases: <function>rowstdevp</function>" +msgstr "Alias: <function>rowstdevp</function>" + +#: C/genius.xml:8297(para) +msgid "" +"Calculate the population standard deviations of rows of a matrix and return a " +"vertical vector." +msgstr "" + +#: C/genius.xml:8302(term) +msgid "<anchor id=\"gel-function-RowStandardDeviation\"/>RowStandardDeviation" +msgstr "<anchor id=\"gel-function-RowStandardDeviation\"/>RowStandardDeviation" + +#: C/genius.xml:8304(synopsis) +#, no-wrap +msgid "RowStandardDeviation (m)" +msgstr "RowStandardDeviation (m)" + +#: C/genius.xml:8305(para) +msgid "Aliases: <function>rowstdev</function>" +msgstr "Alias: <function>rowstdev</function>" + +#: C/genius.xml:8306(para) +msgid "" +"Calculate the standard deviations of rows of a matrix and return a vertical " +"vector." +msgstr "" + +#: C/genius.xml:8311(term) +msgid "<anchor id=\"gel-function-StandardDeviation\"/>StandardDeviation" +msgstr "<anchor id=\"gel-function-StandardDeviation\"/>StandardDeviation" + +#: C/genius.xml:8313(synopsis) +#, no-wrap +msgid "StandardDeviation (m)" +msgstr "StandardDeviation (m)" + +#: C/genius.xml:8314(para) +msgid "Aliases: <function>stdev</function>" +msgstr "Alias: <function>stdev</function>" + +#: C/genius.xml:8315(para) +msgid "Calculate the standard deviation of a whole matrix." +msgstr "" + +#: C/genius.xml:8323(title) +msgid "Polynomials" +msgstr "" + +#: C/genius.xml:8326(term) +msgid "<anchor id=\"gel-function-AddPoly\"/>AddPoly" +msgstr "<anchor id=\"gel-function-AddPoly\"/>AddPoly" + +#: C/genius.xml:8328(synopsis) +#, no-wrap +msgid "AddPoly (p1,p2)" +msgstr "AddPoly (p1,p2)" + +#: C/genius.xml:8329(para) +msgid "Add two polynomials (vectors)." +msgstr "" + +#: C/genius.xml:8334(term) +msgid "<anchor id=\"gel-function-DividePoly\"/>DividePoly" +msgstr "<anchor id=\"gel-function-DividePoly\"/>DividePoly" + +#: C/genius.xml:8336(synopsis) +#, no-wrap +msgid "DividePoly (p,q,&r)" +msgstr "DividePoly (p,q,&r)" + +#: C/genius.xml:8337(para) +msgid "" +"Divide two polynomials (as vectors) using long division. Returns the quotient " +"of the two polynomials. The optional argument <varname>r</varname> is used to " +"return the remainder. The remainder will have lower degree than <varname>q</" +"varname>." +msgstr "" + +#: C/genius.xml:8342(para) +msgid "" +"See <ulink url=\"http://planetmath.org/encyclopedia/PolynomialLongDivision.html" +"\">Planetmath</ulink> for more information." +msgstr "" + +#: C/genius.xml:8350(term) +msgid "<anchor id=\"gel-function-IsPoly\"/>IsPoly" +msgstr "<anchor id=\"gel-function-IsPoly\"/>IsPoly" + +#: C/genius.xml:8352(synopsis) +#, no-wrap +msgid "IsPoly (p)" +msgstr "IsPoly (p)" + +#: C/genius.xml:8353(para) +msgid "Check if a vector is usable as a polynomial." +msgstr "" + +#: C/genius.xml:8358(term) +msgid "<anchor id=\"gel-function-MultiplyPoly\"/>MultiplyPoly" +msgstr "<anchor id=\"gel-function-MultiplyPoly\"/>MultiplyPoly" + +#: C/genius.xml:8360(synopsis) +#, no-wrap +msgid "MultiplyPoly (p1,p2)" +msgstr "MultiplyPoly (p1,p2)" + +#: C/genius.xml:8361(para) +msgid "Multiply two polynomials (as vectors)." +msgstr "" + +#: C/genius.xml:8366(term) +msgid "<anchor id=\"gel-function-NewtonsMethodPoly\"/>NewtonsMethodPoly" +msgstr "<anchor id=\"gel-function-NewtonsMethodPoly\"/>NewtonsMethodPoly" + +#: C/genius.xml:8368(synopsis) +#, no-wrap +msgid "NewtonsMethodPoly (poly,guess,epsilon,maxn)" +msgstr "" + +#: C/genius.xml:8369(para) +msgid "" +"Find a root of a polynomial using Newton's method. <varname>poly</varname> is " +"the polynomial as a vector and <varname>guess</varname> is the initial guess. " +"The function returns after two successive values are within <varname>epsilon</" +"varname> of each other, or after <varname>maxn</varname> tries, in which case " +"the function returns <constant>null</constant> indicating failure." +msgstr "" + +#: C/genius.xml:8374(para) +msgid "" +"See also <link linkend=\"gel-function-NewtonsMethod\"><function>NewtonsMethod</" +"function></link>." +msgstr "" + +#: C/genius.xml:8377(para) +msgid "" +"Example to find the square root of 10: <screen><prompt>genius></prompt> " +"<userinput>NewtonsMethodPoly([-10,0,1],3,10^-10,100)</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8390(term) +msgid "<anchor id=\"gel-function-Poly2ndDerivative\"/>Poly2ndDerivative" +msgstr "<anchor id=\"gel-function-Poly2ndDerivative\"/>Poly2ndDerivative" + +#: C/genius.xml:8392(synopsis) +#, no-wrap +msgid "Poly2ndDerivative (p)" +msgstr "Poly2ndDerivative (p)" + +#: C/genius.xml:8393(para) +msgid "Take second polynomial (as vector) derivative." +msgstr "" + +#: C/genius.xml:8398(term) +msgid "<anchor id=\"gel-function-PolyDerivative\"/>PolyDerivative" +msgstr "<anchor id=\"gel-function-PolyDerivative\"/>PolyDerivative" + +#: C/genius.xml:8400(synopsis) +#, no-wrap +msgid "PolyDerivative (p)" +msgstr "PolyDerivative (p)" + +#: C/genius.xml:8401(para) +msgid "Take polynomial (as vector) derivative." +msgstr "" + +#: C/genius.xml:8406(term) +msgid "<anchor id=\"gel-function-PolyToFunction\"/>PolyToFunction" +msgstr "<anchor id=\"gel-function-PolyToFunction\"/>PolyToFunction" + +#: C/genius.xml:8408(synopsis) +#, no-wrap +msgid "PolyToFunction (p)" +msgstr "PolyToFunction (p)" + +#: C/genius.xml:8409(para) +msgid "Make function out of a polynomial (as vector)." +msgstr "" + +#: C/genius.xml:8414(term) +msgid "<anchor id=\"gel-function-PolyToString\"/>PolyToString" +msgstr "<anchor id=\"gel-function-PolyToString\"/>PolyToString" + +#: C/genius.xml:8416(synopsis) +#, no-wrap +msgid "PolyToString (p,var...)" +msgstr "PolyToString (p,var...)" + +#: C/genius.xml:8417(para) +msgid "Make string out of a polynomial (as vector)." +msgstr "" + +#: C/genius.xml:8422(term) +msgid "<anchor id=\"gel-function-SubtractPoly\"/>SubtractPoly" +msgstr "<anchor id=\"gel-function-SubtractPoly\"/>SubtractPoly" + +#: C/genius.xml:8424(synopsis) +#, no-wrap +msgid "SubtractPoly (p1,p2)" +msgstr "SubtractPoly (p1,p2)" + +#: C/genius.xml:8425(para) +msgid "Subtract two polynomials (as vectors)." +msgstr "" + +#: C/genius.xml:8430(term) +msgid "<anchor id=\"gel-function-TrimPoly\"/>TrimPoly" +msgstr "<anchor id=\"gel-function-TrimPoly\"/>TrimPoly" + +#: C/genius.xml:8432(synopsis) +#, no-wrap +msgid "TrimPoly (p)" +msgstr "TrimPoly (p)" + +#: C/genius.xml:8433(para) +msgid "Trim zeros from a polynomial (as vector)." +msgstr "" + +#: C/genius.xml:8441(title) +msgid "Set Theory" +msgstr "" + +#: C/genius.xml:8444(term) +msgid "<anchor id=\"gel-function-Intersection\"/>Intersection" +msgstr "<anchor id=\"gel-function-Intersection\"/>Intersection" + +#: C/genius.xml:8446(synopsis) +#, no-wrap +msgid "Intersection (X,Y)" +msgstr "Intersection (X,Y)" + +#: C/genius.xml:8447(para) +msgid "" +"Returns a set theoretic intersection of X and Y (X and Y are vectors " +"pretending to be sets)." +msgstr "" + +#: C/genius.xml:8452(term) +msgid "<anchor id=\"gel-function-IsIn\"/>IsIn" +msgstr "<anchor id=\"gel-function-IsIn\"/>IsIn" + +#: C/genius.xml:8454(synopsis) +#, no-wrap +msgid "IsIn (x,X)" +msgstr "IsIn (x,X)" + +#: C/genius.xml:8455(para) +msgid "" +"Returns <constant>true</constant> if the element x is in the set X (where X is " +"a vector pretending to be a set)." +msgstr "" + +#: C/genius.xml:8460(term) +msgid "<anchor id=\"gel-function-IsSubset\"/>IsSubset" +msgstr "<anchor id=\"gel-function-IsSubset\"/>IsSubset" + +#: