Permutations lack their underlying permutation group

[magviana]

one should be able to pass the symmetric group in which, say, (23) belongs to

as to enable its evaluation within the group of interest (in the example below, S_4):

cpmat(as.cycle(allperms(4)[3]))
as.cycle(allperms(4)[3]) fp<-as.function(as.cycle(allperms(4)[3]))
fp(1) ## 1 fp(2) ## 3 fp(3) ## 2 fp(4) ## error

[RobinHankin]

Here is an excerpt of the email I sent in reply to magviana before I realised that there was new issue on github:

Your diagnosis of the problem is quite right, and the error is caused by the coercion to cycle form. This issue was a major major headache when I was developing the package (exceeded only by the problem of the identity element):

 > as.function(allperms(4)[3])
function (a) 

x[, a]

<environment: 0x7fe299d741f8>

> f <- as.function(allperms(4)[3])

> f(4)

[1] 4

In general, word form is better for dealing with permutation matrices. In your case we are thinking about the cycle (23) and we can use the second argument of as.word():

> as.function(as.word(as.cycle(2:3),n=9))(8)

[1] 8

Note also that most of the package is vectorized:

> as.function(allperms(4))(4)

 [1] 4 3 4 2 3 2 4 3 4 1 3 1 4 2 4 1 2 1 3 2 3 1 2 1