diff options
| author | Jiri (George) Lebl <jiri.lebl@gmail.com> | 2016-07-08 23:47:47 +0200 |
|---|---|---|
| committer | Jiri (George) Lebl <jiri.lebl@gmail.com> | 2016-07-08 23:47:47 +0200 |
| commit | 4d497cedd6076a839823a19b0c40b2757305ef27 (patch) | |
| tree | c8cff9ed42b17c4643a208b9f2c7edeaa8ad6df2 /help | |
| parent | 254ac92f7ada6f0f3e5a8b2056c4ff1808a4f646 (diff) | |
Fri Jul 08 23:46:02 2016 Jiri (George) Lebl <jirka@5z.com>
* src/funclib.c: fix StripZeroColumns when a zero matrix is passed
in.
* help/C/genius.xml: fix Planetmath links (thanks to Anders Jonsson).
Also add a couple more wikipedia links and a couple of details in
various places.
* src/calc.h: raise year to 2016
Diffstat (limited to 'help')
| -rw-r--r-- | help/C/genius.xml | 327 |
1 files changed, 204 insertions, 123 deletions
diff --git a/help/C/genius.xml b/help/C/genius.xml index 4535c291..17de6900 100644 --- a/help/C/genius.xml +++ b/help/C/genius.xml @@ -4,7 +4,7 @@ <!ENTITY app "<application>Genius Mathematics Tool</application>"> <!ENTITY appname "Genius"> <!ENTITY appversion "1.0.21"> - <!ENTITY date "January 2016"> + <!ENTITY date "July 2016"> <!ENTITY legal SYSTEM "legal.xml"> @@ -3815,7 +3815,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V </para> <para> See - <ulink url="http://en.wikipedia.org/wiki/Catalan%27s_constant">Wikipedia</ulink>, or + <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. </para> </listitem> @@ -3833,7 +3833,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V <para> 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://planetmath.org/MascheroniConstant">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/Euler-MascheroniConstant.html">Mathworld</ulink> for more information. </para> </listitem> @@ -3847,7 +3847,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V <para> 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://planetmath.org/GoldenRatio">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/GoldenRatio.html">Mathworld</ulink> for more information. </para> </listitem> @@ -3881,7 +3881,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V <para> 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://planetmath.org/E">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/e.html">Mathworld</ulink> for more information. </para> </listitem> @@ -3898,7 +3898,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V <para> 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://planetmath.org/Pi">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/Pi.html">Mathworld</ulink> for more information. </para> </listitem> @@ -3924,8 +3924,8 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V <para> 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://planetmath.org/AbsoluteValue">Planetmath (absolute value)</ulink>, + <ulink url="http://planetmath.org/ModulusOfComplexNumber">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. @@ -4155,7 +4155,7 @@ value then <function>Sign</function> returns the direction or 0. <para> 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://planetmath.org/LogarithmFunction">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/ExponentialFunction.html">Mathworld</ulink> for more information. </para> </listitem> @@ -4186,7 +4186,7 @@ value then <function>Sign</function> returns the direction or 0. <para> 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://planetmath.org/LogarithmFunction">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/NaturalLogarithm.html">Mathworld</ulink> for more information. </para> </listitem> @@ -4296,7 +4296,8 @@ number is specified) of the given size returned. For example, </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/SquareRoot.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Square_root">Wikipedia</ulink> or + <ulink url="http://planetmath.org/SquareRoot">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4457,7 +4458,8 @@ number is specified) of the given size returned. For example, <para>Calculates the cosine function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html">Planetmath</ulink> for more information. + <ulink url="http://en.wikipedia.org/wiki/Trigonometric_functions">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DefinitionsInTrigonometry">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4469,7 +4471,8 @@ number is specified) of the given size returned. For example, <para>Calculates the hyperbolic cosine function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HyperbolicFunctions.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hyperbolic_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HyperbolicFunctions">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4481,7 +4484,8 @@ number is specified) of the given size returned. For example, <para>The cotangent function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html">Planetmath</ulink> for more information. + <ulink url="http://en.wikipedia.org/wiki/Trigonometric_functions">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DefinitionsInTrigonometry">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4493,7 +4497,8 @@ number is specified) of the given size returned. For example, <para>The hyperbolic cotangent function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HyperbolicFunctions.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hyperbolic_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HyperbolicFunctions">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4505,7 +4510,8 @@ number is specified) of the given size returned. For example, <para>The cosecant function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html">Planetmath</ulink> for more information. + <ulink url="http://en.wikipedia.org/wiki/Trigonometric_functions">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DefinitionsInTrigonometry">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4517,7 +4523,8 @@ number is specified) of the given size returned. For example, <para>The hyperbolic cosecant function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HyperbolicFunctions.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hyperbolic_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HyperbolicFunctions">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4529,7 +4536,8 @@ number is specified) of the given size returned. For example, <para>The secant function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html">Planetmath</ulink> for more information. + <ulink url="http://en.wikipedia.org/wiki/Trigonometric_functions">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DefinitionsInTrigonometry">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4541,7 +4549,8 @@ number is specified) of the given size returned. For example, <para>The hyperbolic secant function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HyperbolicFunctions.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hyperbolic_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HyperbolicFunctions">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4553,7 +4562,8 @@ number is specified) of the given size returned. For example, <para>Calculates the sine function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html">Planetmath</ulink> for more information. + <ulink url="http://en.wikipedia.org/wiki/Trigonometric_functions">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DefinitionsInTrigonometry">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4565,7 +4575,8 @@ number is specified) of the given size returned. For example, <para>Calculates the hyperbolic sine function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HyperbolicFunctions.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hyperbolic_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HyperbolicFunctions">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4577,7 +4588,8 @@ number is specified) of the given size returned. For example, <para>Calculates the tan function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html">Planetmath</ulink> for more information. + <ulink url="http://en.wikipedia.org/wiki/Trigonometric_functions">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DefinitionsInTrigonometry">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4589,7 +4601,8 @@ number is specified) of the given size returned. For example, <para>The hyperbolic tangent function.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HyperbolicFunctions.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hyperbolic_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HyperbolicFunctions">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -4610,7 +4623,8 @@ number is specified) of the given size returned. For example, </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/RelativelyPrime.html">Planetmath</ulink> or + <ulink url="https://en.wikipedia.org/wiki/Coprime_integers">Wikipedia</ulink> or + <ulink url="http://planetmath.org/RelativelyPrime">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/RelativelyPrime.html">Mathworld</ulink> for more information. </para> </listitem> @@ -4641,7 +4655,7 @@ number is specified) of the given size returned. For example, <para> 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://planetmath.org/ChineseRemainderTheorem">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/ChineseRemainderTheorem.html">Mathworld</ulink> for more information. </para> </listitem> @@ -4682,8 +4696,8 @@ number is specified) of the given size returned. For example, is a prime, using the Silver-Pohlig-Hellman algorithm.</para> <para> 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://en.wikipedia.org/wiki/Discrete_logarithm">Wikipedia</ulink>, + <ulink url="http://planetmath.org/DiscreteLogarithm">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/DiscreteLogarithm.html">Mathworld</ulink> for more information. </para> </listitem> @@ -4708,8 +4722,8 @@ number is specified) of the given size returned. For example, </para> <para> 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://en.wikipedia.org/wiki/Euler_phi">Wikipedia</ulink>, + <ulink url="http://planetmath.org/EulerPhifunction">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/TotientFunction.html">Mathworld</ulink> for more information. </para> </listitem> @@ -4860,7 +4874,7 @@ precalculated and returned in the second column.</para> <para> 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://planetmath.org/MersenneNumbers">Planetmath</ulink>, <ulink url="http://mathworld.wolfram.com/MersennePrime.html">Mathworld</ulink> or <ulink url="http://www.mersenne.org/">GIMPS</ulink> for more information. @@ -4935,7 +4949,7 @@ precalculated and returned in the second column.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PrimeNumber.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/PrimeNumber">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/PrimeNumber.