Fixing index in tutorial.

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index d5bea846342325744ea73283293dc31c2815760d..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.
 
@@ -5772,11 +5772,11 @@ almost any kind of object (anything that is @code{subs()}able):
     idx i(symbol("i"), 3), j(symbol("j"), 3), k(symbol("k"), 3);
     symbol A("A"), B("B"), a("a"), b("b"), c("c");
                                            
-    cout << indexed(A, i, j).symmetrize() << endl;
+    cout << ex(indexed(A, i, j)).symmetrize() << endl;
      // -> 1/2*A.j.i+1/2*A.i.j
-    cout << indexed(A, i, j, k).antisymmetrize(lst(i, j)) << endl;
+    cout << ex(indexed(A, i, j, k)).antisymmetrize(lst(i, j)) << endl;
      // -> -1/2*A.j.i.k+1/2*A.i.j.k
-    cout << lst(a, b, c).symmetrize_cyclic(lst(a, b, c)) << endl;
+    cout << ex(lst(a, b, c)).symmetrize_cyclic(lst(a, b, c)) << endl;
      // -> 1/3*@{a,b,c@}+1/3*@{b,c,a@}+1/3*@{c,a,b@}
 @}
 @end example
@@ -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()}
@@ -6539,7 +6542,9 @@ Sometimes you might want to prevent GiNaC from inserting these extra symbols
 @}
 @end example
 
-With this parser, it's also easy to implement interactive GiNaC programs:
+With this parser, it's also easy to implement interactive GiNaC programs.
+When running the following program interactively, remember to send an
+EOF marker after the input, e.g. by pressing Ctrl-D on an empty line:
 
 @example
 #include <iostream>
@@ -7098,6 +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
@@ -7133,14 +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.