#!/usr/bin/perl -w
# Copyright 2010, 2011, 2012, 2013 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath 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-PlanePath 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-PlanePath. If not, see <http://www.gnu.org/licenses/>.
use 5.004;
use strict;
use Test;
plan tests => 1;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::Hypot;
# uncomment this to run the ### lines
# use Smart::Comments '###';
#------------------------------------------------------------------------------
# A199015 -- partial sums of A008441
MyOEIS::compare_values
(anum => 'A199015',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Hypot->new(points=>'square_centred');
my @got;
my $n = $path->n_start;
my $num = 0;
my $want_norm = 2;
while (@got < $count) {
my ($x,$y) = $path->n_to_xy($n);
my $norm = $x*$x + $y*$y;
if ($norm > $want_norm) {
### push: $num
push @got, $num/4;
$want_norm += 8;
} else {
### point: "$n at $x,$y norm=$norm total num=$num"
$n++;
$num++;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A005883 -- count points with norm==4*n+1
# Theta series of square lattice with respect to deep hole.
#
# same as "odd" turned 45-degrees
#
# 3 . 2 . 2 . 3
#
# . . . . . . .
#
# 2 . 1 . 1 . 2
#
# . . . o . . .
#
# 2 . 1 . 1 . 2
#
# . . . . . . .
#
# 3 . 2 . 2 . 3
#
# 4, 8, 4, 8,8,0,12,8,0,8,8,8,4,8,0,8,16,0,8,0,4
MyOEIS::compare_values
(anum => 'A005883',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Hypot->new(points=>'square_centred');
my @got;
my $n = $path->n_start;
my $num = 0;
my $want_norm = 2;
while (@got < $count) {
my ($x,$y) = $path->n_to_xy($n);
my $norm = $x*$x + $y*$y;
if ($norm > $want_norm) {
### push: $num
push @got, $num;
$want_norm += 8;
$num = 0;
} else {
### point: "$n at $x,$y norm=$norm total num=$num"
$n++;
$num++;
}
}
return \@got;
});
# A008441 = A005883/4
# how many ways to write n = x(x+1)/2 + y(y+1)/2 sum two triangulars
MyOEIS::compare_values
(anum => 'A008441',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Hypot->new(points=>'square_centred');
my @got;
my $n = $path->n_start;
my $num = 0;
my $want_norm = 2;
while (@got < $count) {
my ($x,$y) = $path->n_to_xy($n);
my $norm = $x*$x + $y*$y;
if ($norm > $want_norm) {
### push: $num
push @got, $num/4;
$want_norm += 8;
$num = 0;
} else {
### point: "$n at $x,$y norm=$norm total num=$num"
$n++;
$num++;
}
}
return \@got;
});
# MyOEIS::compare_values
# (anum => 'A005883',
# func => sub {
# my ($count) = @_;
# my @got;
# my $path = Math::PlanePath::Hypot->new (points => 'square_centred');
# my $n = $path->n_start;
# my $i = 0;
# for (my $i = 0; @got < $count; $i++) {
# my $points = 0;
# for (;;) {
# my $h = $path->n_to_rsquared($n);
# if ($h > 4*$i+1) {
# last;
# }
# $points++;
# $n++;
# }
# ### $points
# push @got, $points;
# }
# return \@got;
# });
#------------------------------------------------------------------------------
# A004020 Theta series of square lattice with respect to edge.
# 2,4,2,4,4
#
# 2 . 2 .
#
# . . . . . .
#
# . 1 o 1 .
#
# . . . .
#
# . 2 . 2 .
#
# Y mod 2 == 0
# X mod 2 == 1
# X+2Y mod 4 == 1
sub xy_is_edge {
my ($x, $y) = @_;
return ($y%2 == 0 && $x%2 == 1);
}
MyOEIS::compare_values
(anum => q{A004020}, # with zeros
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Hypot->new;
my @got;
my $n = $path->n_start;
my $num = 0;
my $want_norm = 1;
while (@got < $count) {
my ($x,$y) = $path->n_to_xy($n);
if (! xy_is_edge($x,$y)) {
$n++;
next;
}
my $norm = $path->n_to_rsquared($n);
if ($norm > $want_norm) {
### push: $num
push @got, $num;
$want_norm += 4;
$num = 0;
} else {
### point: "$n at $x,$y norm=$norm total num=$num"
$n++;
$num++;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A093837 - denominators N(r) / r^2
{
my $path = Math::PlanePath::Hypot->new;
sub Nr {
my ($r) = @_;
my $n = $path->xy_to_n($r,0);
for (;;) {
my $m = $n+1;
my ($x,$y) = $path->n_to_xy($m);
if ($x*$x+$y*$y > $r*$r) {
return $n;
}
$n = $m;
}
}
}
MyOEIS::compare_values
(anum => q{A093837},
func => sub {
my ($count) = @_;
require Math::BigRat;
my @got;
for (my $r = 1; @got < $count; $r++) {
my $Nr = Nr($r);
my $rsquared = $r*$r;
my $frac = Math::BigRat->new("$Nr/$rsquared");
push @got, $frac->denominator;
}
return \@got;
});
#------------------------------------------------------------------------------
# A093832 - N(r) / r^2 > pi
use Math::Trig 'pi';
MyOEIS::compare_values
(anum => q{A093832},
func => sub {
my ($count) = @_;
require Math::BigRat;
my @got;
for (my $r = 1; @got < $count; $r++) {
my $Nr = Nr($r);
my $rsquared = $r*$r;
if ($Nr / $rsquared > pi) {
push @got, $r;
}
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;