# deCone -- produce an affine arrangement from a central one

## Synopsis

• Usage:
deCone(A,x) or deCone(A,i)
• Inputs:
• x, , a hyperplane of A
• i, an integer, the index of a hyperplane of A
• Outputs:
• , the dehomogenization of A over x

## Description

The decone of a central arrangement at a hyperplane H=H_i or H=ker x is the affine arrangement obtained by choosing a chart in projective space with H as the hyperplane at infinity.
 i1 : A := arrangement "X3" o1 = {x , x , x , x + x , x + x , x + x } 1 2 3 1 2 1 3 2 3 o1 : Hyperplane Arrangement  i2 : dA := deCone(A,2) o2 = {x , x , x + x , x + 1, x + 1} 1 2 1 2 1 2 o2 : Hyperplane Arrangement  i3 : factor poincare A 2 o3 = (1 + T)(1 + 5T + 7T ) o3 : Expression of class Product i4 : poincare dA 2 o4 = 1 + 5T + 7T o4 : ZZ[T]