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### Range

Range | intervals | interval sets | interval maps | condition
--- | --- | --- | --- | ---
`interval_type hull(const T&)` |  | O(1) | O(1) |
`T hull(const T&, const T&)` | O(1) |  |  |
`domain_type lower(const T&)` | O(1) | O(1) | O(1) |
`domain_type upper(const T&)` | O(1) | O(1) | O(1) |
`domain_type first(const T&)` | O(1) | O(1) | O(1) | `is_discrete<domain_type>::value`
`domain_type last(const T&)` | O(1) | O(1) | O(1) | `is_discrete<domain_type>::value`

The table above shows the availability of functions `hull`, `lower`, `upper`, `first` and `last` on intervals and interval containers that are all of constant time complexity. Find the functions description and some simple properties below.

Range | Types | Description
--- | --- | ---
`interval_type hull(const T&)` | S M | `hull(x)` returns the smallest interval that contains all intervals of an interval container `x`.
`T hull(const T&, const T&)` | S M | `hull(i,j)` returns the smallest interval that contains intervals `i` abd 'j'.
`domain_type lower(const T&)` | i S M | `lower(x)` returns the lower bound of an interval or interval container `x`.
`domain_type upper(const T&)` | i S M | `upper(x)` returns the upper bound of an interval or interval container `x`.
`domain_type first(const T&)` | i S M | `first(x)` returns the first element of an interval or interval container `x`. `first(const T&)` is defined for a discrete `domain_type` only.
`domain_type last(const T&)` | i S M | `last(x)` returns the last element of an interval or interval container `x`. `last(const T&)` is defined for a discrete `domain_type` only.

    // for interval_containers x:
    lower(hull(x)) == lower(x)
    upper(hull(x)) == upper(x)
    first(hull(x)) == first(x)
    last(hull(x))  == last(x)

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