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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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Dealing with generators #15

Closed aidevnn closed 1 year ago

aidevnn commented 1 year ago

With basics abelians groups or direct products, computing all automorphisms or all homomorphism is possibles from canonics generetors, but it can takes very long time. Generators for abelians subgroups is more complicated, they are not canonics but it is possible.

Dealing with generators will also resolve complex cases of semidirect product. Finding generators quickly for non abelian groups, when they are isomorphic to a semidirect product, it can be probably done, may be a tiny classifier of groups by order is necessary.

Computing finitely presented group by generators and relators with bruteforce is very costly, they can be included in this project but not at this time.

The project uses implicitly many well known theorems and they can be explained in details inside the "future" documentation.

Generators allows also to compute all subgroups, and will be the possible last step to finish dealing with Groups Morphisms, then classic groups will be fast to write, to complete the first objective of this project, and staying accessible for undergraduate level.

aidevnn commented 1 year ago

Finite word groups are now available #23