C/genius.xml:8462(synopsis) +#, no-wrap +msgid "IsSubset (X, Y)" +msgstr "IsSubset (X, Y)" + +#: C/genius.xml:8463(para) +msgid "" +"Returns <constant>true</constant> if X is a subset of Y (X and Y are vectors " +"pretending to be sets)." +msgstr "" + +#: C/genius.xml:8468(term) +msgid "<anchor id=\"gel-function-MakeSet\"/>MakeSet" +msgstr "<anchor id=\"gel-function-MakeSet\"/>MakeSet" + +#: C/genius.xml:8470(synopsis) +#, no-wrap +msgid "MakeSet (X)" +msgstr "MakeSet (X)" + +#: C/genius.xml:8471(para) +msgid "Returns a vector where every element of X appears only once." +msgstr "" + +#: C/genius.xml:8476(term) +msgid "<anchor id=\"gel-function-SetMinus\"/>SetMinus" +msgstr "<anchor id=\"gel-function-SetMinus\"/>SetMinus" + +#: C/genius.xml:8478(synopsis) +#, no-wrap +msgid "SetMinus (X,Y)" +msgstr "SetMinus (X,Y)" + +#: C/genius.xml:8479(para) +msgid "" +"Returns a set theoretic difference X-Y (X and Y are vectors pretending to be " +"sets)." +msgstr "" + +#: C/genius.xml:8484(term) +msgid "<anchor id=\"gel-function-Union\"/>Union" +msgstr "<anchor id=\"gel-function-Union\"/>Union" + +#: C/genius.xml:8486(synopsis) +#, no-wrap +msgid "Union (X,Y)" +msgstr "Union (X,Y)" + +#: C/genius.xml:8487(para) +msgid "" +"Returns a set theoretic union of X and Y (X and Y are vectors pretending to be " +"sets)." +msgstr "" + +#: C/genius.xml:8495(title) +msgid "Commutative Algebra" +msgstr "" + +#: C/genius.xml:8498(term) +msgid "<anchor id=\"gel-function-MacaulayBound\"/>MacaulayBound" +msgstr "<anchor id=\"gel-function-MacaulayBound\"/>MacaulayBound" + +#: C/genius.xml:8500(synopsis) +#, no-wrap +msgid "MacaulayBound (c,d)" +msgstr "MacaulayBound (c,d)" + +#: C/genius.xml:8501(para) +msgid "" +"For a Hilbert function that is c for degree d, given the Macaulay bound for " +"the Hilbert function of degree d+1 (The c^<d> operator from Green's " +"proof)." +msgstr "" + +#: C/genius.xml:8507(term) +msgid "<anchor id=\"gel-function-MacaulayLowerOperator\"/>MacaulayLowerOperator" +msgstr "<anchor id=\"gel-function-MacaulayLowerOperator\"/>MacaulayLowerOperator" + +#: C/genius.xml:8509(synopsis) +#, no-wrap +msgid "MacaulayLowerOperator (c,d)" +msgstr "MacaulayLowerOperator (c,d)" + +#: C/genius.xml:8510(para) +msgid "The c_<d> operator from Green's proof of Macaulay's Theorem." +msgstr "" + +#: C/genius.xml:8516(term) +msgid "<anchor id=\"gel-function-MacaulayRep\"/>MacaulayRep" +msgstr "<anchor id=\"gel-function-MacaulayRep\"/>MacaulayRep" + +#: C/genius.xml:8518(synopsis) +#, no-wrap +msgid "MacaulayRep (c,d)" +msgstr "MacaulayRep (c,d)" + +#: C/genius.xml:8519(para) +msgid "Return the dth Macaulay representation of a positive integer c." +msgstr "" + +#: C/genius.xml:8527(title) +msgid "Miscellaneous" +msgstr "" + +#: C/genius.xml:8530(term) +msgid "<anchor id=\"gel-function-ASCIIToString\"/>ASCIIToString" +msgstr "<anchor id=\"gel-function-ASCIIToString\"/>ASCIIToString" + +#: C/genius.xml:8532(synopsis) +#, no-wrap +msgid "ASCIIToString (vec)" +msgstr "" + +#: C/genius.xml:8533(para) +msgid "Convert a vector of ASCII values to a string." +msgstr "" + +#: C/genius.xml:8538(term) +msgid "<anchor id=\"gel-function-AlphabetToString\"/>AlphabetToString" +msgstr "<anchor id=\"gel-function-AlphabetToString\"/>AlphabetToString" + +#: C/genius.xml:8540(synopsis) +#, no-wrap +msgid "AlphabetToString (vec,alphabet)" +msgstr "" + +#: C/genius.xml:8541(para) +msgid "" +"Convert a vector of 0-based alphabet values (positions in the alphabet string) " +"to a string." +msgstr "" + +#: C/genius.xml:8546(term) +msgid "<anchor id=\"gel-function-StringToASCII\"/>StringToASCII" +msgstr "<anchor id=\"gel-function-StringToASCII\"/>StringToASCII" + +#: C/genius.xml:8548(synopsis) +#, no-wrap +msgid "StringToASCII (str)" +msgstr "StringToASCII (str)" + +#: C/genius.xml:8549(para) +msgid "Convert a string to a vector of ASCII values." +msgstr "" + +#: C/genius.xml:8554(term) +msgid "<anchor id=\"gel-function-StringToAlphabet\"/>StringToAlphabet" +msgstr "<anchor id=\"gel-function-StringToAlphabet\"/>StringToAlphabet" + +#: C/genius.xml:8556(synopsis) +#, no-wrap +msgid "StringToAlphabet (str,alphabet)" +msgstr "" + +#: C/genius.xml:8557(para) +msgid "" +"Convert a string to a vector of 0-based alphabet values (positions in the " +"alphabet string), -1's for unknown letters." +msgstr "" + +#: C/genius.xml:8565(title) +msgid "Symbolic Operations" +msgstr "" + +#: C/genius.xml:8568(term) +msgid "<anchor id=\"gel-function-SymbolicDerivative\"/>SymbolicDerivative" +msgstr "<anchor id=\"gel-function-SymbolicDerivative\"/>SymbolicDerivative" + +#: C/genius.xml:8570(synopsis) +#, no-wrap +msgid "SymbolicDerivative (f)" +msgstr "SymbolicDerivative (f)" + +#: C/genius.xml:8571(para) +msgid "" +"Attempt to symbolically differentiate the function f, where f is a function of " +"one variable." +msgstr "" + +#: C/genius.xml:8572(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>SymbolicDerivative(sin)</userinput>\n" +"= (`(x)=cos(x))\n" +"<prompt>genius></prompt> <userinput>SymbolicDerivative(`(x)=7*x^2)</" +"userinput>\n" +"= (`(x)=(7*(2*x)))\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8584(term) +msgid "<anchor id=\"gel-function-SymbolicDerivativeTry\"/>SymbolicDerivativeTry" +msgstr "<anchor id=\"gel-function-SymbolicDerivativeTry\"/>SymbolicDerivativeTry" + +#: C/genius.xml:8586(synopsis) +#, no-wrap +msgid "SymbolicDerivativeTry (f)" +msgstr "SymbolicDerivativeTry (f)" + +#: C/genius.xml:8587(para) +msgid "" +"Attempt to symbolically differentiate the function f, where f is a function of " +"one variable, returns <constant>null</constant> if unsuccessful but is silent. " +"(See <link linkend=\"gel-function-SymbolicDerivative" +"\"><function>SymbolicDerivative</function></link>)" +msgstr "" + +#: C/genius.xml:8594(term) +msgid "<anchor id=\"gel-function-SymbolicNthDerivative\"/>SymbolicNthDerivative" +msgstr "<anchor id=\"gel-function-SymbolicNthDerivative\"/>SymbolicNthDerivative" + +#: C/genius.xml:8596(synopsis) +#, no-wrap +msgid "SymbolicNthDerivative (f,n)" +msgstr "SymbolicNthDerivative (f,n)" + +#: C/genius.xml:8597(para) +msgid "" +"Attempt to symbolically differentiate a function n times. (See <link linkend=" +"\"gel-function-SymbolicDerivative\"><function>SymbolicDerivative</function></" +"link>)" +msgstr "" + +#: C/genius.xml:8604(term) +msgid "" +"<anchor id=\"gel-function-SymbolicNthDerivativeTry\"/>SymbolicNthDerivativeTry" +msgstr "" +"<anchor id=\"gel-function-SymbolicNthDerivativeTry\"/>SymbolicNthDerivativeTry" + +#: C/genius.xml:8606(synopsis) +#, no-wrap +msgid "SymbolicNthDerivativeTry (f,n)" +msgstr "SymbolicNthDerivativeTry (f,n)" + +#: C/genius.xml:8607(para) +msgid "" +"Attempt to symbolically differentiate a function n times quietly and return " +"<constant>null</constant> on failure (See <link linkend=\"gel-function-" +"SymbolicNthDerivative\"><function>SymbolicNthDerivative</function></link>)" +msgstr "" + +#: C/genius.xml:8614(term) +msgid "" +"<anchor id=\"gel-function-SymbolicTaylorApproximationFunction\"/" +">SymbolicTaylorApproximationFunction" +msgstr "" +"<anchor id=\"gel-function-SymbolicTaylorApproximationFunction\"/" +">SymbolicTaylorApproximationFunction" + +#: C/genius.xml:8616(synopsis) +#, no-wrap +msgid "SymbolicTaylorApproximationFunction (f,x0,n)" +msgstr "SymbolicTaylorApproximationFunction (f,x0,n)" + +#: