marginMap -- Generates a linear map on joint probabilities for discrete variables that replaces marginals for indeterminates.

Synopsis

Usage:
phi = marginMap(i,R)
Inputs:
- i, an integer, the index of the variable to marginalize
- R, a ring, a Markov ring
Outputs:
- phi, a ring map

Description

Returns the ring map F : R -> R such that F p_{u₁,u₂,..., +,...,u_n} = p_{u₁,u₂,...,1,...,u_n} and F p_{u1,u2,..., j,...,un} = p_{u1,u2,..., j,...,un} , for j≥2 .

i1 : marginMap(1,markovRing(3,2))

o1 = map(QQ[p   , p   , p   , p   , p   , p   ],QQ[p   , p   , p   , p   , p   , p   ],{p    - p    - p   , p    - p    - p   , p   , p   , p   , p   })
             1,1   1,2   2,1   2,2   3,1   3,2      1,1   1,2   2,1   2,2   3,1   3,2    1,1    2,1    3,1   1,2    2,2    3,2   2,1   2,2   3,1   3,2

o1 : RingMap QQ[p   , p   , p   , p   , p   , p   ] <--- QQ[p   , p   , p   , p   , p   , p   ]
                 1,1   1,2   2,1   2,2   3,1   3,2           1,1   1,2   2,1   2,2   3,1   3,2

This linear transformation simplifies ideals and/or polynomials involving p_{u₁,u₂,..., +,...,u_n} . In some cases, the resulting ideals are toric ideals as the example at the beginning of the documentation. For more details see the paper "Algebraic Geometry of Bayesian Networks" by Garcia, Stillman, and Sturmfels.

Ways to use `marginMap` :

marginMap(ZZ,Ring)

marginMap -- Generates a linear map on joint probabilities for discrete variables that replaces marginals for indeterminates.

Synopsis

Description

See also

Ways to use marginMap :

Ways to use `marginMap` :