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improve ring_iso_oscar_gap for finite fields #808

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Nov 12, 2021
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improve ring_iso_oscar_gap for finite fields #808

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12 changes: 10 additions & 2 deletions src/Groups/matrices/iso_oscar_gap.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -36,7 +36,8 @@ end
function ring_iso_oscar_gap(F::T) where T <: Union{Nemo.FqNmodFiniteField, Nemo.FqFiniteField}
p = characteristic(F)
d = degree(F)
Fp_gap = GAP.Globals.GF(GAP.Obj(p)) # the prime field in GAP
p_gap = GAP.Obj(p)
Fp_gap = GAP.Globals.GF(p_gap) # the prime field in GAP
e = GAP.Globals.One(Fp_gap)

# prime fields are easy and efficient to deal with, handle them seperately
Expand All @@ -53,7 +54,14 @@ function ring_iso_oscar_gap(F::T) where T <: Union{Nemo.FqNmodFiniteField, Nemo.
f_gap = GAP.Globals.UnivariatePolynomial(Fp_gap, L_gap)

# ... and compute a GAP field G defined via this polynomial
G = GAP.Globals.GF(Fp_gap, f_gap)
# (If the given polynomial is a Conway polynomial then we may call
# GAP's `GF(p, d)`, which avoids GAP's `AlgebraicExtension`.)
if GAP.Globals.IsCheapConwayPolynomial(p_gap, d) &&
f_gap == GAP.Globals.ConwayPolynomial(p_gap, d)
G = GAP.Globals.GF(p_gap, d)
else
G = GAP.Globals.GF(Fp_gap, f_gap)
end

# compute matching bases of both fields
if GAP.Globals.IsAlgebraicExtension(G)
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7 changes: 6 additions & 1 deletion test/Groups/matrixgroups.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -20,12 +20,17 @@
end

# Test a large non-prime field.
F, _ = GF(next_prime(10^6), 2)
# (Oscar chooses a polynomial that is not a Conway polynomial.)
p = next_prime(10^6)
F, _ = GF(p, 2)
f = Oscar.ring_iso_oscar_gap(F)
for x in [ F(3), gen(F) ]
a = f(x)
@test preimage(f, a) == x
end
@test GAP.Globals.DefiningPolynomial(codomain(f)) !=
GAP.Globals.ConwayPolynomial(p, 2)
@test GAP.Globals.IsAlgebraicExtension(codomain(f))

F = GF(29,1)[1]
z = F(2)
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