Cadabra
a field theory motivated approach to computer algebra

factor_in

Collect terms in a sum that differ only by given pre-factors.
Given a list of symbols, this algorithm collects terms in a sum that only differ by pre-factors consisting of these given symbols. As an example,
ex:=a b + a c + a d;
\(\displaystyle{}a b+a c+a d\)
factor_in(_, $b,c$);
\(\displaystyle{}\left(b+c\right) a+a d\)
The name is perhaps most easily understood by thinking of it as a complement to factor_out. Or in case you are familiar with FORM, factor_in is like its antibracket statement. The algorithm of course also works with indexed objects, as in
ex:=A_{m} B_{m} + C_{m} A_{m}; factor_in(_, $B_{n}, C_{n}$);
\(\displaystyle{}A_{m} B_{m}+C_{m} A_{m}\)
\(\displaystyle{}A_{m} B_{m}+C_{m} A_{m}\)
(not yet finished)
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