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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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Multiple indeterminates Polynomials #29

Closed aidevnn closed 2 years ago

aidevnn commented 2 years ago

GL(2,4) isnt supported because it needs $\mathbb{F}_4$ which also needs a better implementation for Galois field. But a better implementation of Field needs a better implementation of Ring, particularly multiple indeterminates polynomials.

The project will go a little over undergraduate level to graduate level, but it will be more stable and it becomes exciting to be able to deal with group extension faster using ring and field theory.

aidevnn commented 2 years ago

GL(n,q) where q = p^m and p is prime can be computed from Examples directory, but it is very slow. A good book for completing the work is "Algorithmes Efficaces en Calcul Formel" which is avalaible for free.

aidevnn commented 2 years ago

The actual code for Fq allows to compute various groups and it can be enough at time. Galois theory and polynomials factorizations require better implementation of multiple indeterminates polynomials and it can be delayed.