Documentation

The standardization map. If there is an underlying linear order on a then st is determined by the unique order preserving map from [0..] to that order. In any case, the standardization map should be equivariant with respect to the group action defined below; i.e., it should hold that

st (u `act` v) == u `act` st v

A (left) group action of Perm on a. As for any group action it should hold that

(u `act` v) `act` w == u `act` (v `act` w)   &&   idperm n `act` v == v

where v,w::a and u::Perm are of size n.

The size of a permutation. The default implementation derived from

size == size . st

This is not a circular definition as size on Perm is implemented independently. If the implementation of st is slow, then it can be worth while to override the standard definiton; any implementation should, however, satisfy the identity above.

The identity permutation of the given size.

The group theoretical inverse. It should hold that

inverse == unst . inverse . st

and this is the default implementation.

Predicate determining if two permutations are order-isomorphic. The default implementation uses

u `ordiso` v  ==  u == st v

Equivalently, one could use

u `ordiso` v  ==  inverse u `act` v == idperm (size u)

The inverse of st. It should hold that

unst w == w `act` idperm (P.size w)

and this is the default implementation.