The following doesn't work, it yields a NotImplementedError:
R.<x> = GF(2)[]
I = R.ideal(x^3+1)
I.primary_decomposition()
However, if I introduce a superfluous variable y, it works:
R.<x,y> = GF(2)[]
I = R.ideal(x^3+1,y)
I.primary_decomposition()
Compare: https://ask.sagemath.org/question/56734/quotient-of-polynomial-ring-over-integers-not-working/
As far as I understood correctly, PolynomialRing(K) is the same as K[], but PolynomialRing(K,1) is different. Let's try it out, it works:
R.<x> = PolynomialRing(GF(2),1)
I = R.ideal(x^3+1)
I.primary_decomposition()
