Set::Infinite::Basic(3pm)				User Contributed Perl Documentation				 Set::Infinite::Basic(3pm)

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->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

       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>

perl v5.10.0							    2008-07-21						 Set::Infinite::Basic(3pm)