`factor` should be made to work in more cases

[DanGrayson]

... such as for elements of (frac (QQ[a])) [x,y,z] or (toField (QQ[a]/f))[x,y,z]. For the former case, clear denominators of the coefficients. For the latter, "factory" provides the functionality. In the former case, the factors should have coefficients without denominators.

[pzinn]

Is it possible to have an example of the desired behavior in each case? I'm curious to see if my package Factor already resolves this.

[DanGrayson]

Macaulay2, version 1.16.0.2
with packages: ConwayPolynomials, Elimination, IntegralClosure, InverseSystems, LLLBases, MinimalPrimes, PrimaryDecomposition, ReesAlgebra, Saturation, TangentCone, Truncations

i1 : (frac (QQ[a])) [x,y,z]

o1 = frac(QQ[a])[x, y, z]

o1 : PolynomialRing

i2 : factor x
stdio:2:1:(3): error: expected coefficient ring of the form ZZ/n, ZZ, QQ, or GF

i3 : (toField (QQ[a]/(a^2+1)))[x,y,z]

      QQ[a]
o3 = ------[][x, y, z]
      2
     a  + 1

o3 : PolynomialRing

i4 : factor x
stdio:4:1:(3): error: expected coefficient ring of the form ZZ/n, ZZ, QQ, or GF

[pzinn]

that's the undesired behavior I'm assuming

[DanGrayson]

Oh, right. The desired behavior is to give the right answer.

[d-torrance]

This was fixed in #1996