# submodules or maybe sub-algebras of CDGA

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 `ya`

and `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.