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FThresholds :: compareFPT

compareFPT -- checks whether a given number is less than, greater than, or equal to the F-pure threshold



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

See also

Ways to use compareFPT :