Given a ring R, this computes whether the ring is F-pure using Fedder’s criterion (by applying frobeniusRoot to I[p] : I).
i1 : R = ZZ/5[x,y,z]/ideal(x^2+y*z); |
i2 : isFpure(R) o2 = true |
i3 : R = ZZ/7[x,y,z]/ideal(x^3+y^3+z^3); |
i4 : isFpure(R) o4 = true |
i5 : R = ZZ/5[x,y,z]/ideal(x^3+y^3+z^3); |
i6 : isFpure(R) o6 = false |
Alternately, one may pass it the defining ideal of a ring.
i7 : S = ZZ/2[x,y,z]; |
i8 : isFpure(ideal(y^2-x^3)) o8 = false |
i9 : isFpure(ideal(z^2-x*y*z+x*y^2+x^2*y)) o9 = true |