Coefficients => ..., default value QQ, optional input to choose the base field in markovRing or gaussianRing
kVariableName => ..., default value "k", symbol used for indeterminates in a ring of Gaussian joint probability distributions
lVariableName => ..., default value "l", symbol used for indeterminates in a ring of Gaussian joint probability distributions
pVariableName => ..., default value "p", symbol used for indeterminates in a ring of Gaussian joint probability distributions
sVariableName => ..., default value "s", symbol used for indeterminates in a ring of Gaussian joint probability distributions
Outputs:
a ring, a ring with indeterminates $s_{(i,j)}$ for $1 \leq i \leq j \leq n$
Description
This function creates a polynomial ring with indeterminates $s_{(i,j)}$ for $1 \leq i \leq j \leq n$. The $s_{(i,j)}$ indeterminates in the gaussianRing are the entries in the covariance matrix of the jointly normal random variables.
i1 : R = gaussianRing 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 : compactMatrixForm =false;
i4 : covarianceMatrix R
o4 = | s s s s s |
| 1,1 1,2 1,3 1,4 1,5 |
| |
| s s s s s |
| 1,2 2,2 2,3 2,4 2,5 |
| |
| s s s s s |
| 1,3 2,3 3,3 3,4 3,5 |
| |
| s s s s s |
| 1,4 2,4 3,4 4,4 4,5 |
| |
| s s s s s |
| 1,5 2,5 3,5 4,5 5,5 |
5 5
o4 : Matrix R <-- R
See also
gaussianRing -- ring of Gaussian correlations on n random variables or a graphical model
Ways to use this method:
gaussianRing(ZZ) -- ring of Gaussian correlations on n random variables