I am looking to simplify an output that I have from previous calculations in Mathematica:
-2 Sin[θ/2]^2
((-1 + Cos[θ]) g[P,P,T,U] - (1 + Cos[θ]) g[Q, Q, T, U] -
(g[P, Q, T, U] + g[Q, P, T, U]) Sin[θ])
However, in this specific problem, I know that g[Q, P, T, U] == g[P, Q, T, U]
, in the sense that g
can be looked at as a tensor with the custom symmetries g[P, Q, R, S] == g[P, Q, S, R] == g[Q, P, R, S] == g[Q, P, S, R] == g[R, S, P, Q] == g[R, S, Q, P] == g[S, R, P, Q] == g[S, R, Q, P]
. (They are the two-electron integrals occurring in quantum chemistry.)
I know that I could use the replacement rule /.{g[Q, P, T, U] -> g[P, Q, T, U]}
, but I have many similar terms, for example I have
-2 Sin[θ/2]^2
((-1 + Cos[θ]) g[R, S, P, P] - (1 + Cos[θ]) g[R, S, Q, Q] -
(g[R, S, P, Q] + g[R, S, Q, P]) Sin[θ])
as well, so I would need to use the replacement rule {g[R, S, Q, P} -> g[R, S, P, Q]}
as well.
This list of different and similar terms is huge, so my question is if there is there a way to tell Mathematica that the given symmetry of the arguments of g
exists, in order to simplify the above expression.
Ultimately, I would like to simplify the expressions of the type
2 Sin[θ/2]^4 (8 Cos[θ/2]^4 g[Q,P,P,Q]+8 g[P,Q,Q,P] Sin[θ/2]^4+2 Sin[θ] ((1+Cos[θ]) g[P,P,P,Q]+(-1+Cos[θ]) g[P,P,Q,P]-g[P,Q,P,P]+Cos[θ] g[P,Q,P,P]+g[P,Q,Q,Q]-Cos[θ] g[P,Q,Q,Q]+g[Q,P,P,P]+Cos[θ] g[Q,P,P,P]-g[Q,P,Q,Q]-Cos[θ] g[Q,P,Q,Q]-g[Q,Q,P,Q]-Cos[θ] g[Q,Q,P,Q]+g[Q,Q,Q,P]-Cos[θ] g[Q,Q,Q,P]+g[P,P,P,P] Sin[θ]-g[P,P,Q,Q] Sin[θ]-g[P,Q,P,Q] Sin[θ]-g[Q,P,Q,P] Sin[θ]-g[Q,Q,P,P] Sin[θ]+g[Q,Q,Q,Q] Sin[θ]))