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

Synopsis

Usage:

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

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