From 627de8efe53389269082bc0c908a10e7e09b9207 Mon Sep 17 00:00:00 2001 From: Richard Kreckel Date: Sat, 11 Apr 2020 01:10:47 +0200 Subject: [PATCH] Minor enhancements to tutorial. --- doc/tutorial/ginac.texi | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi index 386dfeaf..765c966e 100644 --- a/doc/tutorial/ginac.texi +++ b/doc/tutorial/ginac.texi @@ -372,8 +372,8 @@ lambda^2-3*lambda+11 @end example Multivariate polynomials and rational functions may be expanded, -collected and normalized (i.e. converted to a ratio of two coprime -polynomials): +collected, factorized, and normalized (i.e. converted to a ratio of +two coprime polynomials): @example > a = x^4 + 2*x^2*y^2 + 4*x^3*y + 12*x*y^3 - 3*y^4; @@ -382,6 +382,8 @@ polynomials): 4*x*y-y^2+x^2 > expand(a*b); 8*x^5*y+17*x^4*y^2+43*x^2*y^4-24*x*y^5+16*x^3*y^3+3*y^6+x^6 +> factor(%); +(4*x*y+x^2-y^2)^2*(x^2+3*y^2) > collect(a+b,x); 4*x^3*y-y^2-3*y^4+(12*y^3+4*y)*x+x^4+x^2*(1+2*y^2) > collect(a+b,y); @@ -390,6 +392,9 @@ polynomials): 3*y^2+x^2 @end example +Here we have made use of the @command{ginsh}-command @code{%} to pop the +previously evaluated element from @command{ginsh}'s internal stack. + You can differentiate functions and expand them as Taylor or Laurent series in a very natural syntax (the second argument of @code{series} is a relation defining the evaluation point, the third specifies the @@ -414,9 +419,6 @@ x^(-1)-0.5772156649015328606+(0.9890559953279725555)*x -Euler-1/12+Order((x-1/2*Pi)^3) @end example -Here we have made use of the @command{ginsh}-command @code{%} to pop the -previously evaluated element from @command{ginsh}'s internal stack. - Often, functions don't have roots in closed form. Nevertheless, it's quite easy to compute a solution numerically, to arbitrary precision: @@ -5980,7 +5982,7 @@ calls of several @code{expand()} methods with desired flags. The multiple polylogarithm is the most generic member of a family of functions, to which others like the harmonic polylogarithm, Nielsen's generalized polylogarithm and the multiple zeta value belong. -Everyone of these functions can also be written as a multiple polylogarithm with specific +Each of these functions can also be written as a multiple polylogarithm with specific parameters. This whole family of functions is therefore often referred to simply as multiple polylogarithms, containing @code{Li}, @code{G}, @code{H}, @code{S} and @code{zeta}. The multiple polylogarithm itself comes in two variants: @code{Li} and @code{G}. While -- 2.44.0