C/genius.xml:8617(para) +msgid "" +"Attempt to construct the Taylor approximation function around x0 to the nth " +"degree. (See <link linkend=\"gel-function-SymbolicDerivative" +"\"><function>SymbolicDerivative</function></link>)" +msgstr "" + +#: C/genius.xml:8629(term) +msgid "<anchor id=\"gel-function-ExportPlot\"/>ExportPlot" +msgstr "<anchor id=\"gel-function-ExportPlot\"/>ExportPlot" + +#: C/genius.xml:8631(synopsis) +#, no-wrap +msgid "ExportPlot (file,type)" +msgstr "" + +#: C/genius.xml:8632(synopsis) +#, no-wrap +msgid "ExportPlot (file)" +msgstr "" + +#: C/genius.xml:8633(para) +msgid "" +"Export the contents of the plotting window to a file. The type is a string " +"that specifies the file type to use, \"png\", \"eps\", or \"ps\". If the type " +"is not specified, then it is taken to be the extension, in which case the " +"extension must be \".png\", \".eps\", or \".ps\"." +msgstr "" + +#: C/genius.xml:8640(para) +msgid "Note that files are overwritten without asking." +msgstr "" + +#: C/genius.xml:8643(para) +msgid "" +"On successful export, true is returned. Otherwise error is printed and " +"exception is raised." +msgstr "" + +#: C/genius.xml:8647(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> <userinput>ExportPlot(\"file.png" +"\")</userinput>\n" +"<prompt>genius></prompt> <userinput>ExportPlot(\"/directory/file\",\"eps" +"\")</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8658(term) +msgid "<anchor id=\"gel-function-LinePlot\"/>LinePlot" +msgstr "<anchor id=\"gel-function-LinePlot\"/>LinePlot" + +#: C/genius.xml:8660(synopsis) +#, no-wrap +msgid "LinePlot (func1,func2,func3,...)" +msgstr "" + +#: C/genius.xml:8661(synopsis) +#, no-wrap +msgid "LinePlot (func1,func2,func3,x1,x2)" +msgstr "" + +#: C/genius.xml:8662(synopsis) +#, no-wrap +msgid "LinePlot (func1,func2,func3,x1,x2,y1,y2)" +msgstr "" + +#: C/genius.xml:8663(synopsis) +#, no-wrap +msgid "LinePlot (func1,func2,func3,[x1,x2])" +msgstr "" + +#: C/genius.xml:8664(synopsis) +#, no-wrap +msgid "LinePlot (func1,func2,func3,[x1,x2,y1,y2])" +msgstr "" + +#: C/genius.xml:8665(para) +msgid "" +"Plot a function (or several functions) with a line. First (up to 10) arguments " +"are functions, then optionally you can specify the limits of the plotting " +"window as <varname>x1</varname>, <varname>x2</varname>, <varname>y1</varname>, " +"<varname>y2</varname>. If limits are not specified, then the currently set " +"limits apply (See <link linkend=\"gel-function-LinePlotWindow" +"\"><function>LinePlotWindow</function></link>) If the y limits are not " +"specified, then the functions are computed and then the maxima and minima are " +"used." +msgstr "" + +#: C/genius.xml:8676(para) C/genius.xml:8839(para) C/genius.xml:8866(para) +#: C/genius.xml:8968(para) C/genius.xml:9271(para) +msgid "" +"The parameter <link linkend=\"gel-function-LinePlotDrawLegends" +"\"><function>LinePlotDrawLegends</function></link> controls the drawing of the " +"legend." +msgstr "" + +#: C/genius.xml:8681(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> <userinput>LinePlot(sin,cos)</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlot(`(x)=x^2,-1,1,0,1)</" +"userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8691(term) +msgid "<anchor id=\"gel-function-LinePlotClear\"/>LinePlotClear" +msgstr "<anchor id=\"gel-function-LinePlotClear\"/>LinePlotClear" + +#: C/genius.xml:8693(synopsis) +#, no-wrap +msgid "LinePlotClear ()" +msgstr "LinePlotClear ()" + +#: C/genius.xml:8694(para) +msgid "" +"Show the line plot window and clear out functions and any other lines that " +"were drawn." +msgstr "" + +#: C/genius.xml:8702(term) +msgid "<anchor id=\"gel-function-LinePlotDrawLine\"/>LinePlotDrawLine" +msgstr "<anchor id=\"gel-function-LinePlotDrawLine\"/>LinePlotDrawLine" + +#: C/genius.xml:8704(synopsis) +#, no-wrap +msgid "LinePlotDrawLine (x1,y1,x2,y2,...)" +msgstr "LinePlotDrawLine (x1,y1,x2,y2,...)" + +#: C/genius.xml:8705(synopsis) +#, no-wrap +msgid "LinePlotDrawLine (v,...)" +msgstr "LinePlotDrawLine (v,...)" + +#: C/genius.xml:8706(para) +msgid "" +"Draw a line from <varname>x1</varname>,<varname>y1</varname> to <varname>x2</" +"varname>,<varname>y2</varname>. <varname>x1</varname>,<varname>y1</varname>, " +"<varname>x2</varname>,<varname>y2</varname> can be replaced by an <varname>n</" +"varname> by 2 matrix for a longer polyline." +msgstr "" + +#: C/genius.xml:8713(para) +msgid "" +"Extra parameters can be added to specify line color, thickness, arrows, the " +"plotting window, or legend. You can do this by adding an argument string " +"<userinput>\"color\"</userinput>, <userinput>\"thickness\"</userinput>, " +"<userinput>\"window\"</userinput>, <userinput>\"arrow\"</userinput>, or " +"<userinput>\"legend\"</userinput>, and after it specify the color, the " +"thickness, the window as 4-vector, type of arrow, or the legend. (Arrow and " +"window are from version 1.0.6 onwards.)" +msgstr "" + +#: C/genius.xml:8723(para) C/genius.xml:9126(para) +msgid "" +"The color should be either a string indicating the common English word for the " +"color that GTK will recognize such as <userinput>\"red\"</userinput>, " +"<userinput>\"blue\"</userinput>, <userinput>\"yellow\"</userinput>, etc... " +"Alternatively the color can be specified in RGB format as <userinput>\"#rgb\"</" +"userinput>, <userinput>\"#rrggbb\"</userinput>, or <userinput>\"#rrrrggggbbbb" +"\"</userinput>, where the r, g, or b are hex digits of the red, green, and " +"blue components of the color. Finally, since version 1.0.18, the color can " +"also be specified as a real vector specifying the red green and blue " +"components where the components are between 0 and 1, e.g. " +"<userinput>[1.0,0.5,0.1]</userinput>." +msgstr "" + +#: C/genius.xml:8734(para) C/genius.xml:8795(para) +msgid "" +"The window should be given as usual as <userinput>[x1,x2,y1,y2]</userinput>, " +"or alternatively can be given as a string <userinput>\"fit\"</userinput> in " +"which case, the x range will be set precisely and the y range will be set with " +"five percent borders around the line." +msgstr "" + +#: C/genius.xml:8741(para) +msgid "" +"Arrow specification should be <userinput>\"origin\"</userinput>, <userinput>" +"\"end\"</userinput>, <userinput>\"both\"</userinput>, or <userinput>\"none\"</" +"userinput>." +msgstr "" + +#: C/genius.xml:8748(para) C/genius.xml:8802(para) C/genius.xml:9144(para) +#: C/genius.xml:9198(para) +msgid "" +"Finally, legend should be a string that can be used as the legend in the " +"graph. That is, if legends are being printed." +msgstr "" + +#: C/genius.xml:8752(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>LinePlotDrawLine(0,0,1,1,\"color\",\"blue\",\"thickness\",3)</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine([0,0;1,-1;-1,-1])</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine([0,0;1,1],\"arrow\"," +"\"end\")</userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawLine(RungeKuttaFull(`(x," +"y)=y,0,3,100),\"color\",\"blue\",\"legend\",\"The Solution\")</userinput>\n" +"<prompt>genius></prompt> <userinput>for r=0.0 to 1.0 by 0.1 do " +"LinePlotDrawLine([0,0;1,r],\"color\",[r,(1-r),0.5],\"window\",[0,1,0,1])</" +"userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8765(term) +msgid "<anchor id=\"gel-function-LinePlotDrawPoints\"/>LinePlotDrawPoints" +msgstr "<anchor id=\"gel-function-LinePlotDrawPoints\"/>LinePlotDrawPoints" + +#: C/genius.xml:8767(synopsis) +#, no-wrap +msgid "LinePlotDrawPoints (x,y,...)" +msgstr "LinePlotDrawPoints (x,y,...)" + +#: C/genius.xml:8768(synopsis) +#, no-wrap +msgid "LinePlotDrawPoints (v,...)" +msgstr "LinePlotDrawPoints (v,...)" + +#: C/genius.xml:8769(para) +msgid "" +"Draw a point at <varname>x</varname>,<varname>y</varname>. The input can be an " +"<varname>n</varname> by 2 matrix for <varname>n</varname> different points. " +"This function has essentially the same input as <link linkend=\"gel-function-" +"LinePlotDrawLine\">LinePlotDrawLine</link>." +msgstr "" + +#: C/genius.xml:8775(para) +msgid "" +"Extra parameters can be added to specify line color, thickness, the plotting " +"window, or legend. You can do this by adding an argument string <userinput>" +"\"color\"</userinput>, <userinput>\"thickness\"</userinput>, <userinput>" +"\"window\"</userinput>, or <userinput>\"legend\"</userinput>, and after it " +"specify the color, the thickness, the window as 4-vector, or the legend." +msgstr "" + +#: C/genius.xml:8785(para) C/genius.xml:9181(para) +msgid "" +"The color should be either a string indicating the common English word for the " +"color that GTK will recognize such as <userinput>\"red\"</userinput>, " +"<userinput>\"blue\"</userinput>, <userinput>\"yellow\"</userinput>, etc... " +"Alternatively the color can be specified in RGB format as <userinput>\"#rgb\"</" +"userinput>, <userinput>\"#rrggbb\"</userinput>, or <userinput>\"#rrrrggggbbbb" +"\"</userinput>, where the r, g, or b are hex digits of the red, green, and " +"blue components of the color. Finally the color can also be specified as a " +"real vector specifying the red green and blue components where the components " +"are between 0 and 1." +msgstr "" + +#: C/genius.xml:8806(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>LinePlotDrawPoints(0,0,\"color\",\"blue\",\"thickness\",3)</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawPoints([0,0;1,-1;-1,-1])</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>LinePlotDrawPoints(RungeKuttaFull(`(x," +"y)=y,0,3,100),\"color\",\"blue\",\"legend\",\"The Solution\")</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8813(para) +msgid "Available from version 1.0.18 onwards." +msgstr "Tillgängligt i version 1.0.18 och framåt." + +#: C/genius.xml:8820(term) +msgid "<anchor id=\"gel-function-LinePlotParametric\"/>LinePlotParametric" +msgstr "<anchor id=\"gel-function-LinePlotParametric\"/>LinePlotParametric" + +#: C/genius.xml:8822(synopsis) +#, no-wrap +msgid "LinePlotParametric (xfunc,yfunc,...)" +msgstr "" + +#: C/genius.xml:8823(synopsis) +#, no-wrap +msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc)" +msgstr "" + +#: C/genius.xml:8824(synopsis) +#, no-wrap +msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc,x1,x2,y1,y2)" +msgstr "" + +#: C/genius.xml:8825(synopsis) +#, no-wrap +msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc,[x1,x2,y1,y2])" +msgstr "" + +#: C/genius.xml:8826(synopsis) +#, no-wrap +msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc,\"fit\")" +msgstr "" + +#: C/genius.xml:8827(para) +msgid "" +"Plot a parametric function with a line. First come the functions for " +"<varname>x</varname> and <varname>y</varname> then optionally the <varname>t</" +"varname> limits as <userinput>t1,t2,tinc</userinput>, then optionally the " +"limits as <userinput>x1,x2,y1,y2</userinput>." +msgstr "" + +#: C/genius.xml:8832(para) +msgid "" +"If x and y limits are not specified, then the currently set limits apply (See " +"<link linkend=\"gel-function-LinePlotWindow\"><function>LinePlotWindow</" +"function></link>). If instead the string \"fit\" is given for the x and y " +"limits, then the limits are the maximum extent of the graph" +msgstr "" + +#: C/genius.xml:8848(term) +msgid "<anchor id=\"gel-function-LinePlotCParametric\"/>LinePlotCParametric" +msgstr "<anchor id=\"gel-function-LinePlotCParametric\"/>LinePlotCParametric" + +#: C/genius.xml:8850(synopsis) +#, no-wrap +msgid "LinePlotCParametric (func,...)" +msgstr "" + +#: C/genius.xml:8851(synopsis) +#, no-wrap +msgid "LinePlotCParametric (func,t1,t2,tinc)" +msgstr "" + +#: C/genius.xml:8852(synopsis) +#, no-wrap +msgid "LinePlotCParametric (func,t1,t2,tinc,x1,x2,y1,y2)" +msgstr "" + +#: C/genius.xml:8853(para) +msgid "" +"Plot a parametric complex valued function with a line. First comes the " +"function that returns <computeroutput>x+iy</computeroutput>, then optionally " +"the <varname>t</varname> limits as <userinput>t1,t2,tinc</userinput>, then " +"optionally the limits as <userinput>x1,x2,y1,y2</userinput>." +msgstr "" + +#: C/genius.xml:8859(para) +msgid "" +"If limits are not specified, then the currently set limits apply (See <link " +"linkend=\"gel-function-LinePlotWindow\"><function>LinePlotWindow</function></" +"link>). If instead the string \"fit\" is given for the x and y limits, then " +"the limits are the maximum extent of the graph" +msgstr "" + +#: C/genius.xml:8875(term) +msgid "<anchor id=\"gel-function-PlotCanvasFreeze\"/>PlotCanvasFreeze" +msgstr "<anchor id=\"gel-function-PlotCanvasFreeze\"/>PlotCanvasFreeze" + +#: C/genius.xml:8877(synopsis) +#, no-wrap +msgid "PlotCanvasFreeze ()" +msgstr "PlotCanvasFreeze ()" + +#: C/genius.xml:8878(para) +msgid "" +"Freeze drawing of the canvas plot temporarily. Useful if you need to draw a " +"bunch of elements and want to delay drawing everything to avoid flicker in an " +"animation. After everything has been drawn you should call <link linkend=\"gel-" +"function-PlotCanvasThaw\"><function>PlotCanvasThaw</function></link>." +msgstr "" + +#: C/genius.xml:8883(para) +msgid "" +"The canvas is always thawed after end of any execution, so it will never " +"remain frozen. The moment a new command line is shown for example the plot " +"canvas is thawed automatically. Also note that calls to freeze and thaw may be " +"safely nested." +msgstr "" + +#: C/genius.xml:8893(term) +msgid "<anchor id=\"gel-function-PlotCanvasThaw\"/>PlotCanvasThaw" +msgstr "<anchor id=\"gel-function-PlotCanvasThaw\"/>PlotCanvasThaw" + +#: C/genius.xml:8895(synopsis) +#, no-wrap +msgid "PlotCanvasThaw ()" +msgstr "PlotCanvasThaw ()" + +#: C/genius.xml:8896(para) +msgid "" +"Thaw the plot canvas frozen by <link linkend=\"gel-function-PlotCanvasFreeze" +"\"><function>PlotCanvasFreeze</function></link> and redraw the canvas " +"immediately. The canvas is also always thawed after end of execution of any " +"program." +msgstr "" + +#: C/genius.xml:8907(term) +msgid "<anchor id=\"gel-function-PlotWindowPresent\"/>PlotWindowPresent" +msgstr "<anchor id=\"gel-function-PlotWindowPresent\"/>PlotWindowPresent" + +#: C/genius.xml:8909(synopsis) +#, no-wrap +msgid "PlotWindowPresent ()" +msgstr "PlotWindowPresent ()" + +#: C/genius.xml:8910(para) +msgid "" +"Show and raise the plot window, creating it if necessary. Normally the window " +"is created when one of the plotting functions is called, but it is not always " +"raised if it happens to be below other windows. So this function is good to " +"call in scripts where the plot window might have been created before, and by " +"now hidden behind the console or other windows." +msgstr "" + +#: C/genius.xml:8919(para) +msgid "Version 1.0.19 onwards." +msgstr "Version 1.0.19 