new

    $set = Set::Infinite->new;             # empty set
    $set = Set::Infinite->new( 10 );       # single element
    $set = Set::Infinite->new( 10, 20 );   # single range
    $set = Set::Infinite->new( 
              [ 10, 20 ], [ 50, 70 ] );    # two ranges

empty set

    $set = Set::Infinite->new;
    

set with a single element

    $set = Set::Infinite->new( 10 );

    $set = Set::Infinite->new( [ 10 ] );
    

set with a single span

    $set = Set::Infinite->new( 10, 20 );

    $set = Set::Infinite->new( [ 10, 20 ] );
    # 10 <= x <= 20
    

set with a single, open span

    $set = Set::Infinite->new(
        {
            a => 10, open_begin => 0,
            b => 20, open_end => 1,
        }
    );
    # 10 <= x < 20
    

set with multiple spans

    $set = Set::Infinite->new( 10, 20,  100, 200 );

    $set = Set::Infinite->new( [ 10, 20 ], [ 100, 200 ] );

    $set = Set::Infinite->new(
        {
            a => 10, open_begin => 0,
            b => 20, open_end => 0,
        },
        {
            a => 100, open_begin => 0,
            b => 200, open_end => 0,
        }
    );
    

The "new()" method expects ordered parameters.

If you have unordered ranges, you can build the set using "union":

    @ranges = ( [ 10, 20 ], [ -10, 1 ] );
    $set = Set::Infinite->new;
    $set = $set->union( @$_ ) for @ranges;

The data structures passed to "new" must be immutable. So this is not good practice:

    $set = Set::Infinite->new( $object_a, $object_b );
    $object_a->set_value( 10 );

This is the recommended way to do it:

    $set = Set::Infinite->new( $object_a->clone, $object_b->clone );
    $object_a->set_value( 10 );

clone / copy

empty_set

If called from an existing set, the empty set inherits the "type" and "density" characteristics.

universal_set

If called from an existing set, the universal set inherits the "type" and "density" characteristics.

union

    $set = $set->union($b);

Returns the set of all elements from both sets.

This function behaves like an "OR" operation.

    $set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
    $set2 = new Set::Infinite( [ 7, 20 ] );
    print $set1->union( $set2 );
    # output: [1..4],[7..20]

intersection

    $set = $set->intersection($b);

Returns the set of elements common to both sets.

This function behaves like an "AND" operation.

    $set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
    $set2 = new Set::Infinite( [ 7, 20 ] );
    print $set1->intersection( $set2 );
    # output: [8..12]

complement

minus

difference

    $set = $set->complement;

Returns the set of all elements that don't belong to the set.

    $set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
    print $set1->complement;
    # output: (-inf..1),(4..8),(12..inf)

The complement function might take a parameter:

    $set = $set->minus($b);

Returns the set-difference, that is, the elements that don't belong to the given set.

    $set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
    $set2 = new Set::Infinite( [ 7, 20 ] );
    print $set1->minus( $set2 );
    # output: [1..4]

symmetric_difference

real

    $set1 = $set->real;

Returns a set with density "0".

integer

    $set1 = $set->integer;

Returns a set with density "1".

intersects

    $logic = $set->intersects($b);

contains

    $logic = $set->contains($b);

is_empty

is_null

    $logic = $set->is_null;

is_nonempty

is_span

is_singleton

is_subset( $set )

is_proper_subset( $set )

is_disjoint( $set )

is_too_complex

This happens with sets that represent infinite recurrences, such as when you ask for a quantization on a set bounded by -inf or inf.

See also: "count" method.

min

    $i = $set->min;

max

    $i = $set->max;

size

    $i = $set->size;

count

    $i = $set->count;

stringification

    print $set;

    $str = "$set";

See also: "as_string".

comparison

    sort

    > < == >= <= <=>

See also: "spaceship" method.

type

    type( "My::Class::Name" )

Chooses a default object data type.

Default is none (a normal Perl SCALAR).

span

    $set1 = $set->span;

Returns the set span.

until

    0,5,7 -> until 2,6,10

gives

    [0..2), [5..6), [7..10)

start_set

end_set

Given:

    [0..2), [5..6), [7..10)

start_set is:

    0,5,7

end_set is:

    2,6,10

intersected_spans

    $set = $set1->intersected_spans( $set2 );

The method returns a new set, containing all spans that are intersected by the given set.

Unlike the "intersection" method, the spans are not modified. See diagram below:

               set1   [....]   [....]   [....]   [....]
               set2      [................]

       intersection      [.]   [....]   [.]

  intersected_spans   [....]   [....]   [....]

quantize

    quantize( parameters )

        Makes equal-sized subsets.

        Returns an ordered set of equal-sized subsets.

        Example: 

            $set = Set::Infinite->new([1,3]);
            print join (" ", $set->quantize( quant => 1 ) );

        Gives: 

            [1..2) [2..3) [3..4)

select

    select( parameters )

Selects set spans based on their ordered positions

"select" has a behaviour similar to an array "slice".

            by       - default=All
            count    - default=Infinity

 0  1  2  3  4  5  6  7  8      # original set
 0  1  2                        # count => 3 
    1              6            # by => [ -2, 1 ]

offset

    offset ( parameters )

Offsets the subsets. Parameters:

    value   - default=[0,0]
    mode    - default='offset'. Possible values are: 'offset', 'begin', 'end'.
    unit    - type of value. Can be 'days', 'weeks', 'hours', 'minutes', 'seconds'.

iterate

    iterate ( sub { } , @args )

Iterates on the set spans, over a callback subroutine. Returns the union of all partial results.

The callback argument $_[0] is a span. If there are additional arguments they are passed to the callback.

The callback can return a span, a hashref (see "Set::Infinite::Basic"), a scalar, an object, or "undef".

[EXPERIMENTAL] "iterate" accepts an optional "backtrack_callback" argument. The purpose of the "backtrack_callback" is to reverse the iterate() function, overcoming the limitations of the internal backtracking algorithm. The syntax is:

    iterate ( sub { } , backtrack_callback => sub { }, @args )

The "backtrack_callback" can return a span, a hashref, a scalar, an object, or "undef".

For example, the following snippet adds a constant to each element of an unbounded set:

    $set1 = $set->iterate( 
                 sub { $_[0]->min + 54, $_[0]->max + 54 }, 
              backtrack_callback =>  
                 sub { $_[0]->min - 54, $_[0]->max - 54 }, 
              );

first / last

    first / last

In scalar context returns the first or last interval of a set.

In list context returns the first or last interval of a set, and the remaining set (the 'tail').

See also: "min", "max", "min_a", "max_a" methods.

type

    type( "My::Class::Name" )

Chooses a default object data type.

default is none (a normal perl SCALAR).

_backtrack

    $set->_backtrack( 'intersection', $b );

Internal function to evaluate recurrences.

numeric

    $set->numeric;

Internal function to ignore the set "type". It is used in some internal optimizations, when it is possible to use scalar values instead of objects.

fixtype

    $set->fixtype;

Internal function to fix the result of operations that use the numeric() function.

tolerance

    $set = $set->tolerance(0)    # defaults to real sets (default)
    $set = $set->tolerance(1)    # defaults to integer sets

Internal function for changing the set "density".

min_a

    ($min, $min_is_open) = $set->min_a;

max_a

    ($max, $max_is_open) = $set->max_a;

as_string

Stringification of unbounded recurrences is not implemented.

Unbounded recurrences are stringified as "function descriptions", if the class variable $PRETTY_PRINT is set.

spaceship

Comparison of unbounded recurrences is not implemented.