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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 710e06f8bb97ba77c996707265e9aa51c04e4cf6..ffdfbef52ed1c17a2aac9a744e35ab9798f533c2 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) 1999-2018 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2019 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{} 1999-2018 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2019 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{} 1999-2018 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2019 Johannes Gutenberg
 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or
@@ -2172,15 +2172,15 @@ computing determinants, traces, characteristic polynomials and ranks:
 ex matrix::determinant(unsigned algo=determinant_algo::automatic) const;
 ex matrix::trace() const;
 ex matrix::charpoly(const ex & lambda) const;
-unsigned matrix::rank() const;
+unsigned matrix::rank(unsigned algo=solve_algo::automatic) const;
 @end example
 
-The optional @samp{algo} argument of @code{determinant()} allows to
-select between different algorithms for calculating the determinant.
-The asymptotic speed (as parametrized by the matrix size) can greatly
-differ between those algorithms, depending on the nature of the
-matrix' entries.  The possible values are defined in the
-@file{flags.h} header file.  By default, GiNaC uses a heuristic to
+The optional @samp{algo} argument of @code{determinant()} and @code{rank()}
+functions allows to select between different algorithms for calculating the
+determinant and rank respectively. The asymptotic speed (as parametrized
+by the matrix size) can greatly differ between those algorithms, depending
+on the nature of the matrix' entries. The possible values are defined in
+the @file{flags.h} header file. By default, GiNaC uses a heuristic to
 automatically select an algorithm that is likely (but not guaranteed)
 to give the result most quickly.
 
@@ -5131,18 +5131,17 @@ a*(2*x*y+y^2+x^2)
 @cindex @code{ldegree()}
 @cindex @code{coeff()}
 
-The degree and low degree of a polynomial can be obtained using the two
-methods
+The degree and low degree of a polynomial in expanded form can be obtained
+using the two methods
 
 @example
 int ex::degree(const ex & s);
 int ex::ldegree(const ex & s);
 @end example
 
-which also work reliably on non-expanded input polynomials (they even work
-on rational functions, returning the asymptotic degree). By definition, the
-degree of zero is zero. To extract a coefficient with a certain power from
-an expanded polynomial you use
+These functions even work on rational functions, returning the asymptotic
+degree. By definition, the degree of zero is zero. To extract a coefficient
+with a certain power from an expanded polynomial you use
 
 @example
 ex ex::coeff(const ex & s, int n);
@@ -5500,8 +5499,11 @@ ex ex::numer_denom();
 
 These functions will first normalize the expression as described above and
 then return the numerator, denominator, or both as a list, respectively.
-If you need both numerator and denominator, calling @code{numer_denom()} is
-faster than using @code{numer()} and @code{denom()} separately.
+If you need both numerator and denominator, call @code{numer_denom()}: it
+is faster than using @code{numer()} and @code{denom()} separately. And even
+more important: a separate evaluation of @code{numer()} and @code{denom()}
+may result in a spurious sign, e.g. for $x/(x^2-1)$ @code{numer()} may
+return $x$ and @code{denom()} $1-x^2$.
 
 
 @subsection Converting to a polynomial or rational expression