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

Synopsis

Function: cone
Usage:

cone(A,h) or cone(A,x)
Inputs:
- A, a hyperplane arrangement
- x, a ring element, a variable in the ring of A
Outputs:
- a central hyperplane arrangement, 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.

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

Synopsis

Description

Caveat

See also