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5012,7 +5026,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>Calculate the Legendre symbol (a/p).</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/LegendreSymbol.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/LegendreSymbol">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/LegendreSymbol.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5030,8 +5044,8 @@ If <varname>q</varname> is not prime results are bogus.</para> </para> <para> 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://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test">Wikipedia</ulink>, + <ulink url="http://planetmath.org/LucasLhemer">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/Lucas-LehmerTest.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5044,8 +5058,8 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>Returns the <varname>n</varname>th Lucas number.</para> <para> 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://en.wikipedia.org/wiki/Lucas_number">Wikipedia</ulink>, + <ulink url="http://planetmath.org/LucasNumbers">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/LucasNumber.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5076,7 +5090,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para> 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://planetmath.org/MersenneNumbers">Planetmath</ulink>, <ulink url="http://mathworld.wolfram.com/MersennePrime.html">Mathworld</ulink> or <ulink url="http://www.mersenne.org/">GIMPS</ulink> for more information. @@ -5100,7 +5114,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para> 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://planetmath.org/MillerRabinPrimeTest">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5117,8 +5131,8 @@ If <varname>q</varname> is not prime results are bogus.</para> </para> <para> 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://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test">Wikipedia</ulink>, + <ulink url="http://planetmath.org/MillerRabinPrimeTest">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5148,7 +5162,7 @@ If <varname>q</varname> is not prime results are bogus.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/MoebiusFunction.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/MoebiusFunction">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/MoebiusFunction.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5173,7 +5187,7 @@ If <varname>q</varname> is not prime results are bogus.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PrimeNumber.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/PrimeNumber">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/PrimeNumber.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5186,7 +5200,8 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>Returns the p-adic valuation (number of trailing zeros in base <varname>p</varname>).</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PAdicValuation.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/P-adic_order">Wikipedia</ulink> or + <ulink url="http://planetmath.org/PAdicValuation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5213,7 +5228,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>Return the <varname>n</varname>th prime (up to a limit).</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PrimeNumber.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/PrimeNumber">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/PrimeNumber.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5226,6 +5241,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>Return all prime factors of a number as a vector.</para> <para> See + <ulink url="https://en.wikipedia.org/wiki/Prime_factor">Wikipedia</ulink> or <ulink url="http://mathworld.wolfram.com/PrimeFactor.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5239,7 +5255,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <userinput>b^(n-1) == 1 mod n</userinput></para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Pseudoprime.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/Pseudoprime">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/Pseudoprime.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5252,7 +5268,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>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>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Divisibility.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/Divisibility">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/Factor.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5273,7 +5289,7 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>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.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/QuadraticResidue.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/QuadraticResidue">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/QuadraticResidue.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5286,7 +5302,8 @@ If <varname>q</varname> is not prime results are bogus.</para> <para>Run the strong pseudoprime test base <varname>b</varname> on <varname>n</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/StrongPseudoprime.html">Planetmath</ulink> or + <ulink url="https://en.wikipedia.org/wiki/Strong_pseudoprime">Wikipedia</ulink>, + <ulink url="http://planetmath.org/StrongPseudoprime">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/StrongPseudoprime.