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# buckets -- the equivalence classes of group elements of a Model

- Usage:
    `buckets M`
- Inputs:
  - M, an instance of the type Model,
- Outputs:
  - a list, of lists of group elements

## Description

Every group-based phylogenetic model has a finite group G associated to it. Parameters for the model are assigned to equivalence classes of group elements, which are orbits of some subgroup of the automorphism group of G. This function returns the equivalence classes as a list of list of group elements.

    i1 : M = K2Pmodel

    o1 = Model{AList => HashTable{{0, 0} => {1, 0, 0}}                          }
                                  {0, 1} => {0, 1, 0}
                                  {1, 0} => {0, 0, 1}
                                  {1, 1} => {0, 0, 1}
               Automorphisms => HashTable{{2, 3} => HashTable{{0, 0} => {0, 0}}}
                                                              {0, 1} => {0, 1}
                                                              {1, 0} => {1, 1}
                                                              {1, 1} => {1, 0}
                                          {3, 2} => HashTable{{0, 0} => {0, 0}}
                                                              {0, 1} => {0, 1}
                                                              {1, 0} => {1, 1}
                                                              {1, 1} => {1, 0}
               Buckets => {{{0, 0}}, {{0, 1}}, {{1, 0}, {1, 1}}}
               Group => {{0, 0}, {0, 1}, {1, 0}, {1, 1}}

    o1 : Model

    i2 : B = buckets M

    o2 = {{{0, 0}}, {{0, 1}}, {{1, 0}, {1, 1}}}

    o2 : List

## See also

- Model -- a group-based model

## Ways to use buckets:

- `buckets(Model)`

## For the programmer

The object buckets is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PhylogeneticTrees.m2:1639:0.