Cadabra manual: Take

take_match

Select a subset of terms in a sum for further computations.

The take_match and replace_match algorithms enable you to temporarily work only on a part of an expression. You select the terms that you want to work on with take_match. When you are done, put the result back into the larger expression with replace_match. A simple example shows how this works:

ex:=A C + B D G + C D A;

$\displaystyle{}A C+B D G+C D A$

take_match(_, $D Q??$);

$\displaystyle{}B D G+C D A$

substitute(_, $C -> Q$);

$\displaystyle{}B D G+Q D A$

replace_match(_);

$\displaystyle{}A C+B D G+Q D A$

As you can see here, the replacement $C\rightarrow Q$ was only done on the 2nd and 3rd term of the original expression, to which we restricted all manipulations using the take_match command. This of course also works with more complicated, tensorial expressions, as the example below shows.

ex:= A_{m n} \chi B^{m}_{p} + \psi A_{n p};

$\displaystyle{}A_{m n} \chi B^{m}\,_{p}+\psi A_{n p}$

take_match(_, $\chi Q??$);

$\displaystyle{}A_{m n} \chi B^{m}\,_{p}$

substitute(_, $A_{m n} -> C_{m n}$);

$\displaystyle{}C_{m n} \chi B^{m}\,_{p}$

replace_match(_);

$\displaystyle{}C_{m n} \chi B^{m}\,_{p}+\psi A_{n p}$

When you are working on a part of an expression, you can restrict attention further by applying take_match again. The replace_match then puts sub-expressions back into the larger expression in reverse order:

ex:=A B + C B + C D B;

$\displaystyle{}A B+C B+C D B$

take_match(_, $C Q??$);

$\displaystyle{}C B+C D B$

substitute(_, $C -> Q$);

$\displaystyle{}Q B+Q D B$

take_match(_, $D Q??$);

$\displaystyle{}Q D B$

substitute(_, $B -> R$);

$\displaystyle{}Q D R$

replace_match(_);

$\displaystyle{}Q B$

replace_match(_);

$\displaystyle{}A B+Q B$