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5305,7 +5322,8 @@ If <varname>q</varname> is not prime results are bogus.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/GreatestCommonDivisor.html">Planetmath</ulink> or + <ulink url="https://en.wikipedia.org/wiki/Greatest_common_divisor">Wikipedia</ulink>, + <ulink url="http://planetmath.org/GreatestCommonDivisor">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/GreatestCommonDivisor.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5324,7 +5342,8 @@ If <varname>q</varname> is not prime results are bogus.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/LeastCommonMultiple.html">Planetmath</ulink> or + <ulink url="https://en.wikipedia.org/wiki/Least_common_multiple">Wikipedia</ulink>, + <ulink url="http://planetmath.org/LeastCommonMultiple">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/LeastCommonMultiple.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5422,10 +5441,11 @@ If <varname>q</varname> is not prime results are bogus.</para> <listitem> <synopsis>DotProduct (u,v)</synopsis> <para>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.</para> + same size. No conjugates are taken so this is a bilinear form even if working over the complex numbers; This is the bilinear scalar product not the sesquilinear scalar product. See <link linkend="gel-function-HermitianProduct">HermitianProduct</link> for the standard sesquilinear inner product.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DotProduct.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Dot_product">Wikipedia</ulink> or + <ulink url="http://planetmath.org/DotProduct">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5451,6 +5471,7 @@ same size. No conjugates are taken so this is a bilinear form even if working o <para>Get the Hermitian product of two vectors. The vectors must be of the same size. This is a sesquilinear form using the identity matrix.</para> <para> See + <ulink url="https://en.wikipedia.org/wiki/Sesquilinear_form">Wikipedia</ulink> or <ulink url="http://mathworld.wolfram.com/HermitianInnerProduct.html">Mathworld</ulink> for more information. </para> </listitem> @@ -5464,7 +5485,8 @@ same size. No conjugates are taken so this is a bilinear form even if working o <para>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>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/IdentityMatrix.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Identity_matrix">Wikipedia</ulink> or + <ulink url="http://planetmath.org/IdentityMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5487,7 +5509,7 @@ same size. No conjugates are taken so this is a bilinear form even if working o <para> 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. + <ulink url="http://planetmath.org/DiagonalMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5637,7 +5659,7 @@ functions make this check. Values can be any number including complex numbers.< <para> 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. + <ulink url="http://planetmath.org/DiagonalMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5876,7 +5898,7 @@ number of columns times the number of rows.</para> superdiagonal being all ones. It is the Jordan block matrix of one zero eigenvalue.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/JordanCanonicalFormTheorem.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/JordanCanonicalFormTheorem">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/JordanBlock.html">Mathworld</ulink> for more information on Jordan Canonical Form. </para> </listitem> @@ -5911,7 +5933,8 @@ See also <link linkend="gel-function-CharacteristicPolynomialFunction">Character </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/CharacteristicEquation.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Characteristic_polynomial">Wikipedia</ulink> or + <ulink url="http://planetmath.org/CharacteristicEquation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5927,7 +5950,8 @@ See also <link linkend="gel-function-CharacteristicPolynomial">CharacteristicPol </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/CharacteristicEquation.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Characteristic_polynomial">Wikipedia</ulink> or + <ulink url="http://planetmath.org/CharacteristicEquation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5940,6 +5964,10 @@ See also <link linkend="gel-function-CharacteristicPolynomial">CharacteristicPol 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>.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Row_and_column_spaces">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -5969,7 +5997,8 @@ return a matrix whose columns are the basis for the column space of same as the <userinput>'</userinput> operator.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/ConjugateTranspose.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Conjugate_transpose">Wikipedia</ulink> or + <ulink url="http://planetmath.org/ConjugateTranspose">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -5998,6 +6027,10 @@ result as a vector and not added together.</para> <synopsis>CrossProduct (v,w)</synopsis> <para>CrossProduct of two vectors in R<superscript>3</superscript> as a column vector.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Cross_product">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -6014,6 +6047,10 @@ result as a vector and not added together.</para> <listitem> <synopsis>DirectSum (M,N...)