Re: Solving vector equations; is this possible?

> input:
> Solve( system : [ z =3D y+ax, p^tz =3D0 ],
>               for : [ a,z ],
>               with : [ Scalar(a), Vector(x), =85.. ] )
>
> output:
> [ z =3D y+ax, a =3D -(p^ty)/(p^tx) ]
>
> That is: dimension independent formulas in, dimension-independent formula=
s 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