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

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

Synopsis

Description

When checking whether a ring F-pure, 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/5[x,y,z]/ideal((x-1)^3+(y-2)^3+z^3);
i2 : isFpure(R)

o2 = false
i3 : isFpure(R, IsLocal=>true)

o3 = true
i4 : S = ZZ/13[x,y,z]/ideal(x^3+y^3+z^3);
i5 : isFpure(S)

o5 = true
i6 : isFpure(S, IsLocal=>true)

o6 = true

Note there is a difference in the computation done here, and checking it everywhere can sometimes be faster than checking the origin. If IsLocal=>false then the function computes frobeniusRoot applied to I[p] : I, if IsLocal=>true then the function checks wheter or not I[pe] : I is contained in m[pe] where m is the maximal ideal generated by the variables.

Further information