Re: [Axiom-mail] Solving vector equations; is this possible?

[Ralf Hemmecke]

> input:
> Solve( system : [ z = y+ax, p^tz =0 ],
>               for : [ a,z ],
>               with : [ Scalar(a), Vector(x), ….. ] )
>
> output:
> [ z = y+ax, a = -(p^ty)/(p^tx) ]
>
> That is: dimension independent formulas in, dimension-independent formulas out.

This is underspecified. I have to guess what you mean by Scalar(a) and 
Vector(a). In fact, to make Axiom able to do anything you must tell in 
which domain you work. Obviously, in the above input there are two types 
of multiplication. So you have a field K and a vector space V over K. 
Then 2 operations *: (K, V) -> V and *: (V, V) -> K.
(Let's for a moment forget about the transpose (which you seem to 
specify by ^t).)

What you would need in any CAS is a calculus that repects these 
different types of operations *and* their respective properties.

I'm not aware that Axiom has a solver for this, but of course, being a 
CAS, it would be relatively easy to add a few inference rules to derive 
your expected result. Look into 
http://fricas.sourceforge.net/doc/book.pdf and search for ruleset.

I suspect that solving this particular problem is not terribly 
interesting. You probably have other problems to solve.

Be warned, in any existing CAS you might have to do a little programming 
to solve your problem. Simply typing something like "solve(problem)" 
will not work.

Ralf