# pRing -- construct the ring of probability coordinates

## Synopsis

• Usage:
pRing(T,M)
pRing(n,M)
• Inputs:
• T, an instance of the type LeafTree,
• n, an integer, the number of leaves
• M, an instance of the type Model,
• Optional inputs:
• Variable => ..., default value null
• Outputs:
• a ring, of probability coordinates

## Description

The probability coordinates for a phylogenetic tree model have one coordinate for each possible outcome of the model. A possible outcome is any labeling of the leaves of the tree by elements of the group $G$ of the model. Thus the number of coordinates is $|G|^n$ where $n$ is the number of leaves.

A variable name for the ring can be passed using the optional argument Variable. Otherwise the symbol p is used.

 i1 : pRing(4,CFNmodel) o1 = QQ[p ..p ] 0,0,0,0 1,1,1,1 o1 : PolynomialRing i2 : pRing(3,JCmodel) o2 = QQ[p ..p ] 0,0,0 3,3,3 o2 : PolynomialRing