The Order enum

This page describes the enum class Order in libsemigroups_pybind11 for representing the order of words.

Full API

class Order

An enum class for the possible orderings of words and strings.

The values in this enum can be used as the arguments for functions such as ToddCoxeter.standardize or WordRange.order to specify which ordering should be used. The normal forms for congruence classes are given with respect to one of the orders specified by the values in this enum.

The valid values are:

none = <Order.none: 0>

No ordering

shortlex = <Order.shortlex: 1>

The short-lex ordering. Word are first ordered by length, and then lexicographically.

lex = <Order.lex: 2>

The lexicographic ordering. Note that this is not a well-order, so there may not be a lexicographically least word in a given congruence class of words.

recursive = <Order.recursive: 3>

The recursive-path ordering, as described in [Jan12] (Definition 1.2.14, page 24).