[Maxima] vector times vector; vector^-1?
robert.dodier at gmail.com
Sun Nov 16 19:51:58 CST 2008
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
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.
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