`complete_reduction` option for `reduce`

[YueRen]

groebner_basis has an option complete_reduction, which if set to true ensures that the returned Groebner basis is reduced.

Can we equip reduce with the same option? The default would be false, but if set to true then reduce would also perform tail reductions. I would need it to read off the inequalities and equations of the Groebner cone.

[ederc]

There are already plans to do this, @hannes14 is preparing to provide the corresponding functionality via Singular.jl which can then be used in Oscar.

[wdecker]

At current state, in the case of a global ordering, all returned remainders are fully reduced.

[YueRen]

@wdecker Thanks for the tip! That is more than enough for me for now (and what I thought was a non-tailreduced polynomial turned out to me a mistake on my end).

[joschmitt]

Appears to be resolved. An example from the documentation:

julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);

julia> f1 = x^2+x^2*y; f2 = y^3+x*y*z; f3 = x^3*y^2+z^4;

julia> g = x^3*y+x^5+x^2*y^2*z^2+z^6;

julia> reduce(g, [f1, f2, f3], ordering = lex(R))
x^5 + x^3*y + x^2*y^2*z^2 + z^6

julia> reduce(g, [f1,f2, f3], ordering = lex(R), complete_reduction = true)
x^5 - x^3 + y^6 + z^6