randomArrangement -- generate an arrangement at random

Synopsis

• Usage:

  randomArrangement(n,l,N)

• Inputs:
  • n, an integer, number of hyperplanes
  • l, an integer, dimension of ambient space
  • N, an integer, absolute value of upper bound on coefficients
• Outputs:
  • a hyperplane arrangement, a random, rational arrangement of n hyperplanes in l variables.

Description

i1 : randomArrangement(4,3,5)

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

o1 : Hyperplane Arrangement 

i2 : tally apply(12, i -> poincare randomArrangement(6,3,5))

                       2      3
o2 = Tally{1 + 6T + 15T  + 10T  => 8}
                       2     3
           1 + 6T + 14T  + 9T  => 4

o2 : Tally