[BUGFIX] Fix crash in parser.

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 159d6a0bd2f002c137ae6e0ba270275f7aa90dff..52c5828e95a178e8d2de18d3e66d3fb3c7fb2adb 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -24,7 +24,7 @@
 This is a tutorial that documents GiNaC @value{VERSION}, an open
 framework for symbolic computation within the C++ programming language.
 
-Copyright (C) 1999-2022 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2024 Johannes Gutenberg University Mainz, Germany
 
 Permission is granted to make and distribute verbatim copies of
 this manual provided the copyright notice and this permission notice
@@ -52,7 +52,7 @@ notice identical to this one.
 
 @page
 @vskip 0pt plus 1filll
-Copyright @copyright{} 1999-2022 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2024 Johannes Gutenberg University Mainz, Germany
 @sp 2
 Permission is granted to make and distribute verbatim copies of
 this manual provided the copyright notice and this permission notice
@@ -135,7 +135,7 @@ the near future.
 
 @section License
 The GiNaC framework for symbolic computation within the C++ programming
-language is Copyright @copyright{} 1999-2021 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2024 Johannes Gutenberg
 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or
@@ -3242,7 +3242,8 @@ element, which defaults to 4.
 The @code{dirac_trace()} function is a linear functional that is equal to the
 ordinary matrix trace only in @math{D = 4} dimensions. In particular, the
 functional is not cyclic in
-@tex $D \ne 4$
+@tex
+$D \ne 4$
 @end tex
 @ifnottex
 @math{D != 4}
@@ -3253,7 +3254,8 @@ expressions containing @samp{gamma5}, so it's not a proper trace. This
 @cite{The Role of gamma5 in Dimensional Regularization} (@ref{Bibliography}).
 
 The value of the trace itself is also usually different in 4 and in
-@tex $D \ne 4$
+@tex
+$D \ne 4$
 @end tex
 @ifnottex
 @math{D != 4}
@@ -3326,15 +3328,16 @@ You can use this to compare two expressions or for further simplifications:
 @subsubsection A generic Clifford algebra
 
 A generic Clifford algebra, i.e. a
-@tex $2^n$
+@tex
+$2^n$
 @end tex
 @ifnottex
 2^n
 @end ifnottex
-dimensional algebra with
-generators 
-@tex $e_k$
-@end tex 
+dimensional algebra with generators
+@tex
+$e_k$
+@end tex
 @ifnottex
 e_k
 @end ifnottex
@@ -5379,6 +5382,27 @@ some care with subsequent processing of the result:
 Note also, how factors with the same exponents are not fully factorized
 with this method.
 
+@subsection Square-free partial fraction decomposition
+@cindex square-free partial fraction decomposition
+@cindex partial fraction decomposition
+@cindex @code{sqrfree_parfrac()}
+
+GiNaC also supports square-free partial fraction decomposition of
+rational functions:
+@example
+ex sqrfree_parfrac(const ex & a, const symbol & x);
+@end example
+It is called square-free because it assumes a square-free
+factorization of the input's denominator:
+@example
+    ...
+    symbol x("x");
+
+    ex rat = (x-4)/(pow(x,2)*(x+2));
+    cout << sqrfree_parfrac(rat, x) << endl;
+     // -> -2*x^(-2)+3/2*x^(-1)-3/2*(2+x)^(-1)
+@end example
+
 @subsection Polynomial factorization
 @cindex factorization
 @cindex polynomial factorization