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

[Victor Eijkhout]

On Jun 1, 2012, at 2:22 PM, Ralf Hemmecke wrote:

>> input:
>> Solve( system : [ z = y+ax, p^tz =0 ],
>>              for : [ a,z ],
>>              with : [ Scalar(a), Vector(x), ….. ] )
>> 

>  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.

Absolutely. And I'm really looking at the simplest case of real numbers and R^N.

> 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.

Will do.

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

Yeah, it's the simplest example of more complicated stuff I'm doing. Most of it 
too complicated (or just too many instances) to be done by hand.

Victor.