[DOC] Fix typo in series_to_poly() documentation.

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 40fa562493db280cce75c18d1f6afc4c3ccfec47..c97da74233be12c490f82c1260eb4203f9608a35 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) 1999-2021 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2022 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{} 1999-2021 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2022 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
@@ -1866,13 +1866,31 @@ substitutions.  They are also used as arguments to the @code{ex::series}
 method, where the left hand side of the relation specifies the variable
 to expand in and the right hand side the expansion point.  They can also
 be used for creating systems of equations that are to be solved for
-unknown variables.  But the most common usage of objects of this class
+unknown variables.
+
+But the most common usage of objects of this class
 is rather inconspicuous in statements of the form @code{if
 (expand(pow(a+b,2))==a*a+2*a*b+b*b) @{...@}}.  Here, an implicit
 conversion from @code{relational} to @code{bool} takes place.  Note,
 however, that @code{==} here does not perform any simplifications, hence
 @code{expand()} must be called explicitly.
 
+Simplifications of
+relationals may be more efficient if preceded by a call to
+@example
+ex relational::canonical() const
+@end example
+which returns an equivalent relation with the zero
+right-hand side. For example:
+@example
+possymbol p("p");
+relational rel = (p >= (p*p-1)/p);
+if (ex_to<relational>(rel.canonical().normal()))
+       cout << "correct inequality" << endl;
+@end example
+However, a user shall not expect that any inequality can be fully
+resolved by GiNaC.
+
 @node Integrals, Matrices, Relations, Basic concepts
 @c    node-name, next, previous, up
 @section Integrals
@@ -5682,7 +5700,7 @@ using namespace GiNaC;
 ex machin_pi(int degr)
 @{
     symbol x;
-    ex pi_expansion = series_to_poly(atan(x).series(x,degr));
+    ex pi_expansion = series_to_poly(atan(x).series(x==0,degr));
     ex pi_approx = 16*pi_expansion.subs(x==numeric(1,5))
                    -4*pi_expansion.subs(x==numeric(1,239));
     return pi_approx;