5.4 Pattern matching and advanced substitutions

GiNaC allows the use of patterns for checking whether an expression is of a certain form or contains subexpressions of a certain form, and for substituting expressions in a more general way.

A pattern is an algebraic expression that optionally contains wildcards. A wildcard is a special kind of object (of class wildcard) that represents an arbitrary expression. Every wildcard has a label which is an unsigned integer number to allow having multiple different wildcards in a pattern. Wildcards are printed as ‘$label’ (this is also the way they are specified in ginsh). In C++ code, wildcard objects are created with the call

ex wild(unsigned label = 0);

which is simply a wrapper for the wildcard() constructor with a shorter name.

Some examples for patterns:

Notes:

• Wildcards behave like symbols and are subject to the same algebraic rules. E.g., ‘$0+2*$0’ is automatically transformed to ‘3*$0’.
• As shown in the last example, to use wildcards for indices you have to use them as the value of an idx object. This is because indices must always be of class idx (or a subclass).
• Wildcards only represent expressions or subexpressions. It is not possible to use them as placeholders for other properties like index dimension or variance, representation labels, symmetry of indexed objects etc.
• Because wildcards are commutative, it is not possible to use wildcards as part of noncommutative products.
• A pattern does not have to contain wildcards. ‘x’ and ‘x+y’ are also valid patterns.