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[WSS19] Hypercomplex Numbers Package

Posted 6 years ago
POSTED BY: Alec Macher
4 Replies
Posted 1 month ago

On GitHub I can find several Mathematica packages working with either quaternions or octonions. But none that covers both, the hyper complex numbers.

https://github.com/search?q=Quaternions%20language%3AMathematica&type=repositories

https://github.com/search?q=Octonions%20language%3AMathematica&type=repositories

https://github.com/search?q=Hypercomplex%20language%3AMathematica&type=repositories

When searching on GitHub you need to have an account and being logged in. Otherwise you may get an annoying "Whoa There" message.

POSTED BY: Hans Milton
Posted 1 month ago

Very promising, thank you!

But I have two questions:

  1. How could I access your package without joining GitHub?
  2. For a representation of a Clifford algebra in Mathematica, I need to construct and multiply matrices of biquaternions, ie quaternions with complex components, ie ones in which the imaginary parts commute with the other elements of the algebra. But the Cayley-Dickinson procedure assumes all components are real; so the C-D quaternion has four real components, whereas the biquaternion has eight (but because of the commutation I mentioned it is NOT an octonion). Does your package allow such complex components?

Robert Walgate

POSTED BY: Robert Walgate

This package is very outdated. I recommend the GeometricAlgebra paclet instead:

https://resources.wolframcloud.com/PacletRepository/resources/Wolfram/GeometricAlgebra/

As well, here is a Tech Note that shows how to define bi-quaternions using this paclet:

https://www.wolframcloud.com/obj/nikm/Published/GeometricNumbers.nb

POSTED BY: Alec Macher

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