[Qtfm-announce] QTFM version 2.7

[Release a. a. u. <qtf...@li...>]

A new release of the Quaternion Toolbox for Matlab (QTFM) has
been posted on Sourceforge.

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                Quaternion toolbox for Matlab
                http://qtfm.sourceforge.net/
       Mailing list: qtf...@li...<mailto:qtf...@li...>
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Copyright (c) 2005-2019 Stephen J. Sangwine & Nicolas Le Bihan
Email: san...@us...<mailto:san...@us...>
       nic...@gi...<mailto:nic...@gi...>
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                     Release Notes

Version 2.7  20 April 2019

A new function 'polar' implements the polar decomposition of a biquaternion
(trivial in the case of real quaternions). This is equivalent to the polar
decomposition of linear algebra applied to the adjoint matrix. The same
decomposition works for octonions (but in this case there is no adjoint
matrix representation to compare against). The decomposition and the
algorithm for computing it were discovered by Steve Sangwine and Eckhard
Hitzer in July 2018, and are the subject of a journal paper referenced
in the code. Test code has been added for the two new functions.

A new function 'peirce' implements a recently published decomposition due
to Roger M. Oba of a real quaternion into biquaternion idempotents and
complex eigenvalues. It has the remarkable property that many functions of
a quaternion (such as trigonometric functions, powers, roots) may be
implemented using only a complex implementation of the same function.

A bug in the exponential function has been fixed. Nilpotents gave an
incorrect result of 1, rather than the correct 1 + X. In the process of
fixing this, two new functions 'isdivisor' and 'isnilpotent' were written
(for both complexified quaternions and complexified octonions). The log
function has been edited to give a warning when the exponential of a
nilpotent is present, but a fix has been deferred to a later release.

Incremental changes have been made here and there.

*****************
Dr Steve Sangwine
Senior Lecturer
School of Computer Science and
        Electronic Engineering
University of Essex
Wivenhoe Park
Colchester CO4 3SQ
United Kingdom

T: (+44) (0)1206 872401
F: (+44) (0)1206 872684

http://stephen_sangwine.droppages.com/