Polynomial system, apparently for real champs...

[boeledi]

Hi,

I have now been working for a couple of days on the following system without finding any real clue...

Could someone give me a help?
If there wouldn't be any mathematical way to solve (we never know), could someone detail me how to solve it programmatically?

In advance, many thanks

Didier

-x + y + z + 2A sin(y-z) = C
-x + y - z + 2A sin(x-z) = C
x + y - z + 2A sin(x-y) = C

where A, C are constant and A, x, y, z are not equal to 0

[mathwonk]

I suspect you wrote it down wrong, as it is not symmetrical, and the second equation should be x-y+z +2A sin(x-z) = C, when the solution would be x=y=z=C.

As it is, I can see no solution.

note each equation expresses one of the three letters as a single valued function of the other, (for instance the first equation is easily solved for x), so each equation could be graphed using Mathematica, and you could look at the three simultaneous graphs for a common point.