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HyperplaneArrangements :: randomArrangement

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

As N increases, the random arrangement is a generic arrangement with probability tending to 1.

i1 : randomArrangement(4,3,5)

o1 = {4x  - 3x  - 3x , 2x  - 5x , 4x  + 3x  + 2x , 3x }
        1     2     3    1     2    1     2     3    1

o1 : Hyperplane Arrangement

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

                       2      3
o2 = Tally{1 + 6T + 15T  + 10T  => 7}
                       2     3
           1 + 6T + 12T  + 7T  => 1
                       2     3
           1 + 6T + 14T  + 9T  => 3
                      2     3
           1 + 5T + 9T  + 5T  => 1

o2 : Tally

Ways to use `randomArrangement` :

randomArrangement(ZZ,ZZ,ZZ)