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

 

[matt grime]

that isn't a polynomial system, so you're mis-selling the question. as long as C isn't zero then the constraints that A x,y,z are not zero is unnecessary.

 

[Gokul43201]

Are you sure the RHS of your second equation is not -C ? If it is, then your 3 equations are cyclically symmetric. If not, it's harder to solve.

In fact, I'm thinking there probably isn't an analytical solution. So you might have to solve it numerically after all.

 

[TALewis]

And on top of that, it might be difficult to find a numerical solution that's stable and converges.

 

[TALewis]

I'm curious where this problem comes from. Maybe some context would give a few clues on what kind of solution we're looking for.