This function returns -1 if t is less than the F-pure threshold of f. It returns 1 if t is greater than the F-pure threshold f. Finally, it returns 0 if it is equal to the F-pure threshold.
i1 : R = ZZ/7[x,y]; |
i2 : f = y^2-x^3; |
i3 : compareFPT(1/2, f) o3 = -1 |
i4 : compareFPT(5/6, f) o4 = 0 |
i5 : compareFPT(6/7, f) o5 = 1 |
This function can also check the FPT in singular (but still strongly F-regular) ring, so long as the ring is also Q-Gorenstein of index dividing p-1. In the future we hope that this functionality will be extended to all Q-Gorenstein rings. In the following exam, x defines a Cartier divisor which is twice one of the rulings of the cone.
i6 : R = ZZ/5[x,y,z]/ideal(x*y-z^2); |
i7 : f = x; |
i8 : compareFPT(1/3, f) o8 = -1 |
i9 : compareFPT(1/2, f) o9 = 0 |
i10 : compareFPT(13/25, f) o10 = 1 |