och framåt." + +#: C/genius.xml:8924(term) +msgid "" +"<anchor id=\"gel-function-SlopefieldClearSolutions\"/>SlopefieldClearSolutions" +msgstr "" +"<anchor id=\"gel-function-SlopefieldClearSolutions\"/>SlopefieldClearSolutions" + +#: C/genius.xml:8926(synopsis) +#, no-wrap +msgid "SlopefieldClearSolutions ()" +msgstr "" + +#: C/genius.xml:8927(para) +msgid "" +"Clears the solutions drawn by the <link linkend=\"gel-function-" +"SlopefieldDrawSolution\"><function>SlopefieldDrawSolution</function></link> " +"function." +msgstr "" + +#: C/genius.xml:8936(term) +msgid "" +"<anchor id=\"gel-function-SlopefieldDrawSolution\"/>SlopefieldDrawSolution" +msgstr "" +"<anchor id=\"gel-function-SlopefieldDrawSolution\"/>SlopefieldDrawSolution" + +#: C/genius.xml:8938(synopsis) +#, no-wrap +msgid "SlopefieldDrawSolution (x, y, dx)" +msgstr "SlopefieldDrawSolution (x, y, dx)" + +#: C/genius.xml:8939(para) +msgid "" +"When a slope field plot is active, draw a solution with the specified initial " +"condition. The standard Runge-Kutta method is used with increment <varname>dx</" +"varname>. Solutions stay on the graph until a different plot is shown or until " +"you call <link linkend=\"gel-function-SlopefieldClearSolutions" +"\"><function>SlopefieldClearSolutions</function></link>. You can also use the " +"graphical interface to draw solutions and specify initial conditions with the " +"mouse." +msgstr "" + +#: C/genius.xml:8953(term) +msgid "<anchor id=\"gel-function-SlopefieldPlot\"/>SlopefieldPlot" +msgstr "<anchor id=\"gel-function-SlopefieldPlot\"/>SlopefieldPlot" + +#: C/genius.xml:8955(synopsis) +#, no-wrap +msgid "SlopefieldPlot (func)" +msgstr "" + +#: C/genius.xml:8956(synopsis) +#, no-wrap +msgid "SlopefieldPlot (func,x1,x2,y1,y2)" +msgstr "" + +#: C/genius.xml:8957(para) +msgid "" +"Plot a slope field. The function <varname>func</varname> should take two real " +"numbers <varname>x</varname> and <varname>y</varname>, or a single complex " +"number. Optionally you can specify the limits of the plotting window as " +"<varname>x1</varname>, <varname>x2</varname>, <varname>y1</varname>, " +"<varname>y2</varname>. If limits are not specified, then the currently set " +"limits apply (See <link linkend=\"gel-function-LinePlotWindow" +"\"><function>LinePlotWindow</function></link>)." +msgstr "" + +#: C/genius.xml:8973(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> <userinput>Slopefield(`(x," +"y)=sin(x-y),-5,5,-5,5)</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:8982(term) +msgid "<anchor id=\"gel-function-SurfacePlot\"/>SurfacePlot" +msgstr "<anchor id=\"gel-function-SurfacePlot\"/>SurfacePlot" + +#: C/genius.xml:8984(synopsis) +#, no-wrap +msgid "SurfacePlot (func)" +msgstr "" + +#: C/genius.xml:8985(synopsis) +#, no-wrap +msgid "SurfacePlot (func,x1,x2,y1,y2,z1,z2)" +msgstr "" + +#: C/genius.xml:8986(synopsis) +#, no-wrap +msgid "SurfacePlot (func,x1,x2,y1,y2)" +msgstr "" + +#: C/genius.xml:8987(synopsis) +#, no-wrap +msgid "SurfacePlot (func,[x1,x2,y1,y2,z1,z2])" +msgstr "" + +#: C/genius.xml:8988(synopsis) +#, no-wrap +msgid "SurfacePlot (func,[x1,x2,y1,y2])" +msgstr "" + +#: C/genius.xml:8989(para) +msgid "" +"Plot a surface function that takes either two arguments or a complex number. " +"First comes the function then optionally limits as <varname>x1</varname>, " +"<varname>x2</varname>, <varname>y1</varname>, <varname>y2</varname>, " +"<varname>z1</varname>, <varname>z2</varname>. If limits are not specified, " +"then the currently set limits apply (See <link linkend=\"gel-function-" +"SurfacePlotWindow\"><function>SurfacePlotWindow</function></link>). Genius can " +"only plot a single surface function at this time." +msgstr "" + +#: C/genius.xml:8997(para) +msgid "" +"If the z limits are not specified then the maxima and minima of the function " +"are used." +msgstr "" + +#: C/genius.xml:9000(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> <userinput>SurfacePlot(|" +"sin|,-1,1,-1,1,0,1.5)</userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlot(`(x," +"y)=x^2+y,-1,1,-1,1,-2,2)</userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlot(`(z)=|z|^2,-1,1,-1,1,0,2)</" +"userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:9011(term) +msgid "<anchor id=\"gel-function-SurfacePlotClear\"/>SurfacePlotClear" +msgstr "<anchor id=\"gel-function-SurfacePlotClear\"/>SurfacePlotClear" + +#: C/genius.xml:9013(synopsis) +#, no-wrap +msgid "SurfacePlotClear ()" +msgstr "SurfacePlotClear ()" + +#: C/genius.xml:9014(para) +msgid "" +"Show the surface plot window and clear out functions and any other lines that " +"were drawn." +msgstr "" + +#: C/genius.xml:9018(para) +msgid "Available in version 1.0.19 and onwards." +msgstr "Tillgängligt i version 1.0.19 och framåt." + +#: C/genius.xml:9025(term) +msgid "<anchor id=\"gel-function-SurfacePlotData\"/>SurfacePlotData" +msgstr "<anchor id=\"gel-function-SurfacePlotData\"/>SurfacePlotData" + +#: C/genius.xml:9027(synopsis) +#, no-wrap +msgid "SurfacePlotData (data)" +msgstr "SurfacePlotData (data)" + +#: C/genius.xml:9028(synopsis) +#, no-wrap +msgid "SurfacePlotData (data,label)" +msgstr "" + +#: C/genius.xml:9029(synopsis) +#, no-wrap +msgid "SurfacePlotData (data,x1,x2,y1,y2,z1,z2)" +msgstr "" + +#: C/genius.xml:9030(synopsis) +#, no-wrap +msgid "SurfacePlotData (data,label,x1,x2,y1,y2,z1,z2)" +msgstr "" + +#: C/genius.xml:9031(synopsis) +#, no-wrap +msgid "SurfacePlotData (data,[x1,x2,y1,y2,z1,z2])" +msgstr "" + +#: C/genius.xml:9032(synopsis) +#, no-wrap +msgid "SurfacePlotData (data,label,[x1,x2,y1,y2,z1,z2])" +msgstr "" + +#: C/genius.xml:9033(para) +msgid "" +"Plot a surface from data. The data is an n by 3 matrix whose rows are the x, y " +"and z coordinates. The data can also be simply a vector whose length is a " +"multiple of 3 and so contains the triples of x, y, z. The data should contain " +"at least 3 points." +msgstr "" + +#: C/genius.xml:9040(para) +msgid "" +"Optionally we can give the label and also optionally the limits. If limits are " +"not given, they are computed from the data, <link linkend=\"gel-function-" +"SurfacePlotWindow\"><function>SurfacePlotWindow</function></link> is not used, " +"if you want to use it, pass it in explicitly. If label is not given then empty " +"label is used." +msgstr "" + +#: C/genius.xml:9047(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>SurfacePlotData([0,0,0;1,0,1;0,1,1;1,1,3])</userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlotData(data,\"My data\")</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlotData(data,-1,1,-1,1,0,10)</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlotData(data," +"SurfacePlotWindow)</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:9055(para) +msgid "" +"Here's an example of how to plot in polar coordinates, in particular how to " +"plot the function <userinput>-r^2 * theta</userinput>: " +"<screen><prompt>genius></prompt> <userinput>d:=null; for r=0 to 1 by 0.1 do " +"for theta=0 to 2*pi by pi/5 do d=[d;[r*cos(theta),r*sin(theta),-r^2*theta]];</" +"userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlotData(d)</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:9068(term) +msgid "<anchor id=\"gel-function-SurfacePlotDataGrid\"/>SurfacePlotDataGrid" +msgstr "<anchor id=\"gel-function-SurfacePlotDataGrid\"/>SurfacePlotDataGrid" + +#: