## `solvelib::BasicSet` -- the basic infinite sets

#### Introduction

The domain `solvelib::BasicSet` comprises the four sets of integers, reals, rationals, and complex numbers, respectively.

#### Introduction

`Z_`, or equivalently `solvelib::BasicSet``(Dom::Integer)`, represents the set of integers.

`Q_`, or equivalently `solvelib::BasicSet``(Dom::Rational)`, represents the set of rational numbers.

`R_`, or equivalently `solvelib::BasicSet``(Dom::Real)`, represents the set of real numbers.

`C_`, or equivalently `solvelib::BasicSet``(Dom::Complex)`, represents the set of complex numbers.

#### Creating Elements

``solvelib::BasicSet`(Dom::Integer)`
``solvelib::BasicSet`(Dom::Rational)`
``solvelib::BasicSet`(Dom::Real)`
``solvelib::BasicSet`(Dom::Complex)`
`Z_`
`Q_`
`R_`
`C_`

#### Categories

`Cat::Set`

#### Related Domains

`Dom::Interval`

#### Details

- The four basic sets are assigned to the identifiers `Z_`, `Q_`, `R_`, and `C_` during system initialization.

#### Method contains: tests whether some object is a member

- `contains(arithmetical expression a, dom S)`
- - tries to decide whether a ∈S, and returns `TRUE`, `FALSE`, or `UNKNOWN`.
  - Equivalently, `is(a in S)` may be used.

#### Method convert: converts a domain into a basic set

- `convert(any d)`
- - This method converts `d` into a basic set; it returns `FAIL` unless `d` is one of the four domains `Dom::Integer`, `Dom::Rational`, `Dom::Real`, and `Dom::Complex`.

#### Method set2prop: converts a set to a property

- `set2prop(dom S)`
- - This method returns the type of the `Type` library equivalent to `S`.

#### Example 1

The domain of basic sets know about the basic arithmetical and set-theoretic functions.

    >> J:=Dom::Interval(3/2, 21/4):
       Z_ intersect J

                                   {2, 3, 4, 5}

#### Super-Domain

`Dom::BaseDomain`

#### Axioms

`Ax::canonicalRep`

#### Changes

- new function

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