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

On 4/3/07, Andrej Vodopivec <andrej.vodopivec at gmail.com> wrote:
> There is a package solver in maxima for solving equations with
> parameters. It has some bugs but with the current cvs you get

(Testing with Maxima 5.11.0 + CVS solver)

Solver's pdf documentation is 135 (!!!) blank (!!!) pages.  Perhaps it
uses some special fonts?  The HTML version is not well-formatted, and
seems to have been automatically translated from the German and is
hard to understand. From what I can tell, it is a very nice package
for some difficult problems.  However, I couldn't find a clear
presentation of its semantics (but I admit I didn't look very hard),
though there is a detailed presentation of its internals.

             -s

Here are some strange cases:

Solver([],[x]); => []              ??? should be ALL or equivalent
Solver([1=1],[x]) => []        ??? should be ALL
Solver([x=x],[x]) => Error: part called on atom: 0
Solver([x=1],[y])   => [[]]    ??? should be ALL
Solver([x=2, y=3], [x], [y]);
> Is  y - 3   positive, negative, or zero? pos
Error: Solver terminated. (backtrace shows that it knows that it is a
parameter consistency problem, but why did it ask the question in the
first place?)

Solver([a*x=x], [x,a]) => [[x=0]]   ??? what happened to a=1?

Solver([x=x+1],[x]); =>	    [[[- 1]]]      ??? what does this mean?