Set::Infinite::Basic - Sets of intervals 6 =head1 SYNOPSIS

# NAME

Set::Infinite::Basic - Sets of intervals 6 =head1 SYNOPSIS

`  use Set::Infinite::Basic;`
```  \$set = Set::Infinite::Basic->new(1,2);    # [1..2]
print \$set->union(5,6);            # [1..2],[5..6]```

# DESCRIPTION

Set::Infinite::Basic is a Set Theory module for infinite sets.

It works on reals, integers, and objects.

This module does not support recurrences. Recurrences are implemented in Set::Infinite.

# METHODS

## empty_set

Creates an empty_set.

If called from an existing set, the empty set inherits the ``type'' and ``density'' characteristics.

## universal_set

Creates a set containing ``all'' possible elements.

If called from an existing set, the universal set inherits the ``type'' and ``density'' characteristics.

## until

Extends a set until another:

`    0,5,7 -> until 2,6,10`

gives

`    [0..2), [5..6), [7..10)`

Note: this function is still experimental.

## clone

Makes a new object from the object's data.

## Mode functions:

`    \$set = \$set->real;`
`    \$set = \$set->integer;`

## Logic functions:

`    \$logic = \$set->intersects(\$b);`
`    \$logic = \$set->contains(\$b);`
`    \$logic = \$set->is_null;  # also called "is_empty"`

## Set functions:

`    \$set = \$set->union(\$b);`
`    \$set = \$set->intersection(\$b);`
```    \$set = \$set->complement;
\$set = \$set->complement(\$b);   # can also be called "minus" or "difference"```
`    \$set = \$set->simmetric_difference( \$b );`
`    \$set = \$set->span;`
`        result is (min .. max)`

## Scalar functions:

`    \$i = \$set->min;`
`    \$i = \$set->max;`
`    \$i = \$set->size;`
`    \$i = \$set->count;  # number of spans`

`    print`
`    sort, <=>`

## Global functions:

`    separators(@i)`
`        chooses the interval separators.`
`        default are [ ] ( ) '..' ','.`
`    INFINITY`
`        returns an 'Infinity' number.`
`    NEG_INFINITY`
`        returns a '-Infinity' number.`
`    iterate ( sub { } )`
```        Iterates over a subroutine.
Returns the union of partial results.```
`    first`
`        In scalar context returns the first interval of a set.`
```        In list context returns the first interval of a set, and the
'tail'.```
`        Works in unbounded sets`
`    type(\$i)`
`        chooses an object data type.`
`        default is none (a normal perl SCALAR).`
`        examples:`
```        type('Math::BigFloat');
type('Math::BigInt');
type('Set::Infinite::Date');
See notes on Set::Infinite::Date below.```
```    tolerance(0)    defaults to real sets (default)
tolerance(1)    defaults to integer sets```
`    real            defaults to real sets (default)`
`    integer         defaults to integer sets`

## Internal functions:

`    \$set->fixtype;`
`    \$set->numeric;`

# CAVEATS

```    \$set = Set::Infinite->new(10,1);
Will be interpreted as [1..10]```
```    \$set = Set::Infinite->new(1,2,3,4);
Will be interpreted as [1..2],[3..4] instead of [1,2,3,4].
or maybe ->new(1,4)```
```    \$set = Set::Infinite->new(1..3);
Will be interpreted as [1..2],3 instead of [1,2,3].

# INTERNALS

The internal representation of a span is a hash:

```    { a =>   start of span,
b =>   end of span,
open_begin =>   '0' the span starts in 'a'
'1' the span starts after 'a'
open_end =>     '0' the span ends in 'b'
'1' the span ends before 'b'
}```

For example, this set:

`    [100..200),300,(400..infinity)`

is represented by the array of hashes:

```    list => [
{ a => 100, b => 200, open_begin => 0, open_end => 1 },
{ a => 300, b => 300, open_begin => 0, open_end => 0 },
{ a => 400, b => infinity, open_begin => 0, open_end => 1 },
]```

The density of a set is stored in the `tolerance` variable:

`    tolerance => 0;  # the set is made of real numbers.`
`    tolerance => 1;  # the set is made of integers.`

The `type` variable stores the class of objects that will be stored in the set.

`    type => 'DateTime';   # this is a set of DateTime objects`

The infinity value is generated by Perl, when it finds a numerical overflow:

`    \$inf = 100**100**100;`

`    Set::Infinite`
`    Flavio Soibelmann Glock <fglock@pucrs.br>`