If the main argument in the divisor is an Ideal, the Section=>f specifies that we should find the unique effective divisor D such that I is isomorphic to O(D) and such that f maps to 1 under that isomorphism.
i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v) o1 = R o1 : QuotientRing |
i2 : D = divisor(ideal(x,u), Section=>x) o2 = Div(v, x) o2 : WeilDivisor on R |
Note if the section is not in I, then it is interpreted as a rational section and the produced divisor D may not be effective.
If the main argument in the divisor is a module, then the Matrix Mat should be a matrix mapping a free module to M. In this case divisor constructs the unique effective divisor D such that M is isomorphic to O(D) and so that 1 in the matrix map is mapped to 1 in O(D).
i3 : R = QQ[x]; |
i4 : D = divisor(R^1, Section=>matrix{{x^2}}) o4 = 2*Div(x) o4 : WeilDivisor on R |