[Maxima-discuss] Why does 'solve' not work here?

[Name N. <zei...@ya...>]

I don't seem to understand the equation solvers 'solve' / 'to_poly_solve', because I can't get solutions to absolutely trivial equations.
Needing a CAS for such eqns. is surely 'debatable', but that is not my question.

1) --------------------------
(%i3) solve(sin(x)=0,x);
solve: using arc-trig functions to get a solution.
Some solutions will be lost.
(%o3) [x = 0]

so far so good.

2) ------------------------
(%i4) solve([sin(x)=0,sin(y)=0],[x,y]);
(%o4) []

Oops. Why is 'solve' unable to find any solution??

3) -------------------------
Out of despair the next thing I tried was:

(%i5) load(to_poly_solve)$
(%i6) to_poly_solve([sin(x)=0,sin(y)=0],[x,y]);
(%o6) %union([x = %pi*%z1,y = %pi*%z3])

Ok., so polynomializing seemed to help.

4) -----------------------
Now I want to get just a little bit more adventurous

(%i9) to_poly_solve([sin(x-y)-sin(y)=0,sin(y)=0],[x,y]);
Unable to solve
Unable to solve
Unable to solve
(%o9) %solve([sin(y) = 0,-sin(y-x)-sin(y) = 0],[x,y])

:-(  Needless to say that 'solve' doesn't work here either.
---------------------------
I am fully aware, that the eqns. 4) can be rewritten (even with Maxima) such as to get sensible solutions.
But that is not my question, rather, I'd like to know, given eqns. 4) 'as is', if Maxima can find a solution or not?
(I.e. if my usage 'solve' or 'to_poly_solve' is proper?)

Mark