[seqfan] Re: detective work related to Creighton Dement's \\\"Floretions\\\"

Joerg Arndt arndt at jjj.de
Fri Nov 20 22:37:11 CET 2009

* Creighton Kenneth Dement <creighton.k.dement at mail.uni-oldenburg.de> [Nov 21. 2009 07:32]:
> [...]

>
> Here are the very basics which should be any such page.
>
> Let X = A'i  + B'j + C'k + Di' + Ej' + Fk' + G'ii' + H'jj' + I'kk' +
> J'ij' + K'ik' + L'ji' + M'jk' + N'ki' + O'kj' + P'ee'
>
> and Y = a'i  + b'j + c'k + di' + ej' + fk' + g'ii' + h'jj' + i'kk' +
> j'ij' + k'ik' + l'ji' + m'jk' + n'ki' + o'kj' + p'ee'
>
> Then
>
> ibase(X) = A
> jbase(X) = B
> kbase(X) = C
> basei(X) = D
> basej(X) = E
> basek(X) = F
> ibasei(X) = G
> jbasej(X) = H

[about here my brain starts bleeding]

> kbasek(X) = I
> ibasej(X) = J
> ibasek(X) = K
> jbasei(X) = L
> jbasek(X) = M
> kbasei(X) = N
> kbasej(X) = O
> tes(X) = P

Oh dear, _this_ is obfuscation in perfection.
What about the scheme used in sect.37.14, p.831ff
of http://www.jjj.de/fxt/#fxtbook  ?
It's an algebra, dammit.

Get rid of random letters for the components!
As it is, noone will ever dig through this messy notation.

> [...rather random looking functions...]

Can the specific definition be somehow motivated?

>
>
> X*Y =
>
> (Pa - Dg - Ho + Im - Fk - Ej + Oh - Cb - Gd + Nl - Je - Kf - Mi + Ap + Bc
> - Ln)'i
>
> [...etc...]

Does your algebra contain (e.g.) complex numbers, quaternions, octonions?
Is it even isomorphic to the sedenions or some Clifford algebra?

What are the sub-algebras (if it has any)?

Is it (or are any sub-algebras) associative or commutative?

Zero-divisors?

> [...]

btw. your old domain is available for registration,
you may want to (re-)register it.

cheers,   jj

P.S.: a grouchy German is a Sauer-Kraut