Solution of "borderline" eqs. in Mathematica, Maple, and Maxima (was "linsolve")

On 4/4/07, Andrej Vodopivec <andrej.vodopivec at gmail.com> wrote:
> > From the user's point of view, shouldn't these all give the same kind of answer?
> These should all give internal errors.

I think we are using the term "internal error" in different ways.  In
my terminology, an "internal error" is one which reflects a failure in
the internal functioning of the system, and does not explain the
problem in the user's terms.  A "user-level error" is one which
addresses the user with a notification in the user's terms, talking
about the mathematical issue, not the internal functioning.

> Yes, but is also suggests to interpret the result as x=0 and all
> values of a. Similarly
> Solver([a*x=x], [a,x]) => [[a=1]] could be interpreted as a=1 and all
> values of x.

In a general-purpose solving routine, I don't think it's acceptable
for the ordering of the variables to change which solutions are shown.
 In fact, I don't think it's acceptable for a general-purpose solving
routine to show only some solutions without at least giving a warning.

Thanks for your work on this,

               -s