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>

cpanm Set::Infinite

perl -MCPAN -e shell
install Set::Infinite