prune(Arrangement) -- makes a new hyperplane arrangement in a polynomial ring

Synopsis

Function: prune
Usage:

prune A
Inputs:
- A, a hyperplane arrangement,
Optional inputs:
- Exclude => ..., default value {}, this optional input is ignored by this function
Outputs:
- a hyperplane arrangement, an isomorphic to the input but defined over a polynomial ring

Description

A hyperplane arrangement may sensibly be defined over a quotient of a polynomial ring by a linear ideal. However, sometimes this is inconvenient. This method creates an isomorphic hyperplane arrangement in a polynomial ring.

i1 : A = typeA 3

o1 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
       1    2   1    3   1    4   2    3   2    4   3    4

o1 : Hyperplane Arrangement

i2 : A'' = restriction(A,0) -- restrict A to its first hyperplane

o2 = {x  - x , x  - x , x  - x , x  - x , x  - x }
       2    3   2    4   2    3   2    4   3    4

o2 : Hyperplane Arrangement

i3 : ring A''

      QQ[x ..x ]
          1   4
o3 = ------------
     (x  - x , 0)
       1    2

o3 : QuotientRing

i4 : B = prune A''

o4 = {x  - x , x  - x , x  - x , x  - x , x  - x }
       2    3   2    4   2    3   2    4   3    4

o4 : Hyperplane Arrangement

i5 : ring B

o5 = QQ[x ..x ]
         2   4

o5 : PolynomialRing

Ways to use this method: