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 |
The ring in which the monomial resides must have all variable orbits with exactly one index.
The object exponentMatrix is a method function.