Tommy Hofmann

Usually we need `Int` + `+/-inf` and not `fmpz` + `+/-inf`. We don't want the degree to return an `fmpz` or the valuation to return an `fmpz`. I would be...

If we go with `SuperInteger{T}`, we would need to adjust all signatures to accept also `SuperInteger`? With the `Union` approach, everything would just continue to work. And yes, one infinity...

Mr. Type Stable here. It never crossed my mind to change `degree` to return `-inf` for the zero polynomial. I agree that changing the behaviour could lead to some unfortunate...

Since we want to rely on the small union splitting (https://julialang.org/blog/2018/08/union-splitting/), we don't want to return a union of dozens of types. The exact number for which splitting is done...

Makes sense.

Thanks for the report.

Here is the Singular.jl/singular code: ```julia using Singular r,(c1,c2,c3,c4,c5,c6,x,y,z,u,v,w,t) = PolynomialRing(QQ,["c1","c2","c3","c4","c5","c6","x","y","z","u","v","w","t"], ordering=ordering_dp(6)*ordering_dp(7)) p = c1+c2*y+c3*y*z+c4*y^2+c5*x+c6*x*y^4*z; q = c1+c2*v+c3*v*w+c4*v^2+c5*u+c6*u*v^4*w; i = Ideal(r, [p,q,derivative(p,x),derivative(p,y),derivative(p,z),derivative(q,u),derivative(q,v),derivative(q,w),1-t*x*y*z*u*v*w]) j = Ideal(r, [x-u,y-v,z-w]) @time saturation(i,j) ``` Here...

As far as I know, the GB computations are hidden from the user for all ideal operations and `singular_assure` is an implementation detail that might vanish any time. It is...

@tthsqe12 Can you confirm that this won't work, since the code for generic (arbitrary) multivariate polynomials always uses `base_ring`, see https://github.com/Nemocas/AbstractAlgebra.jl/blob/master/src/MPoly.jl? I think the graded/decorated polynomials are falling back to...

`base_ring` was there before and we just added the alias `coefficient_ring(x) = base_ring(x)`.