# gaussianMatrices -- matrices whose minors generate the Gaussian conditional independence ideal

## Synopsis

• Usage:
gaussianMatrices(R,S)
• Inputs:
• R, a ring, must be a gaussianRing
• S, a list, of conditional independence statements
• Outputs:
• , whose minors generate the Gaussian conditional independence ideal

## Description

This method displays a list of matrices whose minors generate the Gaussian conditional independence ideal. It is called as a subroutine in conditionalIndependenceIdeal but it is useful to list these matrices explicitly.

 i1 : R = gaussianRing 4; i2 : Stmts = {{{1,2},{3},{4}}, {{1},{3},{}}} o2 = {{{1, 2}, {3}, {4}}, {{1}, {3}, {}}} o2 : List i3 : compactMatrixForm =false; i4 : gaussianMatrices(R,Stmts) o4 = {| s s |, | s |} | 1,3 1,4 | | 1,3 | | | | s s | | 2,3 2,4 | | | | s s | | 3,4 4,4 | o4 : List