# NAME

Set::Formula - Formula calculation for sets

# SYNOPSIS

```
use Set::Formula;
formula_checker (string_containing_formula); # syntax check without debug
formula_checker (string_containing_formula, 1); # syntax check with debug
formula_calcul (string_containing_formula, \%result, \%HoH_sets); # without debug
formula_calcul (string_containing_formula, \%result, \%HoH_sets, 1); # with debug
equality_checker (\%set1, \%set2); # without debug
equality_checker (\%set1, \%set2, 1); # with debug
```

# DESCRIPTION

`formula_checker`

` checks syntax of formula without its calculation.`

`formula_calcul`

` calculates formula without its syntax check.`

`equality_checker`

` checks, if 2 sets are equal.`

Formula should be written in common arithmetic notation (infix notation) and can contain unrestricted amount of nested parentheses ().

Supported set operators are

```
+ - union
- - complement
^ - intersection
```

All these operators are binary operators, i.e. they require 2 operands.

Formulas without parentheses are evaluated from left to right with equal priority for all operators. Parentheses increase priority of partial formula expressions.

White characters including new line in formula are accepted and ignored. Thus formula might be placed into both a single line and multiple lines.

`Return values`

formula_checker ind formula_calcul return nonzero on success, the undefined value otherwise.

equality_checker returns 1 if both sets are equal, else 0.

## TECHNICAL IMPLEMENTATION OF SETS

```
For formula_checker and formula_calcul
--------------------------------------
All formula operands must be highest level keys of a hash of hashes,
that is named in example below as %HoH_sets.
Lowest level keys of this hash of hashes form corresponding sets.
Values of lowest level hashes are irrelevant (can be undefined).
```

Name convention for formula operands: begin with a character, optionally following by any amount of characters, digits, underlines. Operand names are case sensitive.

```
For equality_checker
--------------------
Operands are sets, written in keys of one dimensional hashes.
```

## EXAMPLES

```
use Set::Formula;
@A{qw (bisque red blue yellow)} = ();
@B{qw (bisque brown white yellow)} = ();
@C{qw (magenta pink green )} = ();
@D{qw (magenta pink rose )} = ();
@E{qw (bisque honeydew )} = ();
%HoH_sets = ( A=>\%A, B=>\%B, C=>\%C, D=>\%D, E=>\%E );
```

or alternatively

```
%HoH_sets = (
A => { bisque => 0, red => 0, blue => 0, yellow => 0, },
B => { bisque => 0, brown => 0, white => 0, yellow => 0, },
C => { magenta => 0, pink => 0, green => 0, },
D => { grey => 0, pink => 0, rose => 0, },
E => { bisque => 0, honeydew => 0, }
);
```

A, B, C, D, F are operands. Every of them is a set, written in keys of sublevel hash.

```
$formula = "A ^ ( B + (C ^ D) ) - E";
%result = (); # this hash must be declared, but it must not be emptied before
# call of formula_calcul()
```

Usage of formula_checker() before formula_calcul() is recommended, but is not mandatory

```
formula_checker ($formula) || die "Error in formula\n";
formula_calcul ($formula, \%result, \%HoH_sets) || die "Error in formula\n";
for (keys %result) {print "$_\n"} # prints result of formula calculation
@expected_result{qw (magenta yellow)} = ();
if (equality_checker (\%result, \%expected_result)) { print "equal\n" }
else { print "not equal\n" }
```

## EXPORT

```
formula_checker,
formula_calcul,
equality_checker.
```

# SEE ALSO

```
Part "Basic operations" - L<http://en.wikipedia.org/wiki/Set_(mathematics)>
Infix notation - L<http://en.wikipedia.org/wiki/Infix_notation>
```

# AUTHOR

Mart E. Rivilis, rivilism@cpan.org

# BUGS

Please report any bugs or feature requests via mail to bug-set-formula@rt.cpan.org or at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Set-Formula. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

# SUPPORT

You can find documentation for this module with the perldoc command.

` perldoc Set::Formula`

You can also look for information at:

RT: CPAN's request tracker (report bugs here) http://rt.cpan.org/NoAuth/Bugs.html?Dist=Set-Formula

AnnoCPAN: Annotated CPAN documentation http://annocpan.org/dist/Set-Formula

CPAN Ratings http://cpanratings.perl.org/d/Set-Formula

Search CPAN http://search.cpan.org/dist/Set-Formula/

# COPYRIGHT AND LICENSE

Copyright (C) 2013 by Mart Rivilis

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.8 or, at your option, any later version of Perl 5 you may have available.