Absolute primary decomposition fails for the zero ideal

[simonbrandhorst]

@wdecker

julia> R,(x1,x2) = polynomial_ring(QQ,2);

julia> I = ideal(R,0*x1)
ideal(0)

julia> absolute_primary_decomposition(I)
ERROR: Polynomial must be irreducible

[fieker]

On Tue, Apr 04, 2023 at 11:56:29PM -0700, simonbrandhorst wrote:

@wdecker

julia> R,(x1,x2) = polynomial_ring(QQ,2);

julia> I = ideal(R,0*x1)
ideal(0)

julia> absolute_primary_decomposition(I)
ERROR: Polynomial must be irreducible

Singular returns the polynomial 1 which will not define a field. -- Reply to this email directly or view it on GitHub: https://github.com/oscar-system/Oscar.jl/issues/2212 You are receiving this because you are subscribed to this thread.

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[wdecker]

I will change this so that a vector with one entry will be returned: (ideal(0), ideal(0), ideal(0), 1) Any objections?

[thofma]

Why not return the empty list? Would that also work?

[simonbrandhorst]

The zero ideal should be primary because it is prime. Then (ideal(0), ideal(0), ideal(0), 1) looks consistent to me?

[wdecker]

Yes, a polynomial ring over QQ has no zero-divisors.

[simonbrandhorst]

If we want to make it type stable, we could also create a number field QQ[x]/(x-1) with rationals_as_number_field. That would also make it easier to use in further code.

[wdecker]

resolved in PR #2229