toricDivisor(List,NormalToricVariety) -- make a torus-invariant Weil divisor

Synopsis

• Function: toricDivisor
• Usage:
toricDivisor(L, X)
• Inputs:
• L, a list, of integers coefficients for the irreducible torus-invariant divisors on X
• X, ,
• Optional inputs:
• CoefficientRing => ..., default value QQ, make the toric divisor associated to a polyhedron
• Variable => ..., default value x, make the toric divisor associated to a polyhedron
• WeilToClass => ..., default value null, make the toric divisor associated to a polyhedron
• Outputs:

Description

Given a list of integers and a normal toric variety, this method returns the torus-invariant Weil divisor such the coefficient of the $i$-th irreducible torus-invariant divisor is the $i$-th entry in the list. The indexing of the irreducible torus-invariant divisors is inherited from the indexing of the rays in the associated fan. In this package, the rays are ordered and indexed by the nonnegative integers.

 i1 : PP2 = toricProjectiveSpace 2; i2 : D = toricDivisor({2,-7,3},PP2) o2 = 2*PP2 - 7*PP2 + 3*PP2 0 1 2 o2 : ToricDivisor on PP2 i3 : assert(D == 2* PP2_0 - 7*PP2_1 + 3*PP2_2) i4 : assert(D == toricDivisor(entries D, variety D))

Although this is a general method for making a torus-invariant Weil divisor, it is typically more convenient to simple enter the appropriate linear combination of torus-invariant Weil divisors.