# cmVolumes -- Computes the Chern-Mather volumes of a projective toric variety

## Synopsis

• Usage:
cmVolumes(A)
• Inputs:
• A, , a full rank integer matrix with the vector (1,1,...,1) in its row space defining a projective toric variety X_A
• Optional inputs:
• ForceAmat (missing documentation) => , default value false, if A defines a codimension two toric variety a faster method will be used by default, setting this to true forces the general purpose method
• Output (missing documentation) => a list, default value List, this can be set to HashTable to return a HashTable with all computed values
• TextOutput (missing documentation) => ..., default value Quiet,
• Outputs:
• cmv, a list, the Chern-Mather volumes of the projective toric variety X_A, ordered from dimension X_A to dimension zero.

## Description

This function computes the Chern-Mather volumes of the projective toric variety X_A, these are the coefficients of the Chern-Mather class ordered from dimension X_A to dimension zero. We do not assume that X_A is normal.

 i1 : A=matrix{{0, 0, 0, 1, 1,5}, {7,0, 1, 3, 0, -2},{1,1, 1, 1, 1, 1}} o1 = | 0 0 0 1 1 5 | | 7 0 1 3 0 -2 | | 1 1 1 1 1 1 | 3 6 o1 : Matrix ZZ <--- ZZ i2 : cmVolumes(A) o2 = {35, 20, -12} o2 : List i3 : A=matrix{{3, 0, 0, 1, 1,2}, {3,5,0,2,1,3},{0, 1, 2, 0, 2,0},{1, 1, 1, 1, 1,1}} o3 = | 3 0 0 1 1 2 | | 3 5 0 2 1 3 | | 0 1 2 0 2 0 | | 1 1 1 1 1 1 | 4 6 o3 : Matrix ZZ <--- ZZ i4 : cm=cmVolumes(A) o4 = {28, 31, 23, 20} o4 : List

## Ways to use cmVolumes :

• "cmVolumes(Matrix)"

## For the programmer

The object cmVolumes is .