Mod2CohomologyRingPresentation(G):: Group --> PresentedGradedAlgebra
Mod2CohomologyRingPresentation(G,n):: Group --> PresentedGradedAlgebra
Mod2CohomologyRingPresentation(A):: Group --> PresentedGradedAlgebra
Mod2CohomologyRingPresentation(R):: Group --> PresentedGradedAlgebra

When applied to a finite 2-group G this function returns a presentation for the mod-2 cohomology ring H^\ast(G,\mathbb F). The Lyndon-Hochschild-Serre spectral sequence is used to prove that the presentation is complete.

When the function is applied to a 2-group G and positive integer n the function first constructs n+1 terms of a free \mathbb FG-resolution R, then constructs the finite-dimensional graded algebra A=H^{(\ast \le n)}(G,\mathbb F), and finally uses A to approximate a presentation for H^*(G,\mathbb F). For "sufficiently large" n the approximation will be a correct presentation for H^\ast(G,\mathbb F).

Alternatively, the function can be applied directly to either the resolution R or graded algebra A.

This function was written by Paul Smith. It uses the Singular commutative algebra package to handle the Lyndon-Hochschild-Serre spectral sequence.