Unfortunately, I'm relatively new to SAGE and haven't found the answer
to this anywhere:

The basic objects I would like to use are PolynomialRings over a field
of characteristic 2 in n variables, Let's say

R.<x,y> = PolynomialRing(GF(2), 'x,y')

I would like to act on this by exterior algebras on n variables, say
E[Q]  by sending

Q(x) = 1
Q(y) = x^8

but I would like this to be a derivation, i.e., has a product rule :
Q(x*y) = Q(x)*y + x*Q(y).

How would I do this?

I appreciate any help that could be offered.

-Scott

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