On 03/14/2013 06:51 AM, someone wrote:
Why not a middle ground? For some things it would be silly not to
support n dimensions, like dot product, but for others, like cross
product, the n-dimensional generalization is more complicated, and
(if I understand correctly), not even technically a vector. For those
cases, you could give an error if n > 3.
Yes, I implicitly excluded the wedge/cross product from my wish
to have vectors in Rn. This is where we can make to border towards
geometric/Grassmann/exterior/Clifford Algebra things. (But make sure
one can enter that world from vector expressions)
Actually, here is another cross product in R7:
http://en.wikipedia.org/wiki/Seven-dimensional_cross_product
And for R1, R2 we can trivially pad vectors to R3.
Maybe one could even fill up R4,R5,R6 to R7? But that
I never tried.
Could someone write up a list if everything that would be tricky to
do in n dimensions (rather than 3)? Someone mentioned creating a wiki
page. That would be a good place for this.
Actually, I the abstract algebra code & paper I mentioned, all basic
axioms of vector algebra are valid in Rn *except* the cross product.
By the way, you say Rn, but is there a reason to not use Cn instead?
Or maybe it won't actually matter for 99% of the code.
Oh sure! The base field should not matter. (Probably char 0, maybe
not even necessary to assume that.) Anyway, at least R and C should
be supported, they should not be hard-coded though.
You might want to look at the book "New Foundations for Classical
Mechanics (2nd edition)" by David Hestenes, Kluwer Academic Publishers.
Especially interesting is the spinor formulation of the two body problem
which gives an harmonic oscillator in the spinor variables. This is
especially important for a perturbation analysis of the n-body problem
since perturbed harmonic oscillators have nice convergence properties.
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