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Divisor :: isLinearEquivalent

isLinearEquivalent -- whether two Weil divisors are linearly equivalent

Synopsis

Description

Given two Weil divisors, this method checks whether they are linearly equivalent.

i1 : R = QQ[x, y, z]/ ideal(x * y - z^2);
i2 : D1 = divisor({3, 8}, {ideal(x, z), ideal(y, z)})

o2 = 8*Div(y, z) + 3*Div(x, z)

o2 : WeilDivisor on R
i3 : D2 = divisor({8, 1}, {ideal(y, z), ideal(x, z)})

o3 = 8*Div(y, z) + Div(x, z)

o3 : WeilDivisor on R
i4 : isLinearEquivalent(D1, D2)

o4 = true

If IsGraded is set to true (by default it is false), then it treats the divisors as divisors on the $Proj$ of their ambient ring.

i5 : R = QQ[x, y, z]/ ideal(x * y - z^2);
i6 : D1 = divisor({3, 8}, {ideal(x, z), ideal(y, z)})

o6 = 8*Div(y, z) + 3*Div(x, z)

o6 : WeilDivisor on R
i7 : D2 = divisor({8, 1}, {ideal(y, z), ideal(x, z)})

o7 = 8*Div(y, z) + Div(x, z)

o7 : WeilDivisor on R
i8 : isLinearEquivalent(D1, D2, IsGraded => true)

o8 = false

See also

Ways to use isLinearEquivalent :

For the programmer

The object isLinearEquivalent is a method function with options.