# 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->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
``````

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