pRing -- construct the ring of probability coordinates

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

Ways to use pRing:

pRing(LeafTree,Model)
pRing(ZZ,Model)

For the programmer

The object pRing is a method function with options.

The source of this document is in PhylogeneticTrees.m2:1179:0.

pRing -- construct the ring of probability coordinates

Description

See also

Ways to use pRing:

For the programmer