Cadabra
a field theory motivated approach to computer algebra

CommutingAsSum

Makes an object behave as a sum when commuting.
This makes an object behave, for purposes of commutation rules, as a sum.
A(#)::CommutingAsSum; {Q,X,Y,Z}::AntiCommuting; ex:= A(Y)(Z)*A(X);
\(\displaystyle{}\text{Attached property CommutingAsSum to }A(\#).\)
\(\displaystyle{}\text{Attached property AntiCommuting to }(Q, X, Y, Z).\)
\(\displaystyle{}A(Y Z) A(X)\)
sort_product(_);
\(\displaystyle{}-A(X) A(Y Z)\)
The minus sign arises because it would also have been present when sorting the expression (Y+Z)*X.
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