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

On 4/4/07, Andrej Vodopivec <andrej.vodopivec at gmail.com> wrote:
> >        Solver([x=1,x=2],[x]) => [[]]
> >        Solver([x=x+1],[x]) => [[[-1]]]
> >        Solver([x=y,y=x+1],[x,y]) => internal error
> >        Solver([x=y,y=x+1],[x,y]) => internal error
> >
> > From the user's point of view, shouldn't these all give the same kind of answer?
>
> These should all give internal errors.

Besides the question of user vs. internal errors, why should any of
these give errors? Why is an inconsistent system an error condition?
x=x+1 has 0 solutions; x=1 has 1 solution; x^2=1 has 2 solutions; x=x
has an infinity of solutions.  All reasonable return values.

            -s