Richard Fateman <fateman at eecs.berkeley.edu> writes:
> Then the problem is with the multiple-equation solve.
> In fact we do not check that the solutions are valid -- solve may
> return superfluous ones. It is, in general, not possible to prove
> all solutions by back substitutions. I think Mathematica has as
> an option to try to prove validity by substitution.
>
> Anyway, the number of solutions or whether there are any is
> kind of wide open, given the generality of expressions in Maxima.
>
> e.g. solve (x^n=1,x) has n solutions of x=1 but solve says one.
>
> to_poly_solve(x^n=1,x) gives a %union expression...
>
> Although neither solve notices ...
> if n=0 when the solution is x#0
> ....
Right.
So maybe we can limit the scope of this discussion slightly, to ways we
can improve the solve() interface. Since solve() accepts all sorts of
equations (trigonometric, with radicals, special functions ...), we're
not usually going to be able to say "There are no solutions". So I guess
the challenge is working out what we should return when solve/algsys
runs out of inspiration.
Are there any backwards-compatibility issues? I take it that the current
behaviour is what Macsyma etc. did? The reason I ask is that changing
the output format of solve might break people's scripts.
That said, I gave up trying to get one script I wrote to work well with
solve() and switched to calling algsys explicitly (since the output
format is less variable). Maybe we don't need to worry about breaking
things?
Maybe we can answer the following question:
Without strengthening the solver, how can we make it more useful? That
is, how should solve() report each of the following?
(1) There are no solutions
(2) There may be solutions
(3) Here are some solutions. There are no more.
(4) Here are some solutions. There may be some more.
(and over what domain should the above be defined? Are there solutions
to sin(x) = 2?)
Rupert
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