C/genius.xml:9070(synopsis) +#, no-wrap +msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2])" +msgstr "SurfacePlotDataGrid (data,[x1,x2,y1,y2])" + +#: C/genius.xml:9071(synopsis) +#, no-wrap +msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2,z1,z2])" +msgstr "SurfacePlotDataGrid (data,[x1,x2,y1,y2,z1,z2])" + +#: C/genius.xml:9072(synopsis) +#, no-wrap +msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2],label)" +msgstr "" + +#: C/genius.xml:9073(synopsis) +#, no-wrap +msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2,z1,z2],label)" +msgstr "" + +#: C/genius.xml:9074(para) +msgid "" +"Plot a surface from regular rectangular data. The data is given in a n by m " +"matrix where the rows are the x coordinate and the columns are the y " +"coordinate. The x coordinate is divided into equal n-1 subintervals and y " +"coordinate is divided into equal m-1 subintervals. The limits <varname>x1</" +"varname> and <varname>x2</varname> give the interval on the x-axis that we " +"use, and the limits <varname>y1</varname> and <varname>y2</varname> give the " +"interval on the y-axis that we use. If the limits <varname>z1</varname> and " +"<varname>z2</varname> are not given they are computed from the data (to be the " +"extreme values from the data)." +msgstr "" + +#: C/genius.xml:9088(para) +msgid "" +"Optionally we can give the label, if label is not given then empty label is " +"used." +msgstr "" + +#: C/genius.xml:9092(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>SurfacePlotDataGrid([1,2;3,4],[0,1,0,1])</userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlotDataGrid(data,[-1,1,-1,1]," +"\"My data\")</userinput>\n" +"<prompt>genius></prompt> <userinput>d:=null; for i=1 to 20 do for j=1 to 10 " +"d@(i,j) = (0.1*i-1)^2-(0.1*j)^2;</userinput>\n" +"<prompt>genius></prompt> <userinput>SurfacePlotDataGrid(d,[-1,1,0,1],\"half " +"a saddle\")</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:9105(term) +msgid "<anchor id=\"gel-function-SurfacePlotDrawLine\"/>SurfacePlotDrawLine" +msgstr "<anchor id=\"gel-function-SurfacePlotDrawLine\"/>SurfacePlotDrawLine" + +#: C/genius.xml:9107(synopsis) +#, no-wrap +msgid "SurfacePlotDrawLine (x1,y1,z1,x2,y2,z2,...)" +msgstr "SurfacePlotDrawLine (x1,y1,z1,x2,y2,z2,...)" + +#: C/genius.xml:9108(synopsis) +#, no-wrap +msgid "SurfacePlotDrawLine (v,...)" +msgstr "SurfacePlotDrawLine (v,...)" + +#: C/genius.xml:9109(para) +msgid "" +"Draw a line from <varname>x1</varname>,<varname>y1</varname>,<varname>z1</" +"varname> to <varname>x2</varname>,<varname>y2</varname>,<varname>z2</varname>. " +"<varname>x1</varname>,<varname>y1</varname>,<varname>z1</varname>, " +"<varname>x2</varname>,<varname>y2</varname>,<varname>z2</varname> can be " +"replaced by an <varname>n</varname> by 3 matrix for a longer polyline." +msgstr "" + +#: C/genius.xml:9116(para) +msgid "" +"Extra parameters can be added to specify line color, thickness, arrows, the " +"plotting window, or legend. You can do this by adding an argument string " +"<userinput>\"color\"</userinput>, <userinput>\"thickness\"</userinput>, " +"<userinput>\"window\"</userinput>, or <userinput>\"legend\"</userinput>, and " +"after it specify the color, the thickness, the window as 6-vector, or the " +"legend." +msgstr "" + +#: C/genius.xml:9137(para) C/genius.xml:9191(para) +msgid "" +"The window should be given as usual as <userinput>[x1,x2,y1,y2,z1,z2]</" +"userinput>, or alternatively can be given as a string <userinput>\"fit\"</" +"userinput> in which case, the x range will be set precisely and the y range " +"will be set with five percent borders around the line." +msgstr "" + +#: C/genius.xml:9148(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>SurfacePlotDrawLine(0,0,0,1,1,1,\"color\",\"blue\",\"thickness" +"\",3)</userinput>\n" +"<prompt>genius></prompt> " +"<userinput>SurfacePlotDrawLine([0,0,0;1,-1,2;-1,-1,-3])</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:9154(para) C/genius.xml:9208(para) +msgid "Available from version 1.0.19 onwards." +msgstr "Tillgängligt i version 1.0.19 och framåt." + +#: C/genius.xml:9161(term) +msgid "<anchor id=\"gel-function-SurfacePlotDrawPoints\"/>SurfacePlotDrawPoints" +msgstr "<anchor id=\"gel-function-SurfacePlotDrawPoints\"/>SurfacePlotDrawPoints" + +#: C/genius.xml:9163(synopsis) +#, no-wrap +msgid "SurfacePlotDrawPoints (x,y,z,...)" +msgstr "SurfacePlotDrawPoints (x,y,z,...)" + +#: C/genius.xml:9164(synopsis) +#, no-wrap +msgid "SurfacePlotDrawPoints (v,...)" +msgstr "SurfacePlotDrawPoints (v,...)" + +#: C/genius.xml:9165(para) +msgid "" +"Draw a point at <varname>x</varname>,<varname>y</varname>,<varname>z</" +"varname>. The input can be an <varname>n</varname> by 3 matrix for <varname>n</" +"varname> different points. This function has essentially the same input as " +"<link linkend=\"gel-function-SurfacePlotDrawLine\">SurfacePlotDrawLine</link>." +msgstr "" + +#: C/genius.xml:9171(para) +msgid "" +"Extra parameters can be added to specify line color, thickness, the plotting " +"window, or legend. You can do this by adding an argument string <userinput>" +"\"color\"</userinput>, <userinput>\"thickness\"</userinput>, <userinput>" +"\"window\"</userinput>, or <userinput>\"legend\"</userinput>, and after it " +"specify the color, the thickness, the window as 6-vector, or the legend." +msgstr "" + +#: C/genius.xml:9202(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> " +"<userinput>SurfacePlotDrawPoints(0,0,0,\"color\",\"blue\",\"thickness\",3)</" +"userinput>\n" +"<prompt>genius></prompt> " +"<userinput>SurfacePlotDrawPoints([0,0,0;1,-1,2;-1,-1,1])</userinput>\n" +"</screen>" +msgstr "" + +#: C/genius.xml:9215(term) +msgid "" +"<anchor id=\"gel-function-VectorfieldClearSolutions\"/" +">VectorfieldClearSolutions" +msgstr "" +"<anchor id=\"gel-function-VectorfieldClearSolutions\"/" +">VectorfieldClearSolutions" + +#: C/genius.xml:9217(synopsis) +#, no-wrap +msgid "VectorfieldClearSolutions ()" +msgstr "VectorfieldClearSolutions ()" + +#: C/genius.xml:9218(para) +msgid "" +"Clears the solutions drawn by the <link linkend=\"gel-function-" +"VectorfieldDrawSolution\"><function>VectorfieldDrawSolution</function></link> " +"function." +msgstr "" + +#: C/genius.xml:9223(para) C/genius.xml:9242(para) +msgid "Version 1.0.6 onwards." +msgstr "Version 1.0.6 och framåt." + +#: C/genius.xml:9228(term) +msgid "" +"<anchor id=\"gel-function-VectorfieldDrawSolution\"/>VectorfieldDrawSolution" +msgstr "" +"<anchor id=\"gel-function-VectorfieldDrawSolution\"/>VectorfieldDrawSolution" + +#: C/genius.xml:9230(synopsis) +#, no-wrap +msgid "VectorfieldDrawSolution (x, y, dt, tlen)" +msgstr "" + +#: C/genius.xml:9231(para) +msgid "" +"When a vector field plot is active, draw a solution with the specified initial " +"condition. The standard Runge-Kutta method is used with increment <varname>dt</" +"varname> for an interval of length <varname>tlen</varname>. Solutions stay on " +"the graph until a different plot is shown or until you call <link linkend=" +"\"gel-function-VectorfieldClearSolutions" +"\"><function>VectorfieldClearSolutions</function></link>. You can also use the " +"graphical interface to draw solutions and specify initial conditions with the " +"mouse." +msgstr "" + +#: C/genius.xml:9247(term) +msgid "<anchor id=\"gel-function-VectorfieldPlot\"/>VectorfieldPlot" +msgstr "<anchor