[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 54fd09a69a2fb137d95ec5206b0390cb2aaba137..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) 1999-2020 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{} 1999-2020 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
@@ -135,7 +135,7 @@ the near future.
 
 @section License
 The GiNaC framework for symbolic computation within the C++ programming
-language is Copyright @copyright{} 1999-2020 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2021 Johannes Gutenberg
 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or
@@ -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
@@ -4855,7 +4873,7 @@ presented this would be impractical.
 One solution to this dilemma is the @dfn{Visitor} design pattern,
 which is implemented in GiNaC (actually, Robert Martin's Acyclic Visitor
 variation, described in detail in
-@uref{http://objectmentor.com/publications/acv.pdf}). Instead of adding
+@uref{https://condor.depaul.edu/dmumaugh/OOT/Design-Principles/acv.pdf}). Instead of adding
 virtual functions to the class hierarchy to implement operations, GiNaC
 provides a single "bouncing" method @code{accept()} that takes an instance
 of a special @code{visitor} class and redirects execution to the one
@@ -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;
@@ -8663,9 +8681,9 @@ inserted.  But it may be useful to remember that this is not what
 happens.  Knowing this will enable you to write much more efficient
 code.  If you still have an uncertain feeling with copy-on-write
 semantics, we recommend you have a look at the
-@uref{http://www.parashift.com/c++-faq-lite/, C++-FAQ lite} by
-Marshall Cline.  Chapter 16 covers this issue and presents an
-implementation which is pretty close to the one in GiNaC.
+@uref{https://isocpp.org/faq, C++-FAQ's} chapter on memory management.
+It covers this issue and presents an implementation which is pretty
+close to the one in GiNaC.
 
 
 @node Internal representation of products and sums, Package tools, Expressions are reference counted, Internal structures