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rank(Flat) -- compute the rank of a flat

Function: rank
Usage:

rank F
Inputs:
- F, a flat in an hyperplane arrangement,
Outputs:
- an integer, the codimension of the intersection of the hyperplanes containing $F$

Description

The rank of a flat $F$ is the codimension of the intersection of the hyperplanes containing $F$ (i.e. whose indices are in $F$).

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(rank F == 2)

See also

rank(CentralArrangement) -- compute the rank of a central hyperplane arrangement

Ways to use this method:

rank(Flat) -- compute the rank of a flat

The source of this document is in HyperplaneArrangements.m2:1596:0.