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

• Usage:

  gaussianMatrices(R,S)

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

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