Abstract functions for calculating conjugate elements, conjugacy classes, and representatives.
Abstract functions for calculating conjugate elements, conjugacy classes, and representatives.
(conj-conj conjugation-function [L G] t)
Conjoining the next minimal conjugate to list L.
Conjoining the next minimal conjugate to list L.
(conj-conj-fn conjugation-function G)
Conjoing a new element to a conjugate rep sequence, or starting a new sequence.
Conjoing a new element to a conjugate rep sequence, or starting a new sequence.
(conjrep-by-minimum conjugation-function thing symmetries)
Naive brute force implementation of finding the minimal conjugacy class representative of a thing by going through all of its conjugates induced by the given symmetries using a conjugation function. The conjugation function has the form: thing symmetry -> conjugated thing. Assumption is that things can be compared.
Naive brute force implementation of finding the minimal conjugacy class representative of a thing by going through all of its conjugates induced by the given symmetries using a conjugation function. The conjugation function has the form: thing symmetry -> conjugated thing. Assumption is that things can be compared.
(conjugateset conjugation-function things sym)
Generalized conjugation function for sets.
Generalized conjugation function for sets.
(min-rep-and-class T conjrepfunc)
Finds the minimal conjugacy class representative and its class using the given function for calculating representatives in the collection T. Returns a pair of the minimal representative and its conjugates from T (may not be the whole class). Same as conjrep-by-minimum, but collects conjugate things.
Finds the minimal conjugacy class representative and its class using the given function for calculating representatives in the collection T. Returns a pair of the minimal representative and its conjugates from T (may not be the whole class). Same as conjrep-by-minimum, but collects conjugate things.
(minconjugators conjugation-function t symmetries)
Finds the minimal conjugate of t under permutations G. Also returns the subset of G that takes t to that rep.
Finds the minimal conjugate of t under permutations G. Also returns the subset of G that takes t to that rep.
(seqconjrep conjugation-function L G)
The conjugacy class representative of a sequence of elements L under permutations G.
The conjugacy class representative of a sequence of elements L under permutations G.
(setconjrep conjugation-function things symmetries)
Given a set of things, it returns the conjugacy class representative set (the minimal possible in lexicographic order).
Given a set of things, it returns the conjugacy class representative set (the minimal possible in lexicographic order).
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