## `Cat::OrderedSet` -- the category of ordered sets

#### Introduction

`Cat::OrderedSet` represents the category of ordered sets.

#### Generating the category

`Cat::OrderedSet()`

#### Categories

`Cat::BaseCategory`

#### Details

- An `Cat::OrderedSet` is a set with a (complete) order relation `<` (`_less`).
- Use the axiom `Ax::canonicalOrder` to state that elements of a domain are canonically ordered as MuPAD expressions (i.e. ordered with respect to the kernel function `_less`).

#### Method _less: compares if element is less

- `_less(dom x, dom y)`
- - Must return `TRUE` if `x` is less than `y`.
  - An implementation is provided if this domain has axiom `Ax::canonicalOrder`.

#### Method _leequal: compares if element is less or equal

- `_leequal(dom x, dom y)`
- - Returns `TRUE` if `x` is less than or equal to `y`.
  - The implementation provided uses the methods `"_less"` and `"equal"`.

#### Method max: returns maximum

- `max(dom x...)`
- - Returns the maximum of its arguments.

#### Method min: returns minimum

- `min(dom x...)`
- - Returns the minimum of its arguments.

#### Method sort: sort list of elements

- `sort(Type::ListOf(dom) l)`
- - Sorts the elements of list `l` in ascending order.

#### Changes

- no changes

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