Functions word() and cycle() are rather formal functions
which make no attempt to coerce their arguments into sensible forms.
The user should use permutation(), which detects the form of the
input and dispatches to as.word() or as.cycle(), which are
much more user-friendly and try quite hard to Do The Right Thing (tm).
Functions word() and cycle() are the only functions in the
package which assign class word or cycle to an
object.
Function word() takes a matrix and returns a word object;
silently coerces to integer.
Function cycle() takes a “cyclist”, that is, a list whose
elements are lists whose elements are vectors (which are disjoint
cycles); and returns an object of class “cycle”. It
nicifies its input with nicify_cyclist() before returning it.
A word is a matrix whose rows correspond to permutations in word
format.
A cycle is a list whose elements correspond to permutations in
cycle form. A cycle object comprises elements which are
informally dubbed ‘cyclists’. A cyclist is a list of integer
vectors corresponding to the cycles of the permutation.
Function cycle2word() converts cycle objects to word objects.
Function shift_cycle() is a convenience wrapper for
as.cycle(seq_len(n)); cyc_len() is a synonym.
It is a very common error (at least, it is for me) to use cycle()
when you meant as.cycle().
The print method is sensitive to the value of option
‘print_word_as_cycle’, documented at print.Rd.
Function as.matrix.word() coerces a vector of permutations in word form to
a matrix, each row of which is a word. To get a permutation matrix (that is, a
square matrix of ones and zeros with exactly one entry of 1 in each row and each column),
use perm_matrix().
In function as.word(), argument n cannot act to reduce the
size of the word, only increase it. If you want to reduce the size, use
trim() or tidy(). This function does not call
word() except directly (e.g. it does not call
size<-.word(), as this would give a recursion).