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Divisor :: isPrincipal

isPrincipal -- whether a Weil divisor is globally principal

Synopsis

Description

Returns true if the Weil divisor D is principal, otherwise false. If IsGraded is set to true, then this checks whether the divisor corresponds to a principal divisor on the Proj of the ambient ring. Note that this function may return a false negative if the defining equations of the divisor are not homogeneous (it warns the user if this occurs).

i1 : R = QQ[x, y, z];
i2 : D = divisor(x);

o2 : WeilDivisor on R
i3 : isPrincipal(D, IsGraded => true)

o3 = false

By default, IsGraded is set to false. Regardless of the format, the check is done by determining whether or not O(D) is free.

i4 : R = QQ[x, y, z]/ideal(x^2 - y*z);
i5 : D = divisor(x);

o5 : WeilDivisor on R
i6 : E = divisor(ideal(x,z));

o6 : WeilDivisor on R
i7 : isPrincipal( D )

o7 = true
i8 : isPrincipal( E )

o8 = false

See also

Ways to use isPrincipal :