# cone(Arrangement,RingElement) -- Cone of an arrangement

## Synopsis

• Function: cone
• Usage:
cone(A,h) or cone(A,x)
• Inputs:
• x, , a variable in the ring of A
• Outputs:
• , the cone over A.

## Description

The cone of an affine arrangement is obtained from an arrangement by adding a linear hyperplane and homogenizing the remaining hyperplane equations with respect to it.
 i1 : R := QQ[x,y]; i2 : dA := arrangement {x,y,x-y,x-1,y-1} o2 = {x, y, x - y, x - 1, y - 1} o2 : Hyperplane Arrangement  i3 : A := cone(dA,symbol z) o3 = {x, y, x - y, x - z, y - z, z} o3 : Hyperplane Arrangement  i4 : {dA,A} / isCentral o4 = {false, true} o4 : List

## Caveat

If x is a ring element, no checking is done to verify it is a variable from outside the span of the hyperplanes of A.