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

Synopsis

• 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

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