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Class group is failing for non-monic defining polynomials #214

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thofma opened this issue Mar 17, 2021 · 0 comments
Open

Class group is failing for non-monic defining polynomials #214

thofma opened this issue Mar 17, 2021 · 0 comments

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@thofma
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thofma commented Mar 17, 2021

julia> Qx,x = Hecke.QQ["x"]
(Univariate Polynomial Ring in x over Rational Field, x)

julia> f = 8x^3+4x^2-4x-1
8*x^3 + 4*x^2 - 4*x - 1

julia> K,a = Hecke.NumberField(f, "a", cached = false)
(Number field over Rational Field with defining polynomial 8*x^3 + 4*x^2 - 4*x - 1, a)

julia> class_group(maximal_order(K))

If run often enough, this will fail.

The problem is that the saturate business (in mod_p) calls _, mF = ResidueFieldSmallDegree1(O, P) and then extend_easy(mF). But extend_easy(mF) expects mF.poly_of_the_field to be set. But ResidueFieldSmallDegree1 for non-nice defining polynomials does not do it.

  1. Make ResidueFieldSmallDegree1 do something clever for non-nice defining polynomials by doing something with the leading coefficient.
  2. Accept only primes not dividing the leading coefficient of the defining polynomial.
  3. Combine the conditions and implement something like issuper_nice_prime_for_saturation(K, p), which we can use as a simple check.
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