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#!/usr/bin/perl -w
# Copyright 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 5.010;
use strict;
use warnings;
use List::Util 'min', 'max';
use Math::PlanePath::ChanTree;
use Math::PlanePath::Base::Digits
'round_down_pow',
'digit_split_lowtohigh';
# uncomment this to run the ### lines
use Smart::Comments;
{
# gcd vs count ternary 1 digits
# ternary n_start=>1
# 1 2
# / | \ / | \
# 10 11 12 20 21 22
# / | \
# 100 101 102
require Math::PlanePath::GcdRationals;
require Math::NumSeq::DigitCount;
require Math::BaseCnv;
my $seq = Math::NumSeq::DigitCount->new (digit => 1, radix => 3);
my $k = 3;
my $path = Math::PlanePath::ChanTree->new
(k => $k,
n_start => 1,
);
my $n = $path->n_start;
my $prevlen = 1;
my $prev_gcd = 0;
for (;; $n++) {
my $nk = Math::BaseCnv::cnv($n,10,$k);
my $len = length($nk);
last if $len > 11;
if ($len > $prevlen) {
print "\n";
$prevlen = $len;
}
my ($x,$y) = $path->n_to_xy($n);
my $gcd = Math::PlanePath::GcdRationals::_gcd($x,$y);
my $offset3 = substr($nk,1);
my $offset = Math::BaseCnv::cnv($offset3,$k,10);
my $count = $seq->ith($offset);
my $pow = 3 ** max($count,0);
my $above = ($gcd == $pow && $count>0 ? " ===$pow"
: $gcd > $pow ? ' ***' : '');
if ($gcd > $prev_gcd) {
print "$n $nk $x / $y $gcd $pow (offset $offset) $above\n";
$prev_gcd = $gcd;
}
}
exit 0;
}
{
# X/Y list
require Math::PlanePath::GcdRationals;
require Math::PlanePath::PythagoreanTree;
my $pyth = Math::PlanePath::PythagoreanTree->new (coordinates => 'PQ',
tree_type => 'UAD');
require Math::BaseCnv;
my $k = 3;
my $path = Math::PlanePath::ChanTree->new
(k => $k,
n_start => 1,
);
my $n = $path->n_start;
my $prevlen = 1;
for (;; $n++) {
# my $depth = $path->tree_n_to_depth($n);
# my $n_row = $path->tree_depth_to_n($depth);
# my $n_end = $path->tree_depth_to_n_end($depth);
# my $n_half = ($n_row + $n_end + 1)/2;
# next unless $n >= $n_half;
my $nk = Math::BaseCnv::cnv($n,10,$k);
my $len = length($nk);
last if $len > 5;
if ($len > $prevlen) {
print "\n";
$prevlen = $len;
}
my ($x,$y) = $path->n_to_xy($n);
my $pyth_n = $pyth->xy_to_n($x,$y);
my $pyth_n3;
if (defined $pyth_n) {
$pyth_n3 = Math::BaseCnv::cnv($pyth_n,10,$k);
}
$pyth_n //= 'none';
$pyth_n3 //= 'none';
my $gcd = Math::PlanePath::GcdRationals::_gcd($x,$y);
my $xg = $x/$gcd;
my $yg = $y/$gcd;
print "$n $nk $x / $y $gcd reduced $xg,$yg $pyth_n3\n";
}
exit 0;
}
{
# 1 2 2
# 1 4 6 5 2 6 8 6 2 5 6 4 1 6 10 9 4 14 20 16 6 17 22 16 5 12 14 9
require Math::Polynomial;
Math::Polynomial->string_config({ ascending => 1 });
sub make_poly_k4 {
my ($level) = @_;
my $pow = 4**$level;
my $exp = 0;
my $ret = 0;
foreach my $coeff (1,2,2,1,2,2,1) {
$ret += Math::Polynomial->monomial ($exp, $coeff);
$exp += $pow;
}
return $ret;
}
print make_poly_k4(0),"\n";
print make_poly_k4(1),"\n";
my $poly = 1;
foreach my $level (0 .. 4) {
$poly *= make_poly_k4($level);
foreach my $i (0 .. 30) {
print " ",$poly->coeff($i);
}
print "\n";
}
exit 0;
}
{
# children formulas
foreach my $k (3 .. 8) {
my $half_ceil = int(($k+1) / 2);
foreach my $digit (0 .. $k-1) {
my $c1 = ($digit < $half_ceil ? $digit+1 : $k-$digit);
my $c0 = ($digit <= $half_ceil ? $digit : $k-$digit+1);
my $c2 = ($digit < $half_ceil-1 ? $digit+2 : $k-$digit-1);
print "${c1}x + ${c0}y / ${c2}x + ${c1}y\n";
}
print "\n";
}
exit 0;
}
{
# 1 2 3 2 1 4 7 8 5 2 7 12 13 8 3 8 13 12 7 2 5 8 7 4 1 6 11 14 9 4 15
require Math::Polynomial;
Math::Polynomial->string_config({ ascending => 1 });
sub make_poly_k5 {
my ($level) = @_;
my $pow = 5**$level;
my $exp = 0;
my $ret = 0;
foreach my $coeff (1,2,3,2,1,2,3,2,1) {
$ret += Math::Polynomial->monomial ($exp, $coeff);
$exp += $pow;
}
return $ret;
}
print make_poly_k5(0),"\n";
print make_poly_k5(1),"\n";
my $poly = 1;
foreach my $level (0 .. 4) {
$poly *= make_poly_k5($level);
foreach my $i (0 .. 30) {
print " ",$poly->coeff($i);
}
print "\n";
}
# (1 + 2*x + 3*x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 2*x^7 + x^8)
# * (1 + 2*x^5 + 3*x^10 + 2*x^15 + x^20 + 2*x^25 + 3*x^30 + 2*x^35 + x^40)
# * (1 + 2*x^(25*1) + 3*x^(25*2) + 2*x^(25*3) + x^(25*4) + 2*x^(25*5) + 3*x^(25*6) + 2*x^(25*7) + x^(25*8))
exit 0;
}
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