# 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 XA
• Optional inputs:
• ForceAmat => , 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 XA.

## Description

This function computes the degree and codimension of the projective toric variety XA, we do not assume that XA 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)