id=\"gel-function-VectorfieldPlot\"/>VectorfieldPlot" + +#: C/genius.xml:9249(synopsis) +#, no-wrap +msgid "VectorfieldPlot (funcx, funcy)" +msgstr "" + +#: C/genius.xml:9250(synopsis) +#, no-wrap +msgid "VectorfieldPlot (funcx, funcy, x1, x2, y1, y2)" +msgstr "" + +#: C/genius.xml:9251(para) +msgid "" +"Plot a two dimensional vector field. The function <varname>funcx</varname> " +"should be the dx/dt of the vectorfield and the function <varname>funcy</" +"varname> should be the dy/dt of the vectorfield. The functions should take two " +"real numbers <varname>x</varname> and <varname>y</varname>, or a single " +"complex number. When the parameter <link linkend=\"gel-function-" +"VectorfieldNormalized\"><function>VectorfieldNormalized</function></link> is " +"<constant>true</constant>, then the magnitude of the vectors is normalized. " +"That is, only the direction and not the magnitude is shown." +msgstr "" + +#: C/genius.xml:9264(para) +msgid "" +"Optionally you can specify the limits of the plotting window as <varname>x1</" +"varname>, <varname>x2</varname>, <varname>y1</varname>, <varname>y2</varname>. " +"If limits are not specified, then the currently set limits apply (See <link " +"linkend=\"gel-function-LinePlotWindow\"><function>LinePlotWindow</function></" +"link>)." +msgstr "" + +#: C/genius.xml:9276(para) +msgid "" +"Examples: <screen><prompt>genius></prompt> <userinput>VectorfieldPlot(`(x," +"y)=x^2-y, `(x,y)=y^2-x, -1, 1, -1, 1)</userinput>\n" +"</screen>" +msgstr "" +"Exempel: <screen><prompt>genius></prompt> <userinput>VectorfieldPlot(`(x," +"y)=x^2-y, `(x,y)=y^2-x, -1, 1, -1, 1)</userinput>\n" +"</screen>" + +#: C/genius.xml:9291(title) +msgid "Example Programs in GEL" +msgstr "" + +#: C/genius.xml:9293(para) +msgid "Here is a function that calculates factorials: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:9298(para) +msgid "With indentation it becomes: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:9308(para) +msgid "" +"This is a direct port of the factorial function from the <application>bc</" +"application> manpage. The syntax seems similar to <application>bc</" +"application>, but different in that in GEL, the last expression is the one " +"that is returned. Using the <literal>return</literal> function instead, it " +"would be: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:9321(programlisting) +#, no-wrap +msgid "function f(x) = prod k=1 to x do k\n" +msgstr "" + +#: C/genius.xml:9317(para) +msgid "" +"By far the easiest way to define a factorial function would be using the " +"product loop as follows. This is not only the shortest and fastest, but also " +"probably the most readable version. <placeholder-1/>" +msgstr "" + +#: C/genius.xml:9325(para) +msgid "" +"Here is a larger example, this basically redefines the internal <link linkend=" +"\"gel-function-ref\"><function>ref</function></link> function to calculate the " +"row echelon form of a matrix. The function <function>ref</function> is built " +"in and much faster, but this example demonstrates some of the more complex " +"features of GEL. <placeholder-1/>" +msgstr "" + +#: C/genius.xml:9380(para) +msgid "" +"To configure <application>Genius Mathematics Tool</application>, choose " +"<menuchoice><guimenu>Settings</guimenu><guimenuitem>Preferences</guimenuitem></" +"menuchoice>. There are several basic parameters provided by the calculator in " +"addition to the ones provided by the standard library. These control how the " +"calculator behaves." +msgstr "" + +#: C/genius.xml:9390(title) +msgid "Changing Settings with GEL" +msgstr "" + +#: C/genius.xml:9391(para) +msgid "" +"Many of the settings in Genius are simply global variables, and can be " +"evaluated and assigned to in the same way as normal variables. See <xref " +"linkend=\"genius-gel-variables\"/> about evaluating and assigning to " +"variables, and <xref linkend=\"genius-gel-function-parameters\"/> for a list " +"of settings that can be modified in this way." +msgstr "" + +#: C/genius.xml:9400(programlisting) +#, no-wrap +msgid "MaxDigits = 12\n" +msgstr "MaxDigits = 12\n" + +#: C/genius.xml:9398(para) +msgid "" +"As an example, you can set the maximum number of digits in a result to 12 by " +"typing: <placeholder-1/>" +msgstr "" + +#: C/genius.xml:9406(title) +msgid "Output" +msgstr "" + +#: C/genius.xml:9410(guilabel) +msgid "Maximum digits to output" +msgstr "" + +#: C/genius.xml:9413(para) +msgid "" +"The maximum digits in a result (<link linkend=\"gel-function-MaxDigits" +"\"><function>MaxDigits</function></link>)" +msgstr "" + +#: C/genius.xml:9418(guilabel) +msgid "Results as floats" +msgstr "" + +#: C/genius.xml:9421(para) +msgid "" +"If the results should be always printed as floats (<link linkend=\"gel-" +"function-ResultsAsFloats\"><function>ResultsAsFloats</function></link>)" +msgstr "" + +#: C/genius.xml:9426(guilabel) +msgid "Floats in scientific notation" +msgstr "" + +#: C/genius.xml:9429(para) +msgid "" +"If floats should be in scientific notation (<link linkend=\"gel-function-" +"ScientificNotation\"><function>ScientificNotation</function></link>)" +msgstr "" + +#: C/genius.xml:9434(guilabel) +msgid "Always print full expressions" +msgstr "" + +#: C/genius.xml:9437(para) +msgid "" +"Should we print out full expressions for non-numeric return values (longer " +"than a line) (<link linkend=\"gel-function-FullExpressions" +"\"><function>FullExpressions</function></link>)" +msgstr "" + +#: C/genius.xml:9443(guilabel) +msgid "Use mixed fractions" +msgstr "" + +#: C/genius.xml:9446(para) +msgid "" +"If fractions should be printed as mixed fractions such as \"1 1/3\" rather " +"than \"4/3\". (<link linkend=\"gel-function-MixedFractions" +"\"><function>MixedFractions</function></link>)" +msgstr "" + +#: C/genius.xml:9452(guilabel) +msgid "Display 0.0 when floating point number is less than 10^-x (0=never chop)" +msgstr "" + +#: C/genius.xml:9455(para) +msgid "" +"How to chop output. But only when other numbers nearby are large. See the " +"documentation of the parameter <link linkend=\"gel-function-OutputChopExponent" +"\"><function>OutputChopExponent</function></link>." +msgstr "" + +#: C/genius.xml:9463(guilabel) +msgid "Only chop numbers when another number is greater than 10^-x" +msgstr "" + +#: C/genius.xml:9466(para) +msgid "" +"When to chop output. This is set by the parameter <link linkend=\"gel-function-" +"OutputChopWhenExponent\"><function>OutputChopWhenExponent</function></link>. " +"See the documentation of the parameter <link linkend=\"gel-function-" +"OutputChopExponent\"><function>OutputChopExponent</function></link>." +msgstr "" + +#: C/genius.xml:9474(guilabel) +msgid "Remember output settings across sessions" +msgstr "" + +#: C/genius.xml:9477(para) +msgid "" +"Should the output settings in the <guilabel>Number/Expression output options</" +"guilabel> frame be remembered for next session. Does not apply to the " +"<guilabel>Error/Info output options</guilabel> frame." +msgstr "" + +#: C/genius.xml:9479(para) +msgid "" +"If unchecked, either the default or any previously saved settings are used " +"each time Genius starts up. Note that settings are saved at the end of the " +"session, so if you wish to change the defaults check this box, restart " +"<application>Genius Mathematics Tool</application> and then uncheck it again." +msgstr "" + +#: