File Coverage

blib/lib/Math/NumSeq/PowerPart.pm

Criterion	Covered	Total	%
statement	63	65	96.9
branch	10	14	71.4
condition	4	6	66.6
subroutine	17	17	100.0
pod	4	4	100.0
total	98	106	92.4

# Copyright 2011, 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 .

package Math::NumSeq::PowerPart;
use 5.004;
use strict;

use vars '$VERSION','@ISA';
$VERSION = 71;

use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
        'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;

use Math::NumSeq::PrimeFactorCount;
*_prime_factors = \&Math::NumSeq::PrimeFactorCount::_prime_factors;

# uncomment this to run the ### lines
#use Smart::Comments;


# use constant name => Math::NumSeq::__('Powered Part');
use constant characteristic_non_decreasing => 0;
use constant characteristic_increasing => 0;
use constant characteristic_integer => 1;
use constant characteristic_smaller => 1;
use constant values_min => 1;
use constant i_start => 1;

sub description {
  my ($self) = @_;
  return sprintf(Math::NumSeq::__('Largest %s dividing i.'),
                 ! ref $self || $self->{'power'} == 2 ? 'square'
                 : $self->{'power'} == 3 ? 'cube'
                 : sprintf('%sth',$self->{'power'}));
}

use constant parameter_info_array =>
  [
   { name    => 'power',
     type    => 'integer',
     default => '2',
     minimum => 2,
     width   => 2,
     # description => Math::NumSeq::__(''),
   },
  ];

#------------------------------------------------------------------------------
# cf A008833 - largest square dividing n
#    A008834 - largest cube dividing n
#    A008835 - largest 4th power dividing n
#
my @oeis_anum
  = (
     # OEIS-Catalogue array begin
     undef,
     undef,
     'A000188',  #         # 2 sqrt of largest square dividing n
     'A053150',  # power=3 # 3 cbrt of largest cube dividing n
     'A053164',  # power=4 # 4th root of largest 4th power dividing n
     # OEIS-Catalogue array end
    );
sub oeis_anum {
  my ($self) = @_;
  return $oeis_anum[$self->{'power'}];
}

#------------------------------------------------------------------------------

sub ith {
  my ($self, $i) = @_;
  ### PowerPart ith(): $i

  $i = abs($i);
  my $power = $self->{'power'};
  if ($power < 2) {
    return $i;
  }
  unless ($i >= 0) {
    return undef;
  }
  my ($good, @primes) = _prime_factors($i);
  return undef unless $good;

  my $prev = 0;
  my $count = 0;
  my $ret = 1;
  foreach my $p (@primes) {
    ### $p
    if ($p == $prev) {
      ### same ...
      ### $count
      if (++$count == $power) {
        ### incorporate ...
        $ret *= $p;
        $count = 0;
      }
    } else {
      ### different ...
      $count = 1;
      $prev = $p;
    }
  }
  return $ret;
}

sub pred {
  my ($self, $value) = @_;
  return ($value == int($value) && $value >= 1);
}

1;
__END__