eliminate



I have come across some unexpected behavior in eliminate (Maxima
5.9.2, but I already saw it in 5.9.1):

,----
| (%i1) eliminate([c*x^2=a, c*x = b], [c]);
| 
| (%o1)                           [- x (b x - a)]

OK, as expected.

| (%i2) eliminate([c*x^2=a, c*x = b], [x]);
| 
|                                             2
| (%o2)                          [- c (a c - b )]

Unexpected: This seems to suggest that c=0 solves both equations.  I
would have expected [ a*c - b^2 ] instead.

| (%i3) eliminate([a+x^5, x, f], [x]);
| 
|                                       5
| (%o3)                               [f , a]

Unexpected: Why is f (which is free of x) affected at all?

`----

I do not see anything in the help text to suggest this behavior, and
solve(%o2, [c]) obviously gives a spurious solution c=0.

Is this

- an implementation bug, and if so, a known one?

- a documentation bug (missing, e.g., a warning against using solve on
  the result of eliminate)?

- a user bug?

Best regards,

Albert.