gaussRing -- ring of gaussian correlations on n random variables

Synopsis

• Usage:

  gaussRing n

• Inputs:
  • n, an integer, the number of random variables
• Optional inputs:
  • CoefficientRing (missing documentation) => ..., default value QQ, a coefficient field or ring
  • Variable (missing documentation) => ..., default value "s", a symbol, the variables in the ring will be s_(1,1),...
• Outputs:
  • a ring with indeterminates s_(i,j), 1 <= i <= j <= n, a ring

Description

i1 : R = gaussRing 5;

i2 : gens R

o2 = {s   , s   , s   , s   , s   , s   , s   , s   , s   , s   , s   , s   ,
       1,1   1,2   1,3   1,4   1,5   2,2   2,3   2,4   2,5   3,3   3,4   3,5 
     ------------------------------------------------------------------------
     s   , s   , s   }
      4,4   4,5   5,5

o2 : List

i3 : genericSymmetricMatrix(R,5)

o3 = | s_(1,1) s_(1,2) s_(1,3) s_(1,4) s_(1,5) |
     | s_(1,2) s_(2,2) s_(2,3) s_(2,4) s_(2,5) |
     | s_(1,3) s_(2,3) s_(3,3) s_(3,4) s_(3,5) |
     | s_(1,4) s_(2,4) s_(3,4) s_(4,4) s_(4,5) |
     | s_(1,5) s_(2,5) s_(3,5) s_(4,5) s_(5,5) |

             5      5
o3 : Matrix R  <-- R

See also

• gaussMinors (missing documentation)
• gaussIdeal -- correlation ideal of a Bayesian network of joint Gaussian variables
• gaussTrekIdeal (missing documentation)