Version 14 of Octave

Updated 2007-09-28 21:15:49 by andy

"GNU Octave is a high-level language, primarily intended for numerical computations", according to its home page [L1 ]. Its language "is mostly compatible with Matlab." Additional compatibility functions are available at octave-forge[L2 ].

dead link:: http://merlin.inescn.pt/~qual/tk_octave/index.htm ?

Try http://www.gnu.org/software/octave/ or http://www.octave.org

Tkoctave

octcl: Tcl client for the Octave server. Part of octave-forge[L3 ].

Provocatively, the 2006 second edition of the popular Scientific Computing with MATLAB was retitled, Scientific Computing with MATLAB and Octave. Open source marches on.


Also, octaves are 8-dimensional numbers, just as complex numbers are 2-dimensional and quaternions 4-dimensional, and more dimensions seem not to make any sense anymore, in number theory.

AM I think you will find that octonions are 8-dimensional numbers, they are also called biquaternions.

Their properties or better the lack of familiar properties is rather curious:

  • Complex numbers can not be ordered: "i < 1" makes no sense
  • Quaternions do not commute when multiplied: a * b != b * a
  • Octonions do not have the associative property: a * (b * c) != (a * b) * c

(This latter lack of properties seems to be responsible for there not being a system of 16-dimensional numbers ...)

The existence of octonions does mean that in 7-dimensional space, just as in 3-dimensional space, but in no others, there exists an out-product for vectors.

(Okay, there are all rather impractical faits divers - but I thought you might like to know :)

AMG: Terrific quote about octonions:

The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative. — John C. Baez

AMG again, with a question for AM or whoever else: When you say "out-product", do you mean "outer product", a.k.a. "cross product"? Or am I confusing my terms?


slebetman: Actually, an octave is one "order of magnitude" for base 8 numbers (octals) just like decade is one order of magnitude for base 10 numbers. For example, the octal number 021 is two octaves above zero.

AMG: How about musical octaves? Halving or doubling a note's pitch produces another note that is an octave interval from the first. In Western music at least, the octave is divided into twelve semitones, of which seven are used in any given major or minor key scale. Therefore, if a "root" note is called 1, its octave would be 8.


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