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

[Creighton Kenneth Dement]

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

Getting rid of the "random letters for the components" is the whole
purpose of introducting the projection operators
ibase(X), jbase(X), etc. ...

What is your point other than making jokes? I know you didn't just look at
this stuff today, because you have kindly offered to help me before (if my
memory serves me correctly) and I didn't hear any of this then.

> Does your algebra contain (e.g.) complex numbers, quaternions, octonions?

If "my algebra" contains quaternions, which I believe I mentioned only a
few days ago on this seqfan list, it certainly contains complex numbers.

Sincerely,
Creighton


> * 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
>
>
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