The mod 2 cohomology of a simplicial complex has the structure of a module over the mod 2 Steenrod algebra. I would like to be able to do this in Sage:
sage: x = (some element in a cohomology ring)
sage: a = (some element of SteenrodAlgebra(2))
sage: a * x
I have tried telling Sage that instances of CohomologyRing should be left modules over the Steenrod algebra (using the category framework) and then defining _mul_, _rmul_, _lmul_. I have had no luck: I just get
TypeError: unsupported operand parent(s) for *: 'mod 2 Steenrod algebra, milnor basis' and 'Cohomology ring of RP^6 over Finite Field of size 2'
What should I be doing instead?