Updated remarks on harmonic polylog.

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 04ab4b4056c20112d3316ecafee7a949e297a029..b882f60df5cab55a7e731bd6670ff5ae4a452ac0 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -23,7 +23,7 @@
 This is a tutorial that documents GiNaC @value{VERSION}, an open
 framework for symbolic computation within the C++ programming language.
 
-Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2004 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{} 1999-2003 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2004 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{} 1999-2003 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2004 Johannes Gutenberg
 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or
@@ -4182,8 +4182,9 @@ 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). To extract
-a coefficient with a certain power from an expanded polynomial you use
+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);
@@ -4956,10 +4957,10 @@ Arguments equal to zero get considered, too. Riemann's zeta function @code{zeta}
 evaluates also for negative integers and positive even integers. For example:
 
 @example
-> Li({3,1},{x,1});
+> Li(@{3,1@},@{x,1@});
 S(2,2,x)
-> H({-3,2},1);
--zeta({3,2},{-1,-1})
+> H(@{-3,2@},1);
+-zeta(@{3,2@},@{-1,-1@})
 > S(3,1,1);
 1/90*Pi^4
 @end example
@@ -4972,10 +4973,10 @@ quickly be messed up, for example. Therefore GiNaC offers a C++ function
 @code{Li} (@code{eval()} already cares for the possible downgrade):
 
 @example
-> convert_H_to_Li({0,-2,-1,3},x);
-Li({3,1,3},{-x,1,-1})
-> convert_H_to_Li({2,-1,0},x);
--Li({2,1},{x,-1})*log(x)+2*Li({3,1},{x,-1})+Li({2,2},{x,-1})
+> convert_H_to_Li(@{0,-2,-1,3@},x);
+Li(@{3,1,3@},@{-x,1,-1@})
+> convert_H_to_Li(@{2,-1,0@},x);
+-Li(@{2,1@},@{x,-1@})*log(x)+2*Li(@{3,1@},@{x,-1@})+Li(@{2,2@},@{x,-1@})
 @end example
 
 Every function apart from the multiple polylogarithm @code{Li} can be numerically evaluated for
@@ -4990,10 +4991,13 @@ $x_1x_2\cdots x_i < 1$ holds.
 @example
 > Digits=100;
 100
-> evalf(zeta({3,1,3,1}));
+> evalf(zeta(@{3,1,3,1@}));
 0.005229569563530960100930652283899231589890420784634635522547448972148869544...
 @end example
 
+Note that the convention for arguments on the branch cut in GiNaC as stated above is
+different from the one Remiddi and Vermaseren have chosen for the harmonic polylogarithm.
+
 If a function evaluates to infinity, no exceptions are raised, but the function is returned
 unevaluated, e.g.
 @tex