# randomUnipotent -- constructs a random unipotent matrix

## Synopsis

• Usage:
randomUnipotent n
randomUnipotent(n, R)
• Inputs:
• Outputs:
• , a random $n\times n$ unipotent matrix, over the ring $R$

## Description

This method returns a random unipotent matrix of a given size $n$, which is upper triangular with all diagonal entries equal to $1$. if a ring $R$ is provided, then the output is a matrix over $R$ - by default, the output is a matrix over QQ.

 i1 : randomUnipotent 5 o1 = | 1 9/2 1/2 9/4 1/2 | | 0 1 1 3/4 3/2 | | 0 0 1 3/4 7/4 | | 0 0 0 1 7/9 | | 0 0 0 0 1 | 5 5 o1 : Matrix QQ <--- QQ i2 : randomUnipotent(3, CC) o2 = | 1 .706096+.127435ii .254482+.741046ii | | 0 1 .108386+.348931ii | | 0 0 1 | 3 3 o2 : Matrix CC <--- CC 53 53 i3 : randomUnipotent(3, RR[x,y]) o3 = | 1 .562428 .246268 | | 0 1 .153346 | | 0 0 1 | 3 3 o3 : Matrix (RR [x..y]) <--- (RR [x..y]) 53 53

## Ways to use randomUnipotent :

• "randomUnipotent(ZZ)"
• "randomUnipotent(ZZ,Thing)"

## For the programmer

The object randomUnipotent is .