isEffective(ToricDivisor) -- whether a torus-invariant Weil divisor is effective

Synopsis

Function: isEffective
Usage:

isEffective D
Inputs:
- D, a toric divisor
Outputs:
- a Boolean value, that is true if all the coefficients of the irreducible torus-invariant divisors are nonnegative

A torus-invariant Weil divisor is effective if all the coefficients of the torus-invariant irreducible divisors are nonnegative.

The canonical divisor is not effective, but the anticanonical divisor is.

i1 : PP3 = toricProjectiveSpace 3;

i2 : K = toricDivisor PP3

o2 = - PP3  - PP3  - PP3  - PP3
          0      1      2      3

o2 : ToricDivisor on PP3

i3 : isEffective K

o3 = false

i4 : isEffective (-K)

o4 = true

The torus-invariant irreducible divisors generate the cone of effective divisors.