</synopsis> <para>Direct sum of matrices.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Matrix_addition#directsum">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -6022,6 +6059,10 @@ result as a vector and not added together.</para> <listitem> <synopsis>DirectSumMatrixVector (v)</synopsis> <para>Direct sum of a vector of matrices.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Matrix_addition#directsum">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -6037,8 +6078,8 @@ result as a vector and not added together.</para> </para> <para> 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://en.wikipedia.org/wiki/Eigenvalue">Wikipedia</ulink>, + <ulink url="http://planetmath.org/Eigenvalue">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/Eigenvalue.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6056,8 +6097,8 @@ the eigenvalues and their algebraic multiplicities. </para> <para> 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://en.wikipedia.org/wiki/Eigenvector">Wikipedia</ulink>, + <ulink url="http://planetmath.org/Eigenvector">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/Eigenvector.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6075,7 +6116,8 @@ a sesquilinear form. The vectors will be made orthonormal with respect to <varname>B</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/GramSchmidtOrthogonalization.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process">Wikipedia</ulink> or + <ulink url="http://planetmath.org/GramSchmidtOrthogonalization">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6084,7 +6126,13 @@ a sesquilinear form. The vectors will be made orthonormal with respect to <term><anchor id="gel-function-HankelMatrix"/>HankelMatrix</term> <listitem> <synopsis>HankelMatrix (c,r)</synopsis> - <para>Hankel matrix.</para> + <para>Hankel matrix, a matrix whose skew-diagonals are constant. <varname>c</varname> is the first row and <varname>r</varname> is the + last column. It is assumed that both arguments are vectors and the last element of <varname>c</varname> is the same + as the first element of <varname>r</varname>.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Hankel_matrix">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -6095,7 +6143,8 @@ a sesquilinear form. The vectors will be made orthonormal with respect to <para>Hilbert matrix of order <varname>n</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HilbertMatrix.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hilbert_matrix">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HilbertMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6105,6 +6154,10 @@ a sesquilinear form. The vectors will be made orthonormal with respect to <listitem> <synopsis>Image (T)</synopsis> <para>Get the image (columnspace) of a linear transform.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Row_and_column_spaces">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -6131,7 +6184,8 @@ a sesquilinear form. The vectors will be made orthonormal with respect to <para>Inverse Hilbert matrix of order <varname>n</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HilbertMatrix.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hilbert_matrix">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HilbertMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6143,7 +6197,8 @@ a sesquilinear form. The vectors will be made orthonormal with respect to <para>Is a matrix Hermitian. That is, is it equal to its conjugate transpose.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/HermitianMatrix.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Hermitian_matrix">Wikipedia</ulink> or + <ulink url="http://planetmath.org/HermitianMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6180,7 +6235,7 @@ a sesquilinear form. The vectors will be made orthonormal with respect to does <userinput>M*M' == M'*M</userinput>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/NormalMatrix.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/NormalMatrix">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/NormalMatrix.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6207,7 +6262,8 @@ determinant. </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PositiveDefinite.html">Planetmath</ulink> or + <ulink url="https://en.wikipedia.org/wiki/Positive-definite_matrix">Wikipedia</ulink>, + <ulink url="http://planetmath.org/PositiveDefinite">Planetmath</ulink>, or <ulink url="http://mathworld.wolfram.com/PositiveDefiniteMatrix.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6234,7 +6290,7 @@ determinant. </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PositiveSemidefinite.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/PositiveSemidefinite">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/PositiveSemidefiniteMatrix.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6247,7 +6303,7 @@ determinant. <para>Is a matrix skew-Hermitian. That is, is the conjugate transpose equal to negative of the matrix.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/SkewHermitianMatrix.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/SkewHermitianMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6261,7 +6317,7 @@ determinant. equal the identity.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/UnitaryTransformation.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/UnitaryTransformation">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/UnitaryMatrix.