# Polynomial system, apparently for real champs

1. May 27, 2004

### 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

2. May 27, 2004

### 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.

3. May 27, 2004

### Gokul43201

Staff Emeritus
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.

4. May 27, 2004

### TALewis

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

5. May 27, 2004

### 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.

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