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Fix radical for ideals in polynomial rings over the integers #5185

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Merged
wdecker merged 3 commits into from
Aug 14, 2025
Merged

Fix radical for ideals in polynomial rings over the integers #5185

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961c7b4
Fix up use of elimpart.
HechtiDerLachs Aug 13, 2025
deff0da
Add tests.
HechtiDerLachs Aug 13, 2025
a121cff
Fix doctests round 1.
HechtiDerLachs Aug 14, 2025
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10 changes: 5 additions & 5 deletions src/Rings/mpoly-ideals.jl
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Expand Up @@ -627,16 +627,16 @@ Ideal generated by

julia> RI = radical(I)
Ideal generated by
1326*a*d
663*a*c
102*b*d
51*b*c
663*a*c*d
51*b*c*d
78*a*d
51*b*c
39*a*c
6*a*b*d
3*a*b*c
1326*a*d
663*a*c
663*a*c*d
51*b*c*d
39*a*c*d
3*a*b*c*d
```
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7 changes: 7 additions & 0 deletions src/Rings/mpolyquo-localizations.jl
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Expand Up @@ -1600,7 +1600,14 @@ function simplify(L::MPolyLocRing{<:Any, <:Any, <:Any, <:Any, <:MPolyPowersOfEle
return Lnew, hom(L, Lnew, f), hom(Lnew, L, finv, check=false)
end

# The `simplify` routine uses Singular's "elimpart". This does not work
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@fingolfin fingolfin Aug 13, 2025

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I think this comment should be attached to the next method, as the method it documents right now does not call into Singular at all?

# when the coefficient ring is not a field. Hence, unless that is the case,
# we refrain from doing anything here.
function simplify(L::MPolyQuoRing)
return L, identity_map(L), identity_map(L)
end

function simplify(L::MPolyQuoRing{<:MPolyRingElem{T}}) where {T<:FieldElem}
J = modulus(L)
R = base_ring(L)
is_zero(ngens(R)) && return L, identity_map(L), identity_map(L)
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8 changes: 6 additions & 2 deletions test/Rings/mpoly.jl
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Expand Up @@ -693,5 +693,9 @@ end
@test Oscar.is_known(is_principal, I3) # result is cached
end



@testset "issue 5175" begin
R,(x,y) = polynomial_ring(ZZ,2)
I = ideal(R,[y,2*x-1])
@test !is_one(radical(I))
end

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