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

See also

Ways to use this method:

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:1338:0.