## 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;