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Dimension of an ideal #4244

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Dimension of an ideal #4244

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d34aa4a
allows AlgebraicSolving to compute dimension of ideals (if applicable)
ederc Oct 24, 2024
f6370ad
adds test
ederc Oct 24, 2024
f563f50
removes empty lines
ederc Oct 24, 2024
866ea58
fixes edge case
ederc Oct 24, 2024
e347271
fixes application of f4
ederc Oct 24, 2024
d14c5a8
mpoly-ideals.jl aktualisieren
ederc Oct 24, 2024
3e10a09
fixes another boundary case
ederc Oct 24, 2024
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3 changes: 2 additions & 1 deletion src/Rings/groebner.jl
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Expand Up @@ -328,10 +328,11 @@ end

function is_f4_applicable(I::MPolyIdeal, ordering::MonomialOrdering)
return (ordering == degrevlex(base_ring(I)) && !is_graded(base_ring(I))
&& !is_zero(I)
&& ((coefficient_ring(I) isa FqField
&& absolute_degree(coefficient_ring(I)) == 1
&& characteristic(coefficient_ring(I)) < 2^31)
|| coefficient_ring(I) == QQ))
|| base_ring(I) == QQMPolyRing))
end

@doc raw"""
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7 changes: 6 additions & 1 deletion src/Rings/mpoly-ideals.jl
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Expand Up @@ -1884,8 +1884,13 @@ julia> dim(I)
if I.dim > -1
return I.dim
end
is_one(I) && return -1 # Catch a boundary case
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@lgoettgens lgoettgens Oct 24, 2024 •
edited
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Maybe stupid question: if I remember correctly, this is_one call already computes a groebner basis (possibly via singular). Wouldn't it then be more efficient to use this knowledge in Singular.dimension? Or does AlgebraicSolving.dimension make use of that as well?

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You are right, is_one() computes a GB via Singular. I will work on this tomorrow, there is more that can be optimized, e.g. caching GBs.

is_zero(ngens(base_ring(I))) && return 0 # Catch a boundary case
I.dim = Singular.dimension(singular_groebner_generators(I, false, true))
if is_f4_applicable(I, degrevlex(base_ring(I)))
I.dim = AlgebraicSolving.dimension(AlgebraicSolving.Ideal(I.gens.O))
else
I.dim = Singular.dimension(singular_groebner_generators(I, false, true))
end
return I.dim
end

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1 change: 1 addition & 0 deletions test/Rings/mpoly.jl
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Expand Up @@ -105,6 +105,7 @@ end
S, (a, b, c) = polynomial_ring(QQ, [:a, :b, :c])
J = ideal(S, [(c^2+1)*(c^3+2)^2, b-c^2])
@test_throws ErrorException Oscar.check_base_rings(P, J)
@test dim(J) == 1
r1 = c^2-b
r2 = b^2*c+c^3+2*c^2+2
L = gens(radical(J))
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