Equidimensional decomposition fails over extensions of IF_p

[HechtiDerLachs]

Witnessed on #4137.

Try running the following:

kk = GF(29, 2)
R, (x, y, z) = kk[:x, :y, :z]
I = ideal(R, (x)*(y) + 20, (x)^3 + 20*(x)^2*(z) + 6*(x)*(z)^2 + 10*(x) + 26*(z)^3, 26*(x)^2 + 27*(x)*(z) + 16*(x)*(y) + (z)^3*(y) + 11*(z)^2)
equidimensional_decomposition_weak(I)

On current master I get the following error message:

ERROR: ASSUME failed:  ASSUME(0,hasZpCoefficient(basering)||hasQQCoefficient(basering));
error occurred in or before primdec.lib::equidimMax line 2489: `  return(attrib(rng,"cf_class")==2);`
leaving primdec.lib::equidimMax (2489)
leaving primdec.lib::equidim (2442)

Stacktrace:
 [1] call_singular_library_procedure
   @ ~/.julia/packages/CxxWrap/5IZvn/src/CxxWrap.jl:624 [inlined]
 [2] low_level_caller_rng(lib::String, name::String, ring::Singular.PolyRing{…}, args::Singular.sideal{…})
   @ Singular ~/.julia/packages/Singular/a0LzT/src/caller.jl:379
 [3] equidim(ring::Singular.PolyRing{Singular.n_algExt}, args::Singular.sideal{Singular.spoly{Singular.n_algExt}})
   @ Singular.LibPrimdec ~/.julia/packages/Singular/a0LzT/src/Meta.jl:45
 [4] __compute_equidimensional_decomposition_weak__(I::MPolyIdeal{FqMPolyRingElem})
   @ Oscar ~/Oscar.jl/src/Rings/mpoly-ideals.jl:1225
 [5] #9685
   @ ~/.julia/packages/AbstractAlgebra/R1FMh/src/Attributes.jl:346 [inlined]
 [6] get!(default::Oscar.var"#9685#9687"{MPolyIdeal{FqMPolyRingElem}}, h::Dict{Symbol, Any}, key::Symbol)
   @ Base ./dict.jl:479
 [7] get_attribute!
   @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/R1FMh/src/Attributes.jl:230 [inlined]
 [8] equidimensional_decomposition_weak(I::MPolyIdeal{FqMPolyRingElem})
   @ Oscar ~/Oscar.jl/src/Rings/mpoly-ideals.jl:1212
 [9] top-level scope
   @ REPL[48]:1
Some type information was truncated. Use `show(err)` to see complete types.

Interestingly, some more trivial cases seem to be caught by other means inside Singular. For instance, the ideal generated by x*y did not raise the error.

Should we extend our _expand_coefficient_field to these field extensions? @wdecker , @hannes14 ?

[hannes14]

should be fixed by the new Singular_jll (v404.0.606)

[fingolfin]

Indeed, I now get this:

julia> equidimensional_decomposition_weak(I)
1-element Vector{MPolyIdeal{FqMPolyRingElem}}:
 Ideal (x*y + 20, x^3 + 20*x^2*z + 6*x*z^2 + 10*x + 26*z^3, 26*x^2 + 16*x*y + 27*x*z + y*z^3 + 11*z^2)