gaussianMatrices -- Matrices whose minors form the ideal corresponding to a conditional independence statements.

Synopsis

Usage:
gaussianMatrices(R,G,S)
gaussianMatrices(R,G)
Inputs:
- R, a ring, must be a gaussianRing
- G, an object of class Digraph, a directed acyclic graph
- S, a list, a conditional independence statement that holds for the graph G
Outputs:
- a matrix, whose minors belong to the ideal corresponding to a conditional independence statements.

Description

This method displays a list of matrices whose minors generate the ideal of conditional independence statements. Its main purpose is to visualize these polynomials in a simpler way before they are expanded as sums of monomials.

i1 : G = digraph { {1,{2}}, {2,{3}}, {3,{4,5}},{4,{5}} } ;

i2 : S = localMarkov G;

i3 : R = gaussianRing G;

i4 : gaussianMatrices(R,G,S)

o4 = {| s_(1,4) s_(1,3) |, | s_(1,5) s_(1,4) s_(1,3) |, | s_(1,3) s_(1,2) |}
      | s_(2,4) s_(2,3) |  | s_(2,5) s_(2,4) s_(2,3) |  | s_(2,3) s_(2,2) |
      | s_(3,4) s_(3,3) |  | s_(4,5) s_(4,4) s_(3,4) |
                           | s_(3,5) s_(3,4) s_(3,3) |

o4 : List

i5 : gaussianMatrices(R,G)

o5 = {| s_(1,4) s_(1,5) s_(1,3) |, | s_(1,3) s_(1,4) s_(1,5) s_(1,2) |}
      | s_(2,4) s_(2,5) s_(2,3) |  | s_(2,3) s_(2,4) s_(2,5) s_(2,2) |
      | s_(3,4) s_(3,5) s_(3,3) |

o5 : List

Ways to use `gaussianMatrices` :

gaussianMatrices(Ring,Digraph)
gaussianMatrices(Ring,Digraph,List)

gaussianMatrices -- Matrices whose minors form the ideal corresponding to a conditional independence statements.

Synopsis

Description

See also

Ways to use gaussianMatrices :

Ways to use `gaussianMatrices` :