1Set::Infinite::Basic(3)User Contributed Perl DocumentatioSnet::Infinite::Basic(3)
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NAME

6       Set::Infinite::Basic - Sets of intervals 6 =head1 SYNOPSIS
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8         use Set::Infinite::Basic;
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10         $set = Set::Infinite::Basic->new(1,2);    # [1..2]
11         print $set->union(5,6);            # [1..2],[5..6]
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DESCRIPTION

14       Set::Infinite::Basic is a Set Theory module for infinite sets.
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16       It works on reals, integers, and objects.
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18       This module does not support recurrences. Recurrences are implemented
19       in Set::Infinite.
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METHODS

22   empty_set
23       Creates an empty_set.
24
25       If called from an existing set, the empty set inherits the "type" and
26       "density" characteristics.
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28   universal_set
29       Creates a set containing "all" possible elements.
30
31       If called from an existing set, the universal set inherits the "type"
32       and "density" characteristics.
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34   until
35       Extends a set until another:
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37           0,5,7 -> until 2,6,10
38
39       gives
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41           [0..2), [5..6), [7..10)
42
43       Note: this function is still experimental.
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45   copy
46   clone
47       Makes a new object from the object's data.
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49   Mode functions:
50           $set = $set->real;
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52           $set = $set->integer;
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54   Logic functions:
55           $logic = $set->intersects($b);
56
57           $logic = $set->contains($b);
58
59           $logic = $set->is_null;  # also called "is_empty"
60
61   Set functions:
62           $set = $set->union($b);
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64           $set = $set->intersection($b);
65
66           $set = $set->complement;
67           $set = $set->complement($b);   # can also be called "minus" or "difference"
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69           $set = $set->symmetric_difference( $b );
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71           $set = $set->span;
72
73               result is (min .. max)
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75   Scalar functions:
76           $i = $set->min;
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78           $i = $set->max;
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80           $i = $set->size;
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82           $i = $set->count;  # number of spans
83
84   Overloaded Perl functions:
85           print
86
87           sort, <=>
88
89   Global functions:
90           separators(@i)
91
92               chooses the interval separators.
93
94               default are [ ] ( ) '..' ','.
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96           INFINITY
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98               returns an 'Infinity' number.
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100           NEG_INFINITY
101
102               returns a '-Infinity' number.
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104           iterate ( sub { } )
105
106               Iterates over a subroutine.
107               Returns the union of partial results.
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109           first
110
111               In scalar context returns the first interval of a set.
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113               In list context returns the first interval of a set, and the
114               'tail'.
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116               Works in unbounded sets
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118           type($i)
119
120               chooses an object data type.
121
122               default is none (a normal perl SCALAR).
123
124               examples:
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126               type('Math::BigFloat');
127               type('Math::BigInt');
128               type('Set::Infinite::Date');
129                   See notes on Set::Infinite::Date below.
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131           tolerance(0)    defaults to real sets (default)
132           tolerance(1)    defaults to integer sets
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134           real            defaults to real sets (default)
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136           integer         defaults to integer sets
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138   Internal functions:
139           $set->fixtype;
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141           $set->numeric;
142

CAVEATS

144           $set = Set::Infinite->new(10,1);
145               Will be interpreted as [1..10]
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147           $set = Set::Infinite->new(1,2,3,4);
148               Will be interpreted as [1..2],[3..4] instead of [1,2,3,4].
149               You probably want ->new([1],[2],[3],[4]) instead,
150               or maybe ->new(1,4)
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152           $set = Set::Infinite->new(1..3);
153               Will be interpreted as [1..2],3 instead of [1,2,3].
154               You probably want ->new(1,3) instead.
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INTERNALS

157       The internal representation of a span is a hash:
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159           { a =>   start of span,
160             b =>   end of span,
161             open_begin =>   '0' the span starts in 'a'
162                             '1' the span starts after 'a'
163             open_end =>     '0' the span ends in 'b'
164                             '1' the span ends before 'b'
165           }
166
167       For example, this set:
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169           [100..200),300,(400..infinity)
170
171       is represented by the array of hashes:
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173           list => [
174               { a => 100, b => 200, open_begin => 0, open_end => 1 },
175               { a => 300, b => 300, open_begin => 0, open_end => 0 },
176               { a => 400, b => infinity, open_begin => 0, open_end => 1 },
177           ]
178
179       The density of a set is stored in the "tolerance" variable:
180
181           tolerance => 0;  # the set is made of real numbers.
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183           tolerance => 1;  # the set is made of integers.
184
185       The "type" variable stores the class of objects that will be stored in
186       the set.
187
188           type => 'DateTime';   # this is a set of DateTime objects
189
190       The infinity value is generated by Perl, when it finds a numerical
191       overflow:
192
193           $inf = 100**100**100;
194

SEE ALSO

196           Set::Infinite
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AUTHOR

199           Flavio S. Glock <fglock@gmail.com>
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203perl v5.36.0                      2022-07-22           Set::Infinite::Basic(3)