/ 
Math-GrahamFunction-0.02004
River stage zero No dependents
/ Math::GrahamFunction

NAME

Math::GrahamFunction - Calculate the Graham's Function of a Natural Number.

VERSION

version 0.02004

SYNOPSIS

use Math::GrahamFunction ();

my $calc = Math::GrahamFunction->new({ 'n' => 500 });

my $results = $calc->solve();

print "The Graham Function of 500 is ",
    $results->{'factors'}->[-1],
    "\n";

DESCRIPTION

The Graham Function of a natural number n, which we will denote by G(n), is the minimal number for which there's an increasing series of integers that starts at n and ends at G(n) whose product is a perfect square.

This module calculates the Graham Function of a natural number, along with the entire associated series.

BACKGROUND

On 11 December 2002, Mark Jason Dominus gave a Perl Quiz-of-the-week challenge to write a Perl program to calculate the Graham Function. I came up with a solution for it, whose complexity was polynomial (as opposed to brute force solutions, which are exponential complexity.). This module is derived from my original code, after it was heavily refactored.

More information about the algorithm and the original code can be found here:

http://www.shlomifish.org/lecture/Perl/Graham-Function/

FUNCTIONS

my $calc = Math::GrahamFunction->new({'n' => $n});

Initializes a new object for solving the Graham's Function of the number $n. Call solve() next.

my $results = $calc->solve();

Calculates the Graham's Function series for the number (could be time consuming), and returns a hash ref of results. The only field of interest there is 'factors', which points to an array reference of the series. The series is increasing so $results-{factors}->[0]> is $n and $results-{factors}->[-1]} is the Graham's Function.

$self->_get_num_facts($number)

Get the Square factors of the number $number.

AUTHOR

Shlomi Fish, <shlomif at cpan.org>

KNOWN BUGS

The module may yield different sequences with its "factor in between" optimization than without it. The last number (= the Graham function) is the same, but the numbers in between are different. A future release will provide a flag to disable that optimization.

BUGS

Please report any bugs or feature requests to bug-math-grahamfunction at rt.cpan.org, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Math::GrahamFunction. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

ACKNOWLEDGEMENTS

Mark Jason Dominus ( http://perl.plover.com/ ) for the original Graham Function Quiz-of-the-Week.

imacat (http://www.imacat.idv.tw/) and David Golden for helping me debug a CPAN smoking failure with installing this module on imacat's computer.

SUPPORT

Websites

The following websites have more information about this module, and may be of help to you. As always, in addition to those websites please use your favorite search engine to discover more resources.

Bugs / Feature Requests

Please report any bugs or feature requests by email to bug-math-grahamfunction at rt.cpan.org, or through the web interface at https://rt.cpan.org/Public/Bug/Report.html?Queue=Math-GrahamFunction. You will be automatically notified of any progress on the request by the system.

Source Code

The code is open to the world, and available for you to hack on. Please feel free to browse it and play with it, or whatever. If you want to contribute patches, please send me a diff or prod me to pull from your repository :)

https://github.com/shlomif/perl-math-grahamfunction

git clone git://github.com/shlomif/perl-math-grahamfunction.git

AUTHOR

Shlomi Fish <shlomif@cpan.org>

BUGS

Please report any bugs or feature requests on the bugtracker website https://github.com/shlomif/perl-math-grahamfunction/issues

When submitting a bug or request, please include a test-file or a patch to an existing test-file that illustrates the bug or desired feature.

COPYRIGHT AND LICENSE

This software is Copyright (c) 2020 by Shlomi Fish.

This is free software, licensed under:

The MIT (X11) License