C/genius.xml:9491(guilabel) +msgid "Display errors in a dialog" +msgstr "" + +#: C/genius.xml:9494(para) +msgid "" +"If set the errors will be displayed in a separate dialog, if unset the errors " +"will be printed on the console." +msgstr "" + +#: C/genius.xml:9501(guilabel) +msgid "Display information messages in a dialog" +msgstr "" + +#: C/genius.xml:9504(para) +msgid "" +"If set the information messages will be displayed in a separate dialog, if " +"unset the information messages will be printed on the console." +msgstr "" + +#: C/genius.xml:9512(guilabel) +msgid "Maximum errors to display" +msgstr "" + +#: C/genius.xml:9515(para) +msgid "" +"The maximum number of errors to return on one evaluation (<link linkend=\"gel-" +"function-MaxErrors\"><function>MaxErrors</function></link>). If you set this " +"to 0 then all errors are always returned. Usually if some loop causes many " +"errors, then it is unlikely that you will be able to make sense out of more " +"than a few of these, so seeing a long list of errors is usually not helpful." +msgstr "" + +#: C/genius.xml:9527(para) +msgid "" +"In addition to these preferences, there are some preferences that can only be " +"changed by setting them in the workspace console. For others that may affect " +"the output see <xref linkend=\"genius-gel-function-parameters\"/>." +msgstr "" + +#: C/genius.xml:9537(function) +msgid "IntegerOutputBase" +msgstr "IntegerOutputBase" + +#: C/genius.xml:9540(para) +msgid "The base that will be used to output integers" +msgstr "" + +#: C/genius.xml:9546(function) +msgid "OutputStyle" +msgstr "OutputStyle" + +#: C/genius.xml:9549(para) +msgid "" +"A string, can be <literal>\"normal\"</literal>, <literal>\"latex\"</literal>, " +"<literal>\"mathml\"</literal> or <literal>\"troff\"</literal> and it will " +"affect how matrices (and perhaps other stuff) is printed, useful for pasting " +"into documents. Normal style is the default human readable printing style of " +"<application>Genius Mathematics Tool</application>. The other styles are for " +"typsetting in LaTeX, MathML (XML), or in Troff." +msgstr "" + +#: C/genius.xml:9561(title) +msgid "Precision" +msgstr "" + +#: C/genius.xml:9565(guilabel) +msgid "Floating point precision" +msgstr "" + +#: C/genius.xml:9568(para) +msgid "" +"The floating point precision in bits (<link linkend=\"gel-function-" +"FloatPrecision\"><function>FloatPrecision</function></link>). Note that " +"changing this only affects newly computed quantities. Old values stored in " +"variables are obviously still in the old precision and if you want to have " +"them more precise you will have to recompute them. Exceptions to this are the " +"system constants such as <link linkend=\"gel-function-pi\"><function>pi</" +"function></link> or <link linkend=\"gel-function-e\"><function>e</function></" +"link>." +msgstr "" + +#: C/genius.xml:9583(guilabel) +msgid "Remember precision setting across sessions" +msgstr "" + +#: C/genius.xml:9586(para) +msgid "" +"Should the precision setting be remembered for the next session. If unchecked, " +"either the default or any previously saved setting is used each time Genius " +"starts up. Note that settings are saved at the end of the session, so if you " +"wish to change the default check this box, restart genius and then uncheck it " +"again." +msgstr "" + +#: C/genius.xml:9599(title) +msgid "Terminal" +msgstr "" + +#: C/genius.xml:9601(para) +msgid "Terminal refers to the console in the work area." +msgstr "" + +#: C/genius.xml:9608(guilabel) +msgid "Scrollback lines" +msgstr "" + +#: C/genius.xml:9611(para) +msgid "Lines of scrollback in the terminal." +msgstr "" + +#: C/genius.xml:9616(guilabel) +msgid "Font" +msgstr "" + +#: C/genius.xml:9619(para) +msgid "The font to use on the terminal." +msgstr "" + +#: C/genius.xml:9624(guilabel) +msgid "Black on white" +msgstr "" + +#: C/genius.xml:9627(para) +msgid "If to use black on white on the terminal." +msgstr "" + +#: C/genius.xml:9632(guilabel) +msgid "Blinking cursor" +msgstr "" + +#: C/genius.xml:9635(para) +msgid "" +"If the cursor in the terminal should blink when the terminal is in focus. This " +"can sometimes be annoying and it generates idle traffic if you are using " +"Genius remotely." +msgstr "" + +#: C/genius.xml:9642(title) +msgid "Memory" +msgstr "" + +#: C/genius.xml:9646(guilabel) +msgid "Maximum number of nodes to allocate" +msgstr "" + +#: C/genius.xml:9649(para) +msgid "" +"Internally all data is put onto small nodes in memory. This gives a limit on " +"the maximum number of nodes to allocate for computations. This limit avoids " +"the problem of running out of memory if you do something by mistake that uses " +"too much memory, such as a recursion without end. This could slow your " +"computer and make it hard to even interrupt the program." +msgstr "" + +#: C/genius.xml:9657(para) +msgid "" +"Once the limit is reached, <application>Genius Mathematics Tool</application> " +"asks if you wish to interrupt the computation or if you wish to continue. If " +"you continue, no limit is applied and it will be possible to run your computer " +"out of memory. The limit will be applied again next time you execute a program " +"or an expression on the Console regardless of how you answered the question." +msgstr "" + +#: C/genius.xml:9665(para) +msgid "" +"Setting the limit to zero means there is no limit to the amount of memory that " +"genius uses." +msgstr "" + +#: C/genius.xml:9679(title) +msgid "About <application>Genius Mathematics Tool</application>" +msgstr "" + +#: C/genius.xml:9681(para) +msgid "" +"<application>Genius Mathematics Tool</application> was written by Jiří " +"(George) Lebl (<email>jirka@5z.com</email>). The history of " +"<application>Genius Mathematics Tool</application> goes back to late 1997. It " +"was the first calculator program for GNOME, but it then grew beyond being just " +"a desktop calculator. To find more information about <application>Genius " +"Mathematics Tool</application>, please visit the <ulink url=\"http://www.jirka." +"org/genius.html\" type=\"http\">Genius Web page</ulink>." +msgstr "" + +#: C/genius.xml:9688(para) +msgid "" +"To report a bug or make a suggestion regarding this application or this " +"manual, send email to me (the author) or post to the mailing list (see the web " +"page)." +msgstr "" + +#: C/genius.xml:9694(para) +msgid "" +"This program is distributed under the terms of the GNU General Public license " +"as published by the Free Software Foundation; either version 3 of the License, " +"or (at your option) any later version. A copy of this license can be found at " +"this <ulink url=\"http://www.gnu.org/copyleft/gpl.html\" type=\"http\">link</" +"ulink>, or in the file COPYING included with the source code of this program." +msgstr "" + +#: C/genius.xml:9701(para) +msgid "" +"Jiří Lebl was during various parts of the development partially supported for " +"the work by NSF grants DMS 0900885, DMS 1362337, the University of Illinois at " +"Urbana-Champaign, the University of California at San Diego, the University of " +"Wisconsin-Madison, and Oklahoma State University. The software has been used " +"for both teaching and research." +msgstr "" + +#. Put one translator per line, in the form of NAME <EMAIL>, YEAR1, YEAR2 +#: C/genius.xml:0(None) +msgid "translator-credits" +msgstr "" |