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

## Synopsis

• Usage:
gaussianRing(G,kVariableName=>m)
• Inputs:

## 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

• Default value: k
• Function: gaussianRing -- ring of Gaussian correlations on n random variables or a graphical model
• Option key: kVariableName -- optional input to choose the variable names for concentration matrix in gaussianRing