Fails to compute correct Gröbner basis on DynamicPolynomials variable with non-standard monomial ordering

[0708andreas]

I think the issue is best described by the following two examples:

When using variables with a designated monomial order, Gröbner basis computations seem to fail, sometimes (the failure isn't random, it is repeatable. But I don't see a pattern)

julia> using DynamicPolynomials
julia> using Groebner
julia> @polyvar x y z monomial_order=LexOrder
(x, y, z)
julia> isgroebner(groebner([1+z*x, 1+z*y^2]))
false
julia> isgroebner(groebner([1+z*x, 1+z*y^2], ordering=Lex()), ordering=Lex())
true
julia> isgroebner(groebner([1+z*x, 1+z*y^2], ordering=DegLex()), ordering=DegLex())
false

However, with standard monomial order, the problem disappears:

julia> using DynamicPolynomials
julia> using Groebner
julia> @polyvar x y z
(x, y, z)
julia> isgroebner(groebner([1+z*x, 1+z*y^2]))
true
julia> isgroebner(groebner([1+z*x, 1+z*y^2], ordering=Lex()), ordering=Lex())
true
julia> isgroebner(groebner([1+z*x, 1+z*y^2], ordering=DegLex()), ordering=DegLex())
true

The workaround, for now, is to use the default monomial order and specify the wanted order in each call to groebner.

I'm on julia 1.10.0 and using Grobner.jl v0.6.3 from the registry.

Bests, Andreas

[sumiya11]

Hi! Thanks for reporting this, I can reproduce it.
I will have a look.

[sumiya11]

I am a bit confused at the moment -- maybe you know how can I query the ordering ?

For example,

using DynamicPolynomials
@polyvar x y z monomial_order=LexOrder
ordering(x)
# returns
GradedLex()

with

⌃ [102ac46a] MultivariatePolynomials v0.5.3
  [7c1d4256] DynamicPolynomials v0.5.3

[sumiya11]

Hi @0708andreas , the fix is in progress #121

But keep in mind that the arithmetic for LexOrder in DP.jl seems to be incorrect at the moment (unless I have messed up something) JuliaAlgebra/DynamicPolynomials.jl#152

[0708andreas]

Thank you so much. That's an... interesting issue in DP.jl XD

[sumiya11]

@0708andreas I registered a new version of Groebner, should work with the latest DP.jl. Let me know in case you face other issues

[sumiya11]

Note that at the moment I only support LexOrder, Graded{LexOrder}, Graded{Reverse{InverseLexOrder}} natively from DP.jl.
For other orderings, use can use the ordering= keyword with a Groebner.jl equivalent.

[sumiya11]

I will close this issue, feel free to open a new one if you encounter other issues