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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.( rr - ii - jj - kk, 2ri, 2rj, 2rk );
			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.

AUTHOR

Bruce Gray

COPYRIGHT AND LICENSE

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