# 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 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 + 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

## Ways to use randomArrangement :

• "randomArrangement(ZZ,ZZ,ZZ)"

## For the programmer

The object randomArrangement is .