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oscar-system / GenericCharacterTables.jl

Generic character tables for julia
https://oscar-system.github.io/GenericCharacterTables.jl/
GNU General Public License v3.0
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Get rid of number field elements in exponents? #57

Closed SoongNoonien closed 3 months ago

SoongNoonien commented 5 months ago

Currently there are tables like for example 2G2 which rely on number field elements in the exponents of cyclotomics. As all cyclotomics in the character tables evaluate to algebraic numbers for any input the exponents evaluate to rational numbers in any case. In the concrete case of 2G2 this could be fixed by substituting every occurrence of q by sqrt3*q and q^2 by 3*q^2. The new q could then be any power of 3. This would eliminate every occurrence of sqrt3 in the exponents. Unfortunately some sqrt3's would remain in the modulus of some character values. So this means we can't use the same base ring in the moduli as in the exponents anymore. As far as I understand the datatypes in Oscar this means that the q's in the moduli would need to be different form the q's in the exponents. The major advantage of having only to deal with rational expressions in the exponents is that there we have at least some kind of usable theory to compute normal forms. Also I would expect computations to be faster.

I came across this problem while trying to implementent the ring interface for the cyclotomics which seems to be very ugly with the need for supporting both rational and number field elements in the exponents.

SoongNoonien commented 4 months ago

I've talked to Gunter Malle today and he seemed to have no problems with this change. The only thing we should follow is that the new parameter should have a different name, he suggested q0. Apparently q is a standard name in this context and it would be confusing if it meant something different in this package.