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;