Fixing index in tutorial.

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 236d98ddeb93b61c477e6bb48cac78c2591245ec..360acb05a0e98b1a38f8923f7b43920aa266cabc 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) 1999-2011 Johannes Gutenberg University Mainz, Germany
+Copyright (C) 1999-2015 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{} 1999-2011 Johannes Gutenberg University Mainz, Germany
+Copyright @copyright{} 1999-2015 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{} 1999-2011 Johannes Gutenberg
+language is Copyright @copyright{} 1999-2015 Johannes Gutenberg
 University Mainz, Germany.
 
 This program is free software; you can redistribute it and/or
@@ -3334,7 +3334,7 @@ Clifford algebras, which will commute with each other.
 Note that the call @code{clifford_unit(mu, minkmetric())} creates
 something very close to @code{dirac_gamma(mu)}, although
 @code{dirac_gamma} have more efficient simplification mechanism. 
-@cindex @code{clifford::get_metric()}
+@cindex @code{get_metric()}
 The method @code{clifford::get_metric()} returns a metric defining this
 Clifford number.
 
@@ -5858,6 +5858,9 @@ GiNaC contains the following predefined mathematical functions:
 @item @code{log(x)}
 @tab natural logarithm
 @cindex @code{log()}
+@item @code{eta(x,y)}
+@tab Eta function: @code{eta(x,y) = log(x*y) - log(x) - log(y)}
+@cindex @code{eta()}
 @item @code{Li2(x)}
 @tab dilogarithm
 @cindex @code{Li2()}
@@ -7100,6 +7103,25 @@ specifies which parameter to differentiate in a partial derivative in
 case the function has more than one parameter, and its main application
 is for correct handling of the chain rule.
 
+Derivatives of some functions, for example @code{abs()} and
+@code{Order()}, could not be evaluated through the chain rule. In such
+cases the full derivative may be specified as shown for @code{Order()}:
+
+@example
+static ex Order_expl_derivative(const ex & arg, const symbol & s)
+@{
+       return Order(arg.diff(s));
+@}
+@end example
+
+That is, we need to supply a procedure, which returns the expression of
+derivative with respect to the variable @code{s} for the argument
+@code{arg}. This procedure need to be registered with the function
+through the option @code{expl_derivative_func} (see the next
+Subsection). In contrast, a partial derivative, e.g. as was defined for
+@code{cos()} above, needs to be registered through the option
+@code{derivative_func}. 
+
 An implementation of the series expansion is not needed for @code{cos()} as
 it doesn't have any poles and GiNaC can do Taylor expansion by itself (as
 long as it knows what the derivative of @code{cos()} is). @code{tan()}, on
@@ -7135,14 +7157,15 @@ functions without any special options.
 eval_func(<C++ function>)
 evalf_func(<C++ function>)
 derivative_func(<C++ function>)
+expl_derivative_func(<C++ function>)
 series_func(<C++ function>)
 conjugate_func(<C++ function>)
 @end example
 
 These specify the C++ functions that implement symbolic evaluation,
-numeric evaluation, partial derivatives, and series expansion, respectively.
-They correspond to the GiNaC methods @code{eval()}, @code{evalf()},
-@code{diff()} and @code{series()}.
+numeric evaluation, partial derivatives, explicit derivative, and series
+expansion, respectively.  They correspond to the GiNaC methods
+@code{eval()}, @code{evalf()}, @code{diff()} and @code{series()}.
 
 The @code{eval_func()} function needs to use @code{.hold()} if no further
 automatic evaluation is desired or possible.