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6277,7 +6333,7 @@ determinant. </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/JordanCanonicalFormTheorem.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/JordanCanonicalFormTheorem">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/JordanBlock.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6306,7 +6362,7 @@ determinant. <para> 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://planetmath.org/KroneckerProduct">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/KroneckerProduct.html">Mathworld</ulink> for more information. </para> <para>Version 1.0.18 onwards.</para> @@ -6349,7 +6405,7 @@ determinant. <para> 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://planetmath.org/LUDecomposition">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/LUDecomposition.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6362,7 +6418,7 @@ determinant. <para>Get the <varname>i</varname>-<varname>j</varname> minor of a matrix.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Minor.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/Minor">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6394,7 +6450,7 @@ determinant. <varname>T</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Nullspace.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/Nullspace">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6408,7 +6464,7 @@ determinant. the nullspace; the dimension of the kernel of <varname>M</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Nullity.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/Nullity">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6463,7 +6519,7 @@ function of two arguments or it can be a matrix giving a sesquilinear form. <para> 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://planetmath.org/QRDecomposition">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/QRDecomposition.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6476,7 +6532,7 @@ function of two arguments or it can be a matrix giving a sesquilinear form. <para>Return the Rayleigh quotient (also called the Rayleigh-Ritz quotient or ratio) of a matrix and a vector.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/RayleighQuotient.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/RayleighQuotient">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6497,7 +6553,7 @@ function of two arguments or it can be a matrix giving a sesquilinear form. </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/RayleighQuotient.html">Planetmath</ulink> for more information on Rayleigh quotient. + <ulink url="http://planetmath.org/RayleighQuotient">Planetmath</ulink> for more information on Rayleigh quotient. </para> </listitem> </varlistentry> @@ -6510,7 +6566,7 @@ function of two arguments or it can be a matrix giving a sesquilinear form. <para>Get the rank of a matrix.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/SylvestersLaw.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/SylvestersLaw">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6623,7 +6679,7 @@ Hermitian matrix (if the first element is real of course).</para> <para> 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. + <ulink url="http://planetmath.org/ToeplitzMatrix">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6637,7 +6693,7 @@ Hermitian matrix (if the first element is real of course).</para> <para> 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. + <ulink url="http://planetmath.org/Trace">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6651,7 +6707,7 @@ Hermitian matrix (if the first element is real of course).</para> <para> 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. + <ulink url="http://planetmath.org/Transpose">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6732,7 +6788,7 @@ function of two arguments or it can be a matrix giving a sesquilinear form. <para> 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. + <ulink url="http://planetmath.org/Determinant2">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6748,7 +6804,7 @@ divided to make all pivots 1.</para> <para> 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. + <ulink url="http://planetmath.org/RowEchelonForm">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6762,7 +6818,7 @@ divided to make all pivots 1.</para> <para> 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. + <ulink url="http://planetmath.org/ReducedRowEchelonForm">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6780,7 +6836,7 @@ divided to make all pivots 1.</para> <para>Get <varname>n</varname>th Catalan number.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/CatalanNumbers.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/CatalanNumbers">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6802,7 +6858,7 @@ divided to make all pivots 1.</para> <para>Double factorial: <userinput>n(n-2)(n-4)...</userinput></para> <para> See - <ulink url="http://planetmath.org/encyclopedia/DoubleFactorial.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/DoubleFactorial">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6814,7 +6870,7 @@ divided to make all pivots 1.</para> <para>Factorial: <userinput>n(n-1)(n-2)...</userinput></para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Factorial.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/Factorial">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6826,7 +6882,7 @@ divided to make all pivots 1.