The elements of G must have an addition operation meaning that if two elements $g, h \in G$, then $g+h$ must work. The usual choices for G are the list of elements of $\mathbb{Z}/2$ or $(\mathbb{Z}/2)^2$.
i1 : (a,b) = (0_(ZZ/2),1_(ZZ/2)) o1 = (0, 1) o1 : Sequence |
i2 : G = {{a,a}, {a,b}, {b,a}, {b,b}}
o2 = {{0, 0}, {0, 1}, {1, 0}, {1, 1}}
o2 : List
|
The elements of B are lists of the elements of G with the same parameter value.
In the following example, the first two elements of G receive distinct parameters, while the last two share a parameter. This is precisely the Kimura 2-parameter model.
i3 : B = {{G#0}, {G#1}, {G#2,G#3}}
o3 = {{{0, 0}}, {{0, 1}}, {{1, 0}, {1, 1}}}
o3 : List
|
Finally, for every ordered pair of group elements sharing a parameter, aut must provide an automorphism of the group that switches those two group elements. In aut all of the group elements are identified by their index in $G$, and an automorphism is given by a list of permuted index values.
In our example, the pairs requiring an automorphism are \{2,3\} and \{3,2\}.
i4 : aut = {({2,3}, {0,1,3,2}),
({3,2}, {0,1,3,2})}
o4 = {({2, 3}, {0, 1, 3, 2}), ({3, 2}, {0, 1, 3, 2})}
o4 : List
|
i5 : model(G,B,aut)
o5 = 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}}
o5 : Model
|
The object model is a method function.