Add exam for exam_common_factors.

[ginac.git] / doc / tutorial / ginac.texi

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 3b9b4637594eef1703d41bb79410d86ee41c08d8..1ba42151e86a39898c9c2dbef89cc4268c1d5a3f 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -48,7 +48,7 @@ notice identical to this one.
 @title GiNaC @value{VERSION}
 @subtitle An open framework for symbolic computation within the C++ programming language
 @subtitle @value{UPDATED}
-@author @uref{http://www.ginac.de}
+@author @uref{https://www.ginac.de}
 
 @page
 @vskip 0pt plus 1filll
@@ -126,7 +126,7 @@ hand-made documentation like this one is difficult to keep in sync with
 the development, the actual documentation is inside the sources in the
 form of comments.  That documentation may be parsed by one of the many
 Javadoc-like documentation systems.  If you fail at generating it you
-may access it from @uref{http://www.ginac.de/reference/, the GiNaC home
+may access it from @uref{https://www.ginac.de/reference/, the GiNaC home
 page}.  It is an invaluable resource not only for the advanced user who
 wishes to extend the system (or chase bugs) but for everybody who wants
 to comprehend the inner workings of GiNaC.  This little tutorial on the
@@ -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:
 
@@ -484,7 +486,7 @@ required for the configuration, it can be downloaded from
 @uref{http://pkg-config.freedesktop.org}.
 Last but not least, the CLN library
 is used extensively and needs to be installed on your system.
-Please get it from @uref{http://www.ginac.de/CLN/} (it is licensed under
+Please get it from @uref{https://www.ginac.de/CLN/} (it is licensed under
 the GPL) and install it prior to trying to install GiNaC.  The configure
 script checks if it can find it and if it cannot, it will refuse to
 continue.
@@ -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
@@ -6694,8 +6696,8 @@ expression a unique name:
 
 @example
 #include <fstream>
-using namespace std;
 #include <ginac/ginac.h>
+using namespace std;
 using namespace GiNaC;
 
 int main()
@@ -7611,9 +7613,8 @@ product in a C++ @code{struct}:
 
 @example
 #include <iostream>
-using namespace std;
-
 #include <ginac/ginac.h>
+using namespace std;
 using namespace GiNaC;
 
 struct sprod_s @{
@@ -8005,9 +8006,8 @@ as follows:
 #include <iostream>
 #include <string>   
 #include <stdexcept>
-using namespace std;
-
 #include <ginac/ginac.h>
+using namespace std;
 using namespace GiNaC;
 @end example