HigherCup

This is a Mathematica code for computing higher cup products by Steenrod. Our notation is as follows.

A^{(p)} ⌣_i B^{(q)} ⌣_j C^{(r)}
= Cup[A[p], B[q], C[r]][{i, j}]

(Error for wrong numbers of forms and cups.) Associativity is supported in the appropriate way; an overall factor will be factorized. The exterior derivative is implemented as $d=$Del as the usual Mathematica code; here $d$ can act on forms or Cup, which mixes some other forms and higher cups appropriately; it is surely nilpotent and satisfies homomorphism. The Leibniz rule holds.