# Copyright 2012, 2013, 2014 Kevin Ryde
# This file is part of Math-NumSeq.
#
# Math-NumSeq is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-NumSeq is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
# http://www.polprimos.com/imagenespub/poldiv3v.jpg
#
package Math::NumSeq::AllDivisors;
use 5.004;
use strict;
use Math::Prime::XS 0.23 'is_prime'; # version 0.23 fix for 1928099
use Math::Factor::XS 0.39 'factors';
use vars '$VERSION', '@ISA';
$VERSION = 70;
use Math::NumSeq;
@ISA = ('Math::NumSeq');
use Math::NumSeq 7; # v.7 for _is_infinite()
*_is_infinite = \&Math::NumSeq::_is_infinite;
use Math::NumSeq::Primes;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('All Divisors');
use constant description => Math::NumSeq::__('Divisors of the integers.');
use constant default_i_start => 1;
use constant characteristic_smaller => 1;
use constant parameter_info_array =>
[
{
name => 'order',
display => Math::NumSeq::__('Order'),
share_key => 'order_as',
type => 'enum',
default => 'ascending',
choices => ['ascending','descending'],
choices_display => [Math::NumSeq::__('Ascending'),
Math::NumSeq::__('Descending'),
],
description => Math::NumSeq::__('Order for the digits within each integer.'),
},
{
name => 'on_values',
display => Math::NumSeq::__('On Values'),
type => 'enum',
default => 'all',
choices => ['all','composites','odd','even'],
choices_display => [Math::NumSeq::__('All'),
Math::NumSeq::__('Composites'),
Math::NumSeq::__('Odd'),
Math::NumSeq::__('Even')],
description => Math::NumSeq::__('The values to take divisors from, either all integers or just composites or odds or evens.'),
},
];
my %values_min = (all => 2,
composites => 2,
odd => 3,
even => 2);
sub values_min {
my ($self) = @_;
return $values_min{$self->{'on_values'}};
}
#------------------------------------------------------------------------------
# A027749 excluding 1
# A027751 excluding n including 1, being proper divisors
# A161901 with sqrt(n) repeated if an integer
# A161906 list divisors <= sqrt(n)
# A161908 list divisors >= sqrt(n)
my %oeis_anum = ('all,ascending' => 'A027750',
'all,descending' => 'A056538',
# 'composites,ascending' => '',
# OEIS-Catalogue: A027750
# OEIS-Catalogue: A056538 order=descending
);;
sub oeis_anum {
my ($self) = @_;
return $oeis_anum{"$self->{on_values},$self->{order}"};
}
#------------------------------------------------------------------------------
my %rewind = (all => [ n => 2-1, n_step => 1 ],
composites => [ n => 2-1, n_step => 1 ],
odd => [ n => 2-1, n_step => 2 ],
even => [ n => 2-2, n_step => 2 ]);
sub rewind {
my ($self) = @_;
%$self = (%$self,
@{$rewind{$self->{'on_values'}}});
$self->{'pending'} = [ ];
$self->{'i'} = $self->i_start;
}
# ENHANCE-ME: could find divisors by sieve
sub next {
my ($self) = @_;
### AllDigits next(): $self->{'i'}
my $value;
my $pending = $self->{'pending'};
unless (defined ($value = shift @$pending)) {
my $n = ($self->{'n'} += $self->{'n_step'});
if ($self->{'on_values'} eq 'composites') {
while (is_prime($n)) {
$n = ++$self->{'n'};
}
}
@$pending = (1, factors($n), $n); # with 1 and $n too
my $order = $self->{'order'};
if ($order eq 'descending') {
@$pending = reverse @$pending;
}
$value = shift @$pending;
}
return ($self->{'i'}++, $value);
}
sub pred {
my ($self, $value) = @_;
return ($value == int($value));
}
1;
__END__
=for stopwords Ryde Math-NumSeq radix
=head1 NAME
Math::NumSeq::AllDivisors -- divisors of the integers
=head1 SYNOPSIS
use Math::NumSeq::AllDivisors;
my $seq = Math::NumSeq::AllDivisors->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
This is a list of the prime factors of the integers 2, 3, 4, etc
starting i=1
2, 3, 2, 2, 5, 2, 3, 7, 2, 2, 2, 3, 3, 2, 5, 11, ...
\--/ \--/ \-----/ \--/ \--/
4 5 6 7 8 9 10 11
=head2 Order
The optional C<order> parameter (a string) can control the order of the
primes within each integer,
"ascending" the default
"descending"
For example desending rearranges the values to
# order => "descending"
2, 3, 2, 2, 5, 3, 2, 7, 2, 2, 2, 3, 3, 5, 2, 11, ...
\--/ \--/ \-----/ \--/ \--/
4 5 6 7 8 9 10 11
The first difference is 3,2 for 6.
=head2 Multiplicity
Option C<multiplicity =E<gt> "distinct"> can give just one copy of each
prime factor.
# multiplicity => "distinct"
2, 3, 2, 5, 2, 3, 7, 2, 3, 2, 5, 11, ...
\--/ \--/
4 5 6 7 8 9 10 11
=head2 On Values
Option C<on_values> can give the prime factors of just some integers,
"all" the default
"composites" the non-primes from 4 onwards
"odd" odd integers 3 onwards
"even" even integers 2 onwards
"odd" is not simply a matter of filtering out 2s from the sequence, since it
takes the other primes from the even integers too, such as the 3 from 6.
# on_values => "odd"
3, 5, 7, 3, 3, 11, 13, 3, 5, 17,
\--/ \--/
9 15
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::AllDivisors-E<gt>new ()>
=item C<$seq = Math::NumSeq::AllDivisors-E<gt>new (order =E<gt> $str, multiplicity =E<gt> $str, on_values =E<gt> $str)>
Create and return a new sequence object.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> occurs in the sequence. This simply means
C<$value> a prime, or for C<on_values=E<gt>'odd'> an odd prime.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::AllPrimeFactors>,
L<Math::NumSeq::AllDigits>,
L<Math::NumSeq::DivisorCount>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 2012, 2013, 2014 Kevin Ryde
Math-NumSeq is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
=cut