Let us try to start with a minimum working examle. Start with a graded commutative polynomial algebra, say $A<wa1,wb1,wb2,wc1,wc2,ya,yb, degrees = ((1,0),(1,0),(2,0),(1,0),(2,0),(0,1),(0,1)) with differential
d=A.(wa1:a^2, wb1:0, wb2:wb1*yb^2, wc1:0, wc2: wc1*(ya^2 +yb^2).
The differential is of total degree 1, as required, and cohomology computations work fine. The bi-degree of the differential is actually (-1,2), so total degree 1. Furthermore the differential just multiplies by even powers of yaand yb
Thus the algebra A, and its cohomology separates into two submodules, Aeven where the exponents of both ya and yb are even, and Aodd, where at least one of the exponents is odd.
How can I get Sage to create two subcomplexes, and be able to compute their cohomology. As a start, maybe just Aeven, which is a sub-algebra.
I am pretty new to Sage, and Python, so any help would be appreciated.
