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.
i1 : R = QQ[x, y, z]
o1 = R
o1 : PolynomialRing
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i2 : D = divisor(x)
o2 = 1*Div(x) of R
o2 : WDiv
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i3 : isDivPrincipal(D, IsGraded => true)
o3 = false
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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
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i5 : D = divisor(x)
o5 = 1*Div(x) of R
o5 : WDiv
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i6 : E = divisor(x^2 * y)
o6 = 1*Div(y) + 2*Div(x) of R
o6 : WDiv
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i7 : isDivPrincipal( D )
o7 = true
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i8 : isDivPrincipal( E )
o8 = true
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