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GraphicalModels :: gaussianRing(...,kVariableName=>...)

gaussianRing(...,kVariableName=>...) -- symbol used for indeterminates in a ring of Gaussian joint probability distributions

Synopsis

Description

The option gaussianRing(G,kVariableName=>m) changes the symbol used for intedeterminates in the concentration matrix in a polynomial ring created with gaussianRing.

i1 : R = gaussianRing graph({{a,b},{b,c},{c,d},{a,d}})

o1 = R

o1 : PolynomialRing
i2 : compactMatrixForm =false;
i3 : undirectedEdgesMatrix R

o3 = |  k     k       0   k     |
     |   a,a   a,b         a,d  |
     |                          |
     |  k     k     k       0   |
     |   a,b   b,b   b,c        |
     |                          |
     |    0   k     k     k     |
     |         b,c   c,c   c,d  |
     |                          |
     |  k       0   k     k     |
     |   a,d         c,d   d,d  |

             4       4
o3 : Matrix R  <--- R
i4 : gens R

o4 = {k   , k   , k   , k   , k   , k   , k   , k   , s   , s   , s   , s   ,
       a,a   b,b   c,c   d,d   a,b   a,d   b,c   c,d   a,a   a,b   a,c   a,d 
     ------------------------------------------------------------------------
     s   , s   , s   , s   , s   , s   }
      b,b   b,c   b,d   c,c   c,d   d,d

o4 : List
i5 : Rnew = gaussianRing( graph({{a,b},{b,c},{c,d},{a,d}}), kVariableName => kappa)

o5 = Rnew

o5 : PolynomialRing
i6 : gens Rnew

o6 = {kappa   , kappa   , kappa   , kappa   , kappa   , kappa   , kappa   ,
           a,a       b,b       c,c       d,d       a,b       a,d       b,c 
     ------------------------------------------------------------------------
     kappa   , s   , s   , s   , s   , s   , s   , s   , s   , s   , s   }
          c,d   a,a   a,b   a,c   a,d   b,b   b,c   b,d   c,c   c,d   d,d

o6 : List

Further information

Functions with optional argument named kVariableName :