# markovRing -- ring of probability distributions on several discrete random variables

## Synopsis

• Usage:
markovRing(d1,d2,...,dr)
• Inputs:
• di, an integer, Each d_i should be a positive integer
• Outputs:
• R, a ring, A polynomial ring with d1*d2*...*dr variables $p_{(i1,...,ir)}$, with each i_j satisfying 1 <= i_j <= d_j.
• Consequences:
• Information about this sequence of integers is placed into the ring, and is used by other functions in this package. Also, at most one ring for each such sequence is created: the results are cached.

## Description

 i1 : R = markovRing(2,3,4,5); i2 : numgens R o2 = 120 i3 : R_0, R_1, R_119 o3 = (p , p , p ) 1,1,1,1 1,1,1,2 2,3,4,5 o3 : Sequence i4 : coefficientRing R o4 = QQ o4 : Ring

## Caveat

Currently, the user has no choice about the names of the variables. Also, the base field is set to be QQ, without option of changing it. These will hopefully change in a later version.

## For the programmer

The object markovRing is .