vector times vector; vector^-1?



On 11/16/08, Renatus <dositheus at hotmail.com> wrote:

> by simply by-passing declare(..., scalar), which has no effect on arrays,
> and replacing it by a couple of rather clumsy Lisp lines to get the desired
> result.

By the way, what were those lines of Lisp code?

> It would be better if arrays could be consistently declared with scalar or
> non-scalar elements.

How would you like to see it work? I.e. what is a possible syntax.

>  As for the inverse of a vector, it is well defined in Clifford Algebra.

> v^-1[i] := v[i]/sum(v[k]^2,k,1,n),
> so that the scalar product: v^-1 dot v = v dot v^-1 = 1.

Hmm, interesting. Doesn't that hold in any vector space equipped
with an inner product? Maybe we should define v^-1 for all vectors.

But if not for all vectors, I wonder how to distinguish the ones
which should have that property.
clifford_vector(...) instead of vector(...) ?
declare_clifford(x) or declare(x, clifford) or ??
These all seem too clumsy.
I think I like declare(x in clifford_algebra(v, q)) but that assumes
some machinery which Maxima doesn't have at present.

I think an answer to this question about special vectors could
be useful more generally.

best

Robert Dodier