# exponentMatrix -- puts the exponent of a monomial into matrix form

## Synopsis

• Usage:
A = exponentMatrix m
• Inputs:
• m, , an element of a ring created by buildERing.
• Outputs:
• A, ,

## Description

Let R be a ring such that all variables have a single index on which the symmetric group acts. Then monomials in R can be represented by a k by infinite exponent matrix where k is the number of variable orbits.

This representation can be helpful for visualizing the structure of a monomial.

 i1 : R = buildERing({symbol x, symbol y}, {1,1}, QQ, 4); i2 : exponentMatrix(x_0^3*y_2) o2 = | 3 0 0 0 | | 0 0 1 0 | 2 4 o2 : Matrix ZZ <--- ZZ i3 : exponentMatrix(x_0*x_1*y_0*y_3) o3 = | 1 1 0 0 | | 1 0 0 1 | 2 4 o3 : Matrix ZZ <--- ZZ

## Caveat

The ring in which the monomial resides must have all variable orbits with exactly one index.

## Ways to use exponentMatrix :

• "exponentMatrix(RingElement)"

## For the programmer

The object exponentMatrix is .