ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 06 Sep 2023 05:02:04 +0200submodules or maybe sub-algebras of CDGAhttps://ask.sagemath.org/question/73175/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.
vinceWed, 06 Sep 2023 05:02:04 +0200https://ask.sagemath.org/question/73175/