for example (@pxref{Complex expressions}), do @emph{not} evaluate if applied
to such symbols. Likewise @code{log(exp(x))} does not evaluate to @code{x},
because of the unknown imaginary part of @code{x}.
-On the other hand, if you are sure that your symbols will hold only real values, you
-would like to have such functions evaluated. Therefore GiNaC allows you to specify
+On the other hand, if you are sure that your symbols will hold only real
+values, you would like to have such functions evaluated. Therefore GiNaC
+allows you to specify
the domain of the symbol. Instead of @code{symbol x("x");} you can write
@code{realsymbol x("x");} to tell GiNaC that @code{x} stands in for real values.
+@cindex @code{possymbol()}
+Furthermore, it is also possible to declare a symbol as positive. This will,
+for instance, enable the automatic simplification of @code{abs(x)} into
+@code{x}. This is done by declaying the symbol as @code{possymbol x("x");}.
+
@node Numbers, Constants, Symbols, Basic concepts
@c node-name, next, previous, up
@}
@end example
+@cindex @code{is_zero_matrix()}
+The method @code{matrix::is_zero_matrix()} returns @code{true} only if
+all entries of the matrix are zeros. There is also method
+@code{ex::is_zero_matrix()} which returns @code{true} only if the
+expression is zero or a zero matrix.
+
@cindex @code{transpose()}
There are three ways to do arithmetic with matrices. The first (and most
direct one) is to use the methods provided by the @code{matrix} class:
The @code{scalar_products} object @code{sp} acts as a storage for the
scalar products added to it with the @code{.add()} method. This method
takes three arguments: the two expressions of which the scalar product is
-taken, and the expression to replace it with. After @code{sp.add(A, B, 0)},
-@code{simplify_indexed()} will replace all scalar products of indexed
-objects that have the symbols @code{A} and @code{B} as base expressions
-with the single value 0. The number, type and dimension of the indices
-don't matter; @samp{A~mu~nu*B.mu.nu} would also be replaced by 0.
+taken, and the expression to replace it with.
@cindex @code{expand()}
The example above also illustrates a feature of the @code{expand()} method:
@code{idx} as well.
Parameter @code{metr} defines the metric @math{M(i, j)} and can be
represented by a square @code{matrix}, @code{tensormetric} or @code{indexed} class
-object. Optional parameter @code{rl} allows to distinguish different
+object. In fact, any expression either with two free indices or without
+indices at all is admitted as @code{metr}. In the later case an @code{indexed}
+object with two newly created indices with @code{metr} as its
+@code{op(0)} will be used.
+Optional parameter @code{rl} allows to distinguish different
Clifford algebras, which will commute with each other. The last
optional parameter @code{anticommuting} defines if the anticommuting
assumption (i.e.
the matrix @samp{M = [[a, b], [c, d]]}. The parameter @code{G} defines
the metric of the surrounding (pseudo-)Euclidean space. This can be an
indexed object, tensormetric, matrix or a Clifford unit, in the later
-case the optional parameters @code{rl} and @code{anticommuting} are ignored
-even if supplied. The returned value of this function is a list of
-components of the resulting vector.
+case the optional parameters @code{rl} and @code{anticommuting} are
+ignored even if supplied. Depending from the type of @code{v} the
+returned value of this function is either a vector or a list holding vector's
+components.
@cindex @code{clifford_max_label()}
Finally the function
@end example
for checking whether one expression is equal to another, or equal to zero,
-respectively.
+respectively. See also the method @code{ex::is_zero_matrix()},
+@pxref{Matrices}.
@subsection Ordering expressions
git://www.ginac.de / ginac.git / blobdiff