NAME

Math::Quaternion - Hyper-complex numbers as objects with operators

SYNOPSIS

use Math::Quaternion;

DESCRIPTION

This distribution implements an OO class for Quaternions, which are the simplest of the hyper-complex numbers. It adds the operators needed for basic math on the Qs, and should be a good base class for future modules to support the other hyper-complex numbers.

RECOMMENDATIONS

I intend this module to be a high-quality example of Raku numeric OO, usable as a reference for future module authors.

WARNINGS

This module is a mostly-from-scratch re-implementation of Quaternions; its API differs from the excellent Perl Math::Quaternion module.

GLOSSARY

Wikipedia	Raku	Boost	dwh	RAW
a	$.r	R_component_1	real	Real____________ part of a Q (as accessor)
b	$.i	R_component_2	imag_i	First_ imaginary part of a Q (as accessor)
c	$.j	R_component_3	imag_j	Second imaginary part of a Q (as accessor)
d	$.k	R_component_4	imag_k	Third_ imaginary part of a Q (as accessor)
	.coeffs			(r, i, j, k) # List, not arrayref nor vector
	.v			(i, j, k) # List, not arrayref nor vector
				.
norm		abs	abs	sum_of_squares( r,i,j,k ).sqrt
		norm	norm	sum_of_squares( r,i,j,k )
		abs(unreal)	abs_imag	sum_of_squares( i,j,k ).sqrt
		norm(unreal)	norm_imag	sum_of_squares( i,j,k )
			arg	atan2( sum_of_squares( i,j,k ).sqrt, r );
distance				.
				.
		unreal	imag	self.( 0.0, i, j, k );
			conj	self.( r, -i, -j, -k );
			operator *	self.( r, -i, -j, -k );
			signum	absq = sum_of_squares( r,i,j,k ).sqrt; return ( absq == 0.0 ) ?? self !! self.new( r/absq, i/absq, j/absq, k/absq );
			sqr	self.( r*r - i*i - j*j - k*k, 2*r*i, 2*r*j, 2*r*k );
			inverse	self.new: (r,-i,-j,-k) / sum_of_squares( r,i,j,k )
versor				self / sum_of_squares( r,i,j,k ).sqrt
				.
			is_nan	r != r or i != i or j != j or k != k;
			is_inf	any(r,i,j,k) == any(PosInf,NegInf)
			is_neg_inf	all(_,i,j,k) == 0 and r == NEG_INF;
			is_pos_inf	all(_,i,j,k) == 0 and r == POS_INF;
			is_real_inf	all(_,i,j,k) == 0 and r == any(POS_INF,NEG_INF);
	is_real		is_real	all(_,i,j,k) == 0
	is_zero		is_zero	all(r,i,j,k) == 0
	is_complex			all(_,_,j,k) == 0
	is_imaginary		is_imaginary	r == 0
				.
			rotate	When |q| == 1
			sqrt	.

ACKNOWLEDGEMENTS

Thanks to:

• Jonathan Chin for the original Perl Math::Quaternion module.

• Solomon "colomon" Foster for encouraging this module's release.

• Will "Coke" Coleda for fixes to match changes in Rakudo.

• RosettaCode for the challenge that provoked the initial code.

SEE ALSO

• http://en.wikipedia.org/wiki/Quaternion

• http://en.wikipedia.org/wiki/Hypercomplex_number

AUTHOR

Bruce Gray

COPYRIGHT AND LICENSE

Copyright 2010 - 2017 Bruce Gray

Copyright 2024 Raku Community

This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.