arrangement(Flat) -- get the hyperplane arrangement to which a flat belongs

Synopsis

Function: arrangement
Usage:

arrangement F
Inputs:
- F, a flat in an hyperplane arrangement,
Outputs:
- a hyperplane arrangement, to which the flat belongs

Description

A flat is a set of hyperplanes that are maximal with respect to the property that they contain a given affine subspace. In this package, flats are treated as lists of indices of hyperplanes in the arrangement. Given a flat, this method returns the underlying hyperplane arrangement.

i1 : A3 = 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 : F = flat(A3,{3,4,5})

o2 = {3, 4, 5}

o2 : Flat of {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
               1    2   1    3   1    4   2    3   2    4   3    4

i3 : assert(arrangement F === A3)

Ways to use this method: