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Robert Dodier, February 2006:
-----------------------------
There were two files here which implemented two versions of a
permutation function, both of which are superseded by the permutation
function in maxima/src/nset.lisp.
Jaime Villate, November 2017:
-----------------------------
I have added a package that implements some of the permutations
functions of Macsyma (with different names) and will implement many
more functions.
Since Maxima's nset package already includes functions permutations
and random_permutation which return permuted arrangements of a set or
list, I have used the name "perm" for permutations written as a list
of the first n positive integers without repetitions. Thus, perms(int)
will give the list of permutations of degree n, in contrast to
permutations(set) which gives that list of permutations applied to the
elements of a set.
Some differences with Macsyma: permutation_decomp has been named here
perm_cycles and perm_decomp is used for decomposition into the
generators of the permutation group (adjacent transpositions).
perm_cycles returns only cycles and no fixed points; i.e,
[[1,4,5],[3,6]] instead of [[1,4,5],[2],[3,6]].
perm_undecomp does not require a complete set of cycles and fixed
points, such as [[1,4,5],[2],[3,6],[7]]; it accepts just
[[1,4,5],[3,6]], but it needs an extra parameter, namely, the degree
of the group. For example: perm_undecomp([[1,4,5],[3,6]],7)
perms_lex returns the list of permutations of degree n in
lexicographic order, but unlike Macsyma's permutations_lex, the
argument should be just an integer (n) and not a permutation.
perms(n) gives tht complete list of permutations using a
minimum-change ordering, in which is permutation differs from the
previous one by just one adjacent transposition.
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