# 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.

## copy

## 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->symmetric_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
```

## Overloaded Perl functions:

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

# 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;`

# SEE ALSO

` Set::Infinite`

# AUTHOR

` Flavio S. Glock <fglock@gmail.com>`