</para> <para>Falling factorial: <userinput>(n)_k = n(n-1)...(n-(k-1))</userinput></para> <para> See - <ulink url="http://planetmath.org/encyclopedia/FallingFactorial.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/FallingFactorial">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -6846,7 +6902,7 @@ divided to make all pivots 1.</para> <para> 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://planetmath.org/FibonacciSequence">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/FibonacciNumber.html">Mathworld</ulink> for more information. </para> </listitem> @@ -6943,9 +6999,9 @@ divided to make all pivots 1.</para> </para> <para> 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. + <ulink url="http://en.wikipedia.org/wiki/Multinomial_theorem">Wikipedia</ulink>, + <ulink url="http://planetmath.org/MultinomialTheorem">Planetmath</ulink>, or + <ulink url="http://mathworld.wolfram.com/MultinomialCoefficient.html">Mathworld</ulink> for more information. </para> </listitem> </varlistentry> @@ -6986,7 +7042,7 @@ do ( iterations.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PascalsTriangle.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/PascalsTriangle">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7012,7 +7068,7 @@ do ( <para>(Pochhammer) Rising factorial: (n)_k = n(n+1)...(n+(k-1)).</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/RisingFactorial.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/RisingFactorial">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7025,7 +7081,7 @@ do ( <para>Stirling number of the first kind.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/StirlingNumbersOfTheFirstKind.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/StirlingNumbersOfTheFirstKind">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html">Mathworld</ulink> for more information. </para> </listitem> @@ -7039,7 +7095,7 @@ do ( <para>Stirling number of the second kind.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/StirlingNumbersSecondKind.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/StirlingNumbersSecondKind">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html">Mathworld</ulink> for more information. </para> </listitem> @@ -7060,7 +7116,7 @@ do ( <para>Calculate the <varname>n</varname>th triangular number.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/TriangularNumbers.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/TriangularNumbers">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7074,7 +7130,7 @@ do ( <varname>n</varname> can be any real number.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/Choose.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/Choose">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7106,7 +7162,7 @@ do ( <para>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.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/SimpsonsRule.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/SimpsonsRule">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7118,7 +7174,7 @@ do ( <para>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.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/SimpsonsRule.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/SimpsonsRule">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7128,6 +7184,10 @@ do ( <listitem> <synopsis>Derivative (f,x0)</synopsis> <para>Attempt to calculate derivative by trying first symbolically and then numerically.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Derivative">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -7248,6 +7308,10 @@ or <varname>b</varname> can be <constant>null</constant>.</para> <synopsis>NumericalDerivative (f,x0)</synopsis> <para>Aliases: <function>NDerivative</function></para> <para>Attempt to calculate numerical derivative.</para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Derivative">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -7587,7 +7651,7 @@ and has period <userinput>b-a</userinput>.</para> <term><anchor id="gel-function-DirichletKernel"/>DirichletKernel</term> <listitem> <synopsis>DirichletKernel (n,t)</synopsis> - <para>Dirichlet kernel of order n.</para> + <para>Dirichlet kernel of order <varname>n</varname>.</para> </listitem> </varlistentry> @@ -7607,7 +7671,8 @@ and has period <userinput>b-a</userinput>.</para> <para>The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/ErrorFunction.html">Planetmath</ulink> for more information. + <ulink url="https://en.wikipedia.org/wiki/Error_function">Wikipedia</ulink> or + <ulink url="http://planetmath.org/ErrorFunction">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7620,7 +7685,7 @@ and has period <userinput>b-a</userinput>.</para> <varname>t</varname></para> <para> See - <ulink url="http://planetmath.org/encyclopedia/FejerKernel.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/FejerKernel">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7633,7 +7698,7 @@ and has period <userinput>b-a</userinput>.</para> <para>The Gamma function. Currently only implemented for real values.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/GammaFunction.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/GammaFunction">Planetmath</ulink> or <ulink url="http://en.wikipedia.org/wiki/Gamma_function">Wikipedia</ulink> for more information. </para> </listitem> @@ -7702,7 +7767,7 @@ and has period <userinput>b-a</userinput>.