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PhylogeneticTrees :: qRing

qRing -- Constructs the ring of Fourier coordinates

Synopsis

Description

The Fourier coordinates for a phylogenetic tree model have one coordinate for each "friendly coloring" of the tree T. A friendly 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 friendly coloring, with each element of the group represented by an integer between 0 and n-1 where n is the order of the group.

The variables use symbol q.

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

See also

Ways to use qRing :