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Divisor :: isDivPrincipal

isDivPrincipal -- Check if 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]

o1 = R

o1 : PolynomialRing
i2 : D = divisor(x)

o2 = 1*Div(x) of R

o2 : WDiv
i3 : isDivPrincipal(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]

o4 = R

o4 : PolynomialRing
i5 : D = divisor(x)

o5 = 1*Div(x) of R

o5 : WDiv
i6 : E = divisor(x^2 * y)

o6 = 1*Div(y) + 2*Div(x) of R

o6 : WDiv
i7 : isDivPrincipal( D )

o7 = true
i8 : isDivPrincipal( E )

o8 = true

See also

Ways to use isDivPrincipal :