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aidevnn / FastGoat

What C# can do for studying Finite Groups, quotient groups, semi-direct products, homomorphisms, automorphisms group, characters table, minimalistic rings and fields manipulations, polynomials factoring, fields extensions and many more...
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Cohomology, cosets errors #52

Closed aidevnn closed 5 months ago

aidevnn commented 6 months ago

https://github.com/aidevnn/FastGoat/blob/37c332030c6bef1925c82e3f8162c25b5a060ca1/FastGoat/UserGroup/GModuleN/ZNSolver.cs#L585-L588

When computing H2(C2xC2, C2xC8), some errors occur in cosets and many representatives are unnecessary.

aidevnn commented 6 months ago

The AbelianInvariants method, utilized for establishing correspondence between an abelian group and its canonical form, experiences sluggish performance when isomorphism is employed. At times, the implementation based on algebraic proof does not yield the most efficient results.

https://github.com/aidevnn/FastGoat/blob/37c332030c6bef1925c82e3f8162c25b5a060ca1/FastGoat/Structures/Group.tools.cs#L645-L669

For a potential enhancement, revisiting the Quotient of abelian groups and refining the representation of cosets may help to resolve challenges encountered during the computation of cohomologies.