On 13/04/14 13:47, Waldek Hebisch wrote:
** [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.
OK thanks, I did not know this, it looks useful I'll have to experiment
with it. Do you know of any tutorials?
Perhaps the Sourceforge feature-request should be changed to the wish to
have solvers for quaternions and what I would really like: solvers for
Clifford algebra (and possibly better documentation/tutorials for
writers of solvers?).
By the way, is it helpful to put feature-requests on Sourceforge? It is
certainly useful for me to find out that FriCAS has more capability that
I thought. Also It can't do any harm to have more activity on the
project which could also lead to more people finding FriCAS when
searching on Sourceforge.
Martin
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