Index renaming issues, sped up simplify_indexed, used defined NC-objects

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

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 0d337cdb74275d10cb7961edb3d2c0a87f9e830a..3cd6c6179478ce9d05b81261eb9317e53b639744 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -423,7 +423,7 @@ quite easy to compute a solution numerically, to arbitrary precision:
 @cindex fsolve
 @example
 > Digits=50:
-> fsolve(cos(x)-x,x,0,2);
+> fsolve(cos(x)==x,x,0,2);
 0.7390851332151606416553120876738734040134117589007574649658
 > f=exp(sin(x))-x:
 > X=fsolve(f,x,-10,10);
@@ -481,12 +481,10 @@ so if you have a different compiler you are on your own.  For the
 configuration to succeed you need a Posix compliant shell installed in
 @file{/bin/sh}, GNU @command{bash} is fine.  Perl is needed by the built
 process as well, since some of the source files are automatically
-generated by Perl scripts.  Last but not least, Bruno Haible's library
-CLN is extensively used and needs to be installed on your system.
-Please get it either from @uref{ftp://ftp.santafe.edu/pub/gnu/}, from
-@uref{ftp://ftpthep.physik.uni-mainz.de/pub/gnu/, GiNaC's FTP site} or
-from @uref{ftp://ftp.ilog.fr/pub/Users/haible/gnu/, Bruno Haible's FTP
-site} (it is covered by GPL) and install it prior to trying to install
+generated by Perl scripts.  Last but not least, the CLN library
+is used extensively and needs to be installed on your system.
+Please get it from @uref{ftp://ftpthep.physik.uni-mainz.de/pub/gnu/}
+(it is covered by GPL) and install it prior to trying to install
 GiNaC.  The configure script checks if it can find it and if it cannot
 it will refuse to continue.
 
@@ -1910,7 +1908,7 @@ much work if an expression contains the same integral multiple times,
 a lookup table is used.
 
 If you know that an expression holds an integral, you can get the
-integration variable, the left boundary, right boundary and integrant by
+integration variable, the left boundary, right boundary and integrand by
 respectively calling @code{.op(0)}, @code{.op(1)}, @code{.op(2)}, and
 @code{.op(3)}. Differentiating integrals with respect to variables works
 as expected. Note that it makes no sense to differentiate an integral
@@ -1974,6 +1972,38 @@ by @samp{c}) unit matrix. And finally, @code{symbolic_matrix} constructs a
 matrix filled with newly generated symbols made of the specified base name
 and the position of each element in the matrix.
 
+Matrices often arise by omitting elements of another matrix. For
+instance, the submatrix @code{S} of a matrix @code{M} takes a
+rectangular block from @code{M}. The reduced matrix @code{R} is defined
+by removing one row and one column from a matrix @code{M}. (The
+determinant of a reduced matrix is called a @emph{Minor} of @code{M} and
+can be used for computing the inverse using Cramer's rule.)
+
+@cindex @code{sub_matrix()}
+@cindex @code{reduced_matrix()}
+@example
+ex sub_matrix(const matrix&m, unsigned r, unsigned nr, unsigned c, unsigned nc);
+ex reduced_matrix(const matrix& m, unsigned r, unsigned c);
+@end example
+
+The function @code{sub_matrix()} takes a row offset @code{r} and a
+column offset @code{c} and takes a block of @code{nr} rows and @code{nc}
+columns. The function @code{reduced_matrix()} has two integer arguments
+that specify which row and column to remove:
+
+@example
+@{
+    matrix m(3,3);
+    m = 11, 12, 13,
+        21, 22, 23,
+        31, 32, 33;
+    cout << reduced_matrix(m, 1, 1) << endl;
+    // -> [[11,13],[31,33]]
+    cout << sub_matrix(m, 1, 2, 1, 2) << endl;
+    // -> [[22,23],[32,33]]
+@}
+@end example
+
 Matrix elements can be accessed and set using the parenthesis (function call)
 operator:
 
@@ -3778,7 +3808,6 @@ avoided.
 * Built-in Functions::              List of predefined mathematical functions.
 * Multiple polylogarithms::
 * Complex Conjugation::
-* Built-in Functions::              List of predefined mathematical functions.
 * Solving Linear Systems of Equations::
 * Input/Output::                    Input and output of expressions.
 @end menu
@@ -4249,13 +4278,17 @@ contain the same number of elements). Using this form, you would write
 @end example
 
 The optional last argument to @code{subs()} is a combination of
-@code{subs_options} flags. There are two options available:
+@code{subs_options} flags. There are three options available:
 @code{subs_options::no_pattern} disables pattern matching, which makes
 large @code{subs()} operations significantly faster if you are not using
 patterns. The second option, @code{subs_options::algebraic} enables
 algebraic substitutions in products and powers.
 @ref{Pattern Matching and Advanced Substitutions}, for more information
-about patterns and algebraic substitutions.
+about patterns and algebraic substitutions. The third option,
+@code{subs_options::no_index_renaming} disables the feature that dummy
+indices are renamed if the subsitution could give a result in which a
+dummy index occurs more than two times. This is sometimes necessary if
+you want to use @code{subs()} to rename your dummy indices.
 
 @code{subs()} performs syntactic substitution of any complete algebraic
 object; it does not try to match sub-expressions as is demonstrated by the