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Divisor :: divisor(..., Section => ...)

divisor(..., Section => ...) -- optional argument to specify a (global) section to unique construct a divisor

Synopsis

Description

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

Further information

See also