When checking whether a ring or pair is strongly F-regular, the default option is to check this everywhere. If you set IsLocal=>true (default is false), it will only check this at the origin.
i1 : R = ZZ/7[x,y,z]/ideal((x-1)^3+(y-2)^3+z^3); |
i2 : isFregular(R) o2 = false |
i3 : isFregular(R, IsLocal=>true) o3 = true |
i4 : S = ZZ/13[x,y,z]/ideal(x^3+y^3+z^3); |
i5 : isFregular(S) o5 = false |
i6 : isFregular(S, IsLocal=>true) o6 = false |
Here is an example of a pair.
i7 : R = ZZ/13[x,y]; |
i8 : f = (y-2)^2 - (x-3)^3; |
i9 : isFregular(5/6, f) o9 = false |
i10 : isFregular(5/6, f, IsLocal=>true) o10 = true |
i11 : g = y^2 - x^3; |
i12 : isFregular(5/6, g) o12 = false |
i13 : isFregular(5/6, g, IsLocal=>true) o13 = false |