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Improve conversion between OSCAR and GAP prime fields #3611

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Apr 17, 2024
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Improve conversion between OSCAR and GAP prime fields #3611

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25 changes: 21 additions & 4 deletions src/GAP/iso_oscar_gap.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -55,12 +55,18 @@ function _iso_oscar_gap(RO::Union{Nemo.zzModRing, Nemo.ZZModRing})
return MapFromFunc(RO, RG, f, finv)
end

# Assume that `FO` and `FG` are finite fields of the same order
# in Oscar and GAP, respectively.
function _iso_oscar_gap_field_finite_functions(FO::Union{Nemo.fpField, Nemo.FpField}, FG::GAP.GapObj)
_ffe_to_int(a::FqFieldElem) = Nemo._coeff(a, 0)
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_ffe_to_int(a::FqPolyRepFieldElem) = coeff(a, 0)
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_ffe_to_int(a::fqPolyRepFieldElem) = coeff(a, 0)
_ffe_to_int(a::Union{fpFieldElem,FpFieldElem}) = lift(a)

function _make_prime_field_functions(FO, FG)
e = GAPWrap.One(FG)

f(x) = GAP.Obj(lift(x))*e
f = function(x)
y = GAP.julia_to_gap(_ffe_to_int(x))::GapInt
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@ThomasBreuer For now I removed the ZZ(...) from the one _ffe_to_int method and just call GAP.julia_to_gap here, that should work fine for now. On the long run my plan is to use GAP.GapInt instead, see oscar-system/GAP.jl#984

return y*e
end

finv = function(x::GAP.Obj)
y = GAPWrap.IntFFE(x)
Expand All @@ -70,6 +76,12 @@ function _iso_oscar_gap_field_finite_functions(FO::Union{Nemo.fpField, Nemo.FpFi
return (f, finv)
end

# Assume that `FO` and `FG` are finite fields of the same order
# in Oscar and GAP, respectively.
function _iso_oscar_gap_field_finite_functions(FO::Union{Nemo.fpField, Nemo.FpField}, FG::GAP.GapObj)
return _make_prime_field_functions(FO, FG)
end

function _iso_oscar_gap_field_finite_functions(FO::Union{FqPolyRepField, FqField, fqPolyRepField}, FG::GAP.GapObj)
p = characteristic(FO)
d = degree(FO)
Expand All @@ -83,6 +95,11 @@ function _iso_oscar_gap_field_finite_functions(FO::Union{FqPolyRepField, FqField
error("extensions of extension fields are not supported")
end

# handle prime fields first
if d == 1
return _make_prime_field_functions(FO, FG)
end

# Compute the canonical basis of `FG`.
basis_FG = GAPWrap.Basis(FG)
# Test that we do not run into the problem from
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