deCone -- produce an affine arrangement from a central one

Synopsis

• Usage:

  deCone(A,x) or deCone(A,i)

• Inputs:
  • A, a central hyperplane arrangement
  • x, a ring element, a hyperplane of A
  • i, an integer, the index of a hyperplane of A
• Outputs:
  • a hyperplane arrangement, the dehomogenization of A over x

Description

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]

See also

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