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.IX Title "Set::Infinite::Basic 3"
.TH Set::Infinite::Basic 3 2024-07-13 "perl v5.38.2" "User Contributed Perl Documentation"
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.SH NAME
Set::Infinite::Basic \- Sets of intervals
6
=head1 SYNOPSIS
.PP
.Vb 1
\&  use Set::Infinite::Basic;
\&
\&  $set = Set::Infinite::Basic\->new(1,2);    # [1..2]
\&  print $set\->union(5,6);            # [1..2],[5..6]
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
Set::Infinite::Basic is a Set Theory module for infinite sets.
.PP
It works on reals, integers, and objects.
.PP
This module does not support recurrences. Recurrences are implemented in Set::Infinite.
.SH METHODS
.IX Header "METHODS"
.SS empty_set
.IX Subsection "empty_set"
Creates an empty_set.
.PP
If called from an existing set, the empty set inherits
the "type" and "density" characteristics.
.SS universal_set
.IX Subsection "universal_set"
Creates a set containing "all" possible elements.
.PP
If called from an existing set, the universal set inherits
the "type" and "density" characteristics.
.SS until
.IX Subsection "until"
Extends a set until another:
.PP
.Vb 1
\&    0,5,7 \-> until 2,6,10
.Ve
.PP
gives
.PP
.Vb 1
\&    [0..2), [5..6), [7..10)
.Ve
.PP
Note: this function is still experimental.
.SS copy
.IX Subsection "copy"
.SS clone
.IX Subsection "clone"
Makes a new object from the object's data.
.SS "Mode functions:"
.IX Subsection "Mode functions:"
.Vb 1
\&    $set = $set\->real;
\&
\&    $set = $set\->integer;
.Ve
.SS "Logic functions:"
.IX Subsection "Logic functions:"
.Vb 1
\&    $logic = $set\->intersects($b);
\&
\&    $logic = $set\->contains($b);
\&
\&    $logic = $set\->is_null;  # also called "is_empty"
.Ve
.SS "Set functions:"
.IX Subsection "Set functions:"
.Vb 1
\&    $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)
.Ve
.SS "Scalar functions:"
.IX Subsection "Scalar functions:"
.Vb 1
\&    $i = $set\->min;
\&
\&    $i = $set\->max;
\&
\&    $i = $set\->size;  
\&
\&    $i = $set\->count;  # number of spans
.Ve
.SS "Overloaded Perl functions:"
.IX Subsection "Overloaded Perl functions:"
.Vb 1
\&    print    
\&
\&    sort, <=>
.Ve
.SS "Global functions:"
.IX Subsection "Global functions:"
.Vb 1
\&    separators(@i)
\&
\&        chooses the interval separators. 
\&
\&        default are [ ] ( ) \*(Aq..\*(Aq \*(Aq,\*(Aq.
\&
\&    INFINITY
\&
\&        returns an \*(AqInfinity\*(Aq number.
\&
\&    NEG_INFINITY
\&
\&        returns a \*(Aq\-Infinity\*(Aq number.
\&
\&    iterate ( sub { } )
\&
\&        Iterates over a subroutine. 
\&        Returns the union of partial results.
\&
\&    first
\&
\&        In scalar context returns the first interval of a set.
\&
\&        In list context returns the first interval of a set, and the
\&        \*(Aqtail\*(Aq.
\&
\&        Works in unbounded sets
\&
\&    type($i)
\&
\&        chooses an object data type. 
\&
\&        default is none (a normal perl SCALAR).
\&
\&        examples: 
\&
\&        type(\*(AqMath::BigFloat\*(Aq);
\&        type(\*(AqMath::BigInt\*(Aq);
\&        type(\*(AqSet::Infinite::Date\*(Aq);
\&            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
.Ve
.SS "Internal functions:"
.IX Subsection "Internal functions:"
.Vb 1
\&    $set\->fixtype; 
\&
\&    $set\->numeric;
.Ve
.SH CAVEATS
.IX Header "CAVEATS"
.Vb 2
\&    $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.
.Ve
.SH INTERNALS
.IX Header "INTERNALS"
The internal representation of a \fIspan\fR is a hash:
.PP
.Vb 7
\&    { a =>   start of span,
\&      b =>   end of span,
\&      open_begin =>   \*(Aq0\*(Aq the span starts in \*(Aqa\*(Aq
\&                      \*(Aq1\*(Aq the span starts after \*(Aqa\*(Aq
\&      open_end =>     \*(Aq0\*(Aq the span ends in \*(Aqb\*(Aq
\&                      \*(Aq1\*(Aq the span ends before \*(Aqb\*(Aq
\&    }
.Ve
.PP
For example, this set:
.PP
.Vb 1
\&    [100..200),300,(400..infinity)
.Ve
.PP
is represented by the array of hashes:
.PP
.Vb 5
\&    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 },
\&    ]
.Ve
.PP
The \fIdensity\fR of a set is stored in the \f(CW\*(C`tolerance\*(C'\fR variable:
.PP
.Vb 1
\&    tolerance => 0;  # the set is made of real numbers.
\&
\&    tolerance => 1;  # the set is made of integers.
.Ve
.PP
The \f(CW\*(C`type\*(C'\fR variable stores the \fIclass\fR of objects that will be stored in the set.
.PP
.Vb 1
\&    type => \*(AqDateTime\*(Aq;   # this is a set of DateTime objects
.Ve
.PP
The \fIinfinity\fR value is generated by Perl, when it finds a numerical overflow:
.PP
.Vb 1
\&    $inf = 100**100**100;
.Ve
.SH "SEE ALSO"
.IX Header "SEE ALSO"
.Vb 1
\&    Set::Infinite
.Ve
.SH AUTHOR
.IX Header "AUTHOR"
.Vb 1
\&    Flavio S. Glock <fglock@gmail.com>
.Ve