# dualDegCodim -- Computes the degree and codimension of the dual to a projective toric variety

## Synopsis

• Usage:
dualDegCodim(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
• Outputs:
• degCodim, , the polar degrees of the projective toric variety X_A.

## Description

This function computes the degree and codimension of the projective toric variety X_A, we do not assume that X_A is normal. This function uses polarDegrees internally and this information can also be obtained from the polarDegrees function.

 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 : dc=dualDegCodim(A) o2 = HashTable{dualCodim => 1 } dualDegree => 53 o2 : HashTable i3 : dc#"dualCodim" o3 = 1 i4 : dc#"dualDegree" o4 = 53 o4 : QQ i5 : pd=polarDegrees(A); The toric variety has degree = 35 The dual variety has degree = 53, and codimension = 1 Chern-Mather Volumes: (V_0,..,V_(d-1)) = {-12, 20, 35} Polar Degrees: {53, 85, 35} ED Degree = 173 5 4 3 Chern-Mather Class: - 12h + 20h + 35h

## Ways to use dualDegCodim :

• "dualDegCodim(Matrix)"

## For the programmer

The object dualDegCodim is .