next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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

o1 : Hyperplane Arrangement

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

                       2      3
o2 = Tally{1 + 6T + 15T  + 10T  => 12}

o2 : Tally

Ways to use `randomArrangement` :

randomArrangement(ZZ,ZZ,ZZ)