</para> <para>Moebius mapping of the disk to itself mapping a to 0.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/MobiusTransformation.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/MobiusTransformation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7714,7 +7779,7 @@ and has period <userinput>b-a</userinput>.</para> <para>Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity respectively.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/MobiusTransformation.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/MobiusTransformation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7726,7 +7791,7 @@ and has period <userinput>b-a</userinput>.</para> <para>Moebius mapping using the cross ratio taking infinity to infinity and z2,z3 to 1 and 0 respectively.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/MobiusTransformation.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/MobiusTransformation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7738,7 +7803,7 @@ and has period <userinput>b-a</userinput>.</para> <para>Moebius mapping using the cross ratio taking infinity to 1 and z3,z4 to 0 and infinity respectively.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/MobiusTransformation.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/MobiusTransformation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7750,7 +7815,7 @@ and has period <userinput>b-a</userinput>.</para> <para>Moebius mapping using the cross ratio taking infinity to 0 and z2,z4 to 1 and infinity respectively.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/MobiusTransformation.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/MobiusTransformation">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -7779,7 +7844,7 @@ and has period <userinput>b-a</userinput>.</para> <para>The Riemann zeta function. Currently only implemented for real values.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/RiemannZetaFunction.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/RiemannZetaFunction">Planetmath</ulink> or <ulink url="http://en.wikipedia.org/wiki/Riemann_zeta_function">Wikipedia</ulink> for more information. </para> </listitem> @@ -7861,7 +7926,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/CubicFormula.html">Planetmath</ulink>, + <ulink url="http://planetmath.org/CubicFormula">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. </para> @@ -7891,7 +7956,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://mathworld.wolfram.com/EulerForwardMethod.html">Mathworld</ulink>, or + <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. </para> </listitem> @@ -7947,7 +8012,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://mathworld.wolfram.com/EulerForwardMethod.html">Mathworld</ulink>, or + <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. </para> <para>Version 1.0.10 onwards.</para> @@ -8089,7 +8154,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/QuadraticFormula.html">Planetmath</ulink> or + <ulink url="http://planetmath.org/QuadraticFormula">Planetmath</ulink> or <ulink url="http://mathworld.wolfram.com/QuadraticFormula.html">Mathworld</ulink> for more information. </para> </listitem> @@ -8109,7 +8174,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://planetmath.org/encyclopedia/QuarticFormula.html">Planetmath</ulink>, + <ulink url="http://planetmath.org/QuarticFormula">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. </para> @@ -8136,7 +8201,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://mathworld.wolfram.com/Runge-KuttaMethod.html">Mathworld</ulink>, or + <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. </para> </listitem> @@ -8189,7 +8254,7 @@ and has period <userinput>b-a</userinput>.</para> </para> <para> See - <ulink url="http://mathworld.wolfram.com/Runge-KuttaMethod.html">Mathworld</ulink>, or + <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. </para> <para>Version 1.0.10 onwards.</para> @@ -8341,7 +8406,7 @@ and has period <userinput>b-a</userinput>.</para> degree than <varname>q</varname>.</para> <para> See - <ulink url="http://planetmath.org/encyclopedia/PolynomialLongDivision.html">Planetmath</ulink> for more information. + <ulink url="http://planetmath.org/PolynomialLongDivision">Planetmath</ulink> for more information. </para> </listitem> </varlistentry> @@ -8577,6 +8642,10 @@ and has period <userinput>b-a</userinput>.</para> = (`(x)=(7*(2*x))) </screen> </para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Derivative">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -8587,6 +8656,10 @@ and has period <userinput>b-a</userinput>.</para> <para>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>) </para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Derivative">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -8597,6 +8670,10 @@ and has period <userinput>b-a</userinput>.</para> <para>Attempt to symbolically differentiate a function n times. (See <link linkend="gel-function-SymbolicDerivative"><function>SymbolicDerivative</function></link>) </para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Derivative">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> @@ -8607,6 +8684,10 @@ and has period <userinput>b-a</userinput>.</para> <para>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>) </para> + <para> + See + <ulink url="https://en.wikipedia.org/wiki/Derivative">Wikipedia</ulink> for more information. + </para> </listitem> </varlistentry> |