qRing -- construct the ring of Fourier coordinates

Synopsis

Usage:

qRing(T,M)

qRing(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 Fourier coordinates

Description

The Fourier coordinates for a phylogenetic tree model have one coordinate for each consistent coloring of the tree T. A consistent coloring is an assignment of one of the group elements of the model M to each of the leaves of T such that the sum of all the group elements assigned is $0$.

Each variable of the ring is indexed by a sequence representing a consistent coloring with each element of the group represented by an integer between $0$ and $m-1$ where $m$ is the order of the group.

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

i1 : qRing(4,CFNmodel)

o1 = QQ[q       , q       , q       , q       , q       , q       , q       , q       ]
         0,0,0,0   0,0,1,1   0,1,0,1   0,1,1,0   1,0,0,1   1,0,1,0   1,1,0,0   1,1,1,1

o1 : PolynomialRing

i2 : qRing(3,JCmodel)

o2 = QQ[q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     ]
         0,0,0   0,1,1   0,2,2   0,3,3   1,0,1   1,1,0   1,2,3   1,3,2   2,0,2   2,1,3   2,2,0   2,3,1   3,0,3   3,1,2   3,2,1   3,3,0

o2 : PolynomialRing

Ways to use qRing :

qRing(LeafTree,Model)
qRing(ZZ,Model)

For the programmer

The object qRing is a method function with options.

qRing -- construct the ring of Fourier coordinates

Synopsis

Description

See also

Ways to use qRing :

For the programmer