Minor enhancements to tutorial.

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 386dfeafd1d6c92aa8ea84572b1e371eabcb0252..765c966e69462edb3934f7230b2e1f3a4a13b154 100644 (file)
--- 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,
 @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;
 
 @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
 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);
 > 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
 
 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
 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
 
 -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:
 
 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.
 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
 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