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, a normal toric variety,
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:
- a toric divisor,

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.

Ways to use this method: