Set::Infinite::Basic(3) Sets of intervals

## 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.

## 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;
```

## AUTHOR

```    Flavio S. Glock <[email protected]>
```