# support(ToricDivisor) -- make the list of irreducible divisors with nonzero coefficients

## Synopsis

• Function: support
• Usage:
support D
• Inputs:
• D, ,
• Outputs:
• a list, indexing the irreducible torus-invariant divisors whose coefficient in D are nonzero

## Description

The support of a torus-invariant Weil divisor is the set of irreducible torus-invariant divisors which appear with nonzero coefficients in the unique expression for this divisor. In this package, we encode this information by indexing the irreducible torus-invariantdivisors that appear with a nonzero coefficient. The indexing of the irreducible torus-invariant divisors is inherited from the indexing of the rays in the associated fan.

 i1 : PP2 = toricProjectiveSpace 2; i2 : D1 = 2*PP2_0 - 7*PP2_1 + 3*PP2_2 o2 = 2*PP2 - 7*PP2 + 3*PP2 0 1 2 o2 : ToricDivisor on PP2 i3 : support D1 o3 = {0, 1, 2} o3 : List i4 : D2 = PP2_0-5*PP2_2 o4 = PP2 - 5*PP2 0 2 o4 : ToricDivisor on PP2 i5 : support D2 o5 = {0, 2} o5 : List i6 : support (6*PP2_1) o6 = {1} o6 : List