> ** [feature-requests:#10] Add Ability to Write Equation Solvers for a given
> Domain.**
>
> FriCAS has quite good support for say, systems of polynomial equations in
> field or OrderedRing, see numsolve.spad.pamphlet for more details.
>
> Would it be possible to generalise this so that someone writing code for an
> SPAD domain can add their own equation solvers for their domain. With
> variables that represent elements of that domain.
>
> So, for example, we might want to write equations where the variables are
> quaternions. So we need to write a solver which can handle a non-commuting
> algebra.
>
> I suppose someone could write some code in SPAD to do this now? But it really
> needs a proper framework to do it efficiently?
>
You can write solvers just now. Existing solvers are packages
which export 'solve' function. Of course, you need an algorithm
for given domain. Given system of linear equations over quaternions
one can convert it to a bigger linear system over base ring
and call existing solver. Then convert back to quaternions.
In principle similar approach may work for polynomial equations,
but even simple polynomial equations over quaternions will
produce complicated equations over base ring. Directly working
with quaternions may produce better solver.
Anyway, the main problems is to find a method of solving for
given domain.
--
Waldek Hebisch
[email protected]
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