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

• 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.

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