[seqfan] Re: detective work related to "Floretions"
Robert Munafo
mrob27 at gmail.com
Sat Nov 21 03:50:38 CET 2009
A term like "nonassociative algebra" might be suitable for some readers, but
it confuses me. I still think "algebra" is how I solved word problems in 7th
grade (well not quite, but close :-).
The purpose of my investigations is to make this stuff useable by people who
need to be shown simple and concrete examples. I understand that
"commutative" refers to the idea that "3 x 7 = 7 x 3" and that's about it. I
don't know what "sub-algebra" means, or how "an algebra" can "contain"
quaternions? If a "projection operator" is something that takes one type of
number for input and produces another type as output, let's just say that,
and avoid the jargon. I don't need to have taken college level maths courses
to to calculate these sequences.
Also, I really do prefer the separate letters a,b,c,d,e,f,...,o,p rather
than a subscripted coefficient. In my opinion, subscripted coefficients are
for cases where the number of components is variable, unlimited, and/or
exceeds the number of letters in your alphabet(s). None of those applies
here: we have exactly 16 components all the time. It gets worse when there
are two or more dimensions worth of subscripts, like when defining matrix
multiplication.
As for the special-named functions like "ibase()", I just need to understand
and document them, because that's they appear in the existing OEIS database
entries. Think of my work as a Rosetta stone for Creighton's work (-: There
were three languages on the Rosetta stone. Here, we have Creighton's
language, formal algebra language, and "I just want to calculate the d**n
thing" language.
Jonathan Post wrote:
> Wasn't there a comment that identified Floretions as a specific
> nonassociative algebra, in a way that explains where the complex,
> quaternionic, and octonionic structures come from?
Joerg wrote:
> Get rid of random letters for the components!
> As it is, noone will ever dig through this messy notation.
> [...]
> Name the components a0, a1, ..., a15.
> a0 shall be the neutral element (is there such an element?).
Creighton wrote:
>> Getting rid of the "random letters for the components" is the whole
>> purpose of introducting the projection operators ibase(X), jbase(X), etc.
...
Someone wrote:
>>> What are the sub-algebras (if it has any)?
>>> Is it (or are any sub-algebras) associative or commutative?
>>> Zero-divisors?
Someone wrote:
> Does your algebra contain (e.g.) complex numbers, quaternions, octonions?
and Someone wrote:
> Did you make _any_ attempt whatsoever to obtain structural information
about your algebra?
--
Robert Munafo -- mrob.com
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