# isLinearEquivalent -- whether two Weil divisors are linearly equivalent

## Synopsis

• Usage:
flag = isLinearEquivalent(D1, D2)
• Inputs:
• Optional inputs:
• IsGraded => , default value false, specify that we are doing this computation on a projective algebraic variety
• Outputs:
• flag, ,

## 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 = 3*Div(x, z) + 8*Div(y, z) o6 : WeilDivisor on R i7 : D2 = divisor({8, 1}, {ideal(y, z), ideal(x, z)}) o7 = Div(x, z) + 8*Div(y, z) o7 : WeilDivisor on R i8 : isLinearEquivalent(D1, D2, IsGraded => true) o8 = false