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TestIdeals :: isFpure

isFpure -- whether a ring is F-pure

Synopsis

Description

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

Ways to use isFpure :