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

## Synopsis

• Function: isEffective
• Usage:
isEffective D
• Inputs:
• D, ,
• Outputs:
• , that is true if all the coefficients of the irreducible torus-invariant divisors are nonnegative

## Description

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.