## substitute

Generic substitution algorithm.

Generic substitution algorithm.
Takes a rule or a set of rules according to which an expression
should be modified. If more than one rule is given, it tries each rule
in turn, until the first working one is encountered, after which it
continues with the next node.ex:=G_{\mu \nu \rho} + F_{\mu \nu \rho};
substitute(_, $F_{\mu \nu \rho} -> A_{\mu \nu} B_{\rho}$ );

\(\displaystyle{}G_{\mu \nu \rho}+F_{\mu \nu \rho}\)

\(\displaystyle{}G_{\mu \nu \rho}+A_{\mu \nu} B_{\rho}\)

ex:= A_{\mu \nu} B_{\nu \rho} C_{\rho \sigma};
substitute(_, $A_{m n} C_{p q} -> D_{m q}$ );

\(\displaystyle{}A_{\mu \nu} B_{\nu \rho} C_{\rho \sigma}\)

\(\displaystyle{}D_{\mu \sigma} B_{\nu \rho}\)

This command takes full care of dummy index relabelling, as the
following example shows:

{m,n,q,r,s,t,u}::Indices(vector).
ex:= a_{m} b_{n};

\(\displaystyle{}a_{m} b_{n}\)

substitute(_, $a_{q} -> c_{m n} d_{m n q}$ );

\(\displaystyle{}c_{q r} d_{q r m} b_{n}\)

By postfixing a name with a question mark, it becomes a pattern. You do not need this for indices (as the examples
above show) but it is necessary for other types of function arguments.

ex:= \sin{ x }**2 + 3 + \cos{ x }**2;
substitute(ex, $\sin{A?}**2 + \cos{A?}**2 = 1$);

\(\displaystyle{}\sin{x}^{2}+3+\cos{x}^{2}\)

\(\displaystyle{}4\)