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TestIdeals :: isFregular(..., IsLocal => ...)

isFregular(..., IsLocal => ...) -- controls whether F-regularity is checked at the origin or everywhere

Synopsis

Description

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

Further information