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# Copyright 2013, 2014 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/>.
package Math::SquareRadical;
use 5.004;
use strict;
use Carp 'croak';
use Scalar::Util 'blessed';
use vars '$VERSION', '@ISA';
$VERSION = 117;
# uncomment this to run the ### lines
use Smart::Comments;
use overload
'""' => \&stringize;
'0+' => \&numize;
'bool' => \&bool;
# '<=>' => \&spaceship;
'neg' => \&neg;
'+' => \&add,
'-' => \&sub,
'*' => \&mul,
fallback => 1;
sub new {
my ($class, $int, $factor, $root) = @_;
$factor ||= 0;
$root ||= 0;
unless ($root >= 0) {
croak "Negative root for SquareRadical";
}
return bless [ $int, $factor, $root ], $class;
}
sub bool {
my ($self) = @_;
### bool(): @$self
return $self->[0] || $self->[1];
}
sub numize {
my ($self) = @_;
### numize(): @$self
return ($self->[0] + $self->[1]*sqrt($self->[2])) + 0;
}
sub stringize {
my ($self) = @_;
### stringize(): @$self
my $factor = $self->[1];
if ($factor == 0) {
return "$self->[0]";
} else {
return "$self->[0]".($factor >= 0 ? '+' : '').$factor."*sqrt($self->[2])";
}
}
# a+b*sqrt(c) <=> d
# b*sqrt(c) <=> d-a
# b^2*c <=> (d-a)^2 # if both same sign
#
# a+b*sqrt(c) <=> d+e*sqrt(f)
# (a-d)+b*sqrt(c) <=> e*sqrt(f)
# (a-d)^2 + 2*(a-d)*b*sqrt(c) + b^2*c <=> e^2*f
# 2*(a-d)*b*sqrt(c) <=> e^2*f - b^2*c - (a-d)^2
# 4*(a-d)^2*b^2*c <=> (e^2*f - b^2*c - (a-d)^2)^2
#
sub spaceship {
my ($self, $other) = @_;
### spaceship() ...
if (blessed($other) && $other->isa('Math::SquareRadical')) {
if ($self->[1] != $other->[1]) {
croak "Different roots";
}
return bless [ $self->[0] + $other->[0],
$self->[1] + $other->[1] ];
} else {
my $factor = $self->[1];
my $rhs = ($other - $self->[0]);
return (($rhs < 0) <=> ($factor < 0)
|| (($factor*$factor*$self->[2] <=> $rhs*$rhs)
* ($rhs < 0 ? -1 : 1)));
}
}
sub neg {
my ($self) = @_;
### neg(): @$self
return $self->new(- $self->[0],
- $self->[1],
$self->[2]);
}
# c = g^2*f
# a+b*sqrt(c) + d+e*sqrt(f)
# = a+d + b*g*sqrt(f) + e*sqrt(f)
# = (a+d) + (b*g + e)*sqrt(f)
#
sub add {
my ($self, $other) = @_;
### add(): @$self
if (blessed($other) && $other->isa('Math::SquareRadical')) {
my $root1 = $self->[2];
my $root2 = $other->[2];
if ($root1 % $root2 == 0) {
$self->new($self->[0] + $other->[0],
($root1/$root2)*$self->[1] + $other->[1],
$root2);
} elsif ($root1 % $root2 == 0) {
$self->new($self->[0] + $other->[0],
($root1/$root2)*$self->[1] + $other->[1],
$root2);
} else {
croak "Different roots";
}
} else {
return $self->new($self->[0] + $other, $self->[1], $self->[2]);
}
}
# sub sub {
# my ($self, $other, $swap) = @_;
# my $ret;
# if (blessed($other) && $other->isa('Math::SquareRadical')) {
# if ($self->[1] != $other->[1]) {
# croak "Different roots";
# }
# $ret = bless [ $self->[0] - $other->[0],
# $self->[1] - $other->[1] ];
# } else {
# $ret = bless [ $self->[0] - $other, $self->[1] ];
# }
# if ($swap) {
# $ret->[0] = - $ret->[0];
# $ret->[1] = - $ret->[1];
# }
# return $ret;
# }
# (a + b*sqrt(c))*(d + e*sqrt(f))
# = a*d + b*d*sqrt(c) + a*e*sqrt(f) + b*e*sqrt(c*f)
# if c=g^2*f
# = a*d + b*d*g*sqrt(f) + a*e*sqrt(f) + b*e*g*f
sub mul {
my ($self, $other) = @_;
### mul(): @$self
if (blessed($other) && $other->isa('Math::SquareRadical')) {
my $root1 = $self->[2];
my $root2 = $other->[2];
if ($root1 % $root2 == 0) {
my $g2 = $root1/$root2;
my $g = sqrt($g2);
if ($g*$g == $g2) {
$self->new($self->[0] + $other->[0],
$g*$self->[1] + $other->[1],
$root2);
}
} elsif ($root2 % $root1 == 0) {
my $g2 = $root2/$root1;
my $g = sqrt($g2);
if ($g*$g == $g2) {
$self->new($self->[0] + $other->[0],
$self->[1] + $g*$other->[1],
$root1);
}
} else {
croak "Different roots";
}
} else {
return $self->new($self->[0] * $other, $self->[1] * $other, $self->[2]);
}
}
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