isLinearEquivalent -- Check if two Weil divisor are linearly equivalent

Synopsis

Usage:
flag = isLinearEquivalent(D1, D2, IsGraded=>b)
Inputs:
- D1, an object of class WDiv
- D2, an object of class WDiv
- b, a Boolean value
Optional inputs:
- IsGraded => ..., -- Check if two Weil divisor are linearly equivalent
Outputs:
- flag, a Boolean value

Given two Weil divisors, this method checks if they are linearly equivalent or not.

i1 : R = QQ[x, y, z]/ ideal(x * y - z^2)

o1 = R

o1 : QuotientRing

i2 : D1 = divisor({3, 8}, {ideal(x, z), ideal(y, z)})

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

o2 : WDiv

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

o3 = 8*Div(y, z) + 1*Div(x, z) of R

o3 : WDiv

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)

o5 = R

o5 : QuotientRing

i6 : D1 = divisor({3, 8}, {ideal(x, z), ideal(y, z)})

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

o6 : WDiv

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

o7 = 8*Div(y, z) + 1*Div(x, z) of R

o7 : WDiv

i8 : isLinearEquivalent(D1, D2, IsGraded => true)

o8 = false