trim fails in ZZ[x]

This ideal in ZZ[x] should be the unit ideal, but trim thinks it's not.

i1 : R = ZZ[x]

o1 = R

o1 : PolynomialRing

i2 : f = x^2+x+1

2
o2 = x + x + 1

o2 : R

i3 : g = x^4+x^3+x^2+x+1

4 3 2
o3 = x + x + x + x + 1

o3 : R

i4 : trim ideal(f,g)

o4 = ideal(x + 1)

o4 : Ideal of R

i5 : (x^3+1)*f - x*g

o5 = 1

o5 : R

Start by reproducing the reported ZZ[x] transcript and inspect the trim entry point for ideals. Confirm that trim ideal(f,g) returns the unit ideal for the shown f and g, then add regression coverage for this example and run the relevant test suite.

Written by the indexing model from the issue text.