       system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg6375] [mg6375] system of equations
• From: u632419 <u632419 at csi.uottawa.ca>
• Date: Fri, 14 Mar 1997 14:54:23 -0500 (EST)
• Organization: University of Ottawa
• Sender: owner-wri-mathgroup at wolfram.com

```Hello everyone,

I have to solve the system of equations below in Mathematica but I have
trouble figuring out how to impose the constrains the constraints
"0<= Q1 <= Q2 <= Q3 <= Q4" in Mathematica (I know that I have 8 cases
for the constraints). Daniel Lichtblau was helped me to solve the
special case where Q1 = Q2 = Q3 = Q4 but I am sure that I have some
more cases to solve.
I think these are all the available cases of this constraint
0 <= Q1 <= Q2 <= Q3 <= Q4 if I break down.

1) 0 < Q1 = Q2 = Q3 = Q4

2) 0 < Q1 = Q2 = Q3 < Q4

3) 0 < Q1 = Q2 < Q3 = Q4

4) 0 < Q1 = Q2 < Q3 < Q4

5) 0 < Q1 < Q2 < Q3 < Q4

6) 0 < Q1 < Q2 < Q3 = Q4

7) 0 < Q1 < Q2 = Q3 = Q4

8) 0 < Q1 < Q2 = Q3 < Q4

I have the book by Stephen Wolfram, but it does not seem to be helpful
in this regard. If anyone has a good idea how I might do this, let me
know via e-mail or posting.

Thank you

- Dinh N.

Please email me at: u632419 at csi.uottawa.ca

------ Begin of problem ----------------------

INPUT: 0 < Q1 <= Q2 <= Q3 <= Q4 ,    Q4^2 <= (Q1^2 + Q2^2 + Q3^2) / 2

FIND:  V11, V12, V13, V14, V21, V22, V23, V24	SUCH THAT

V11^2 + V12^2 + V13^2 + V14^2 = 1

V21^2 + V22^2 + V23^2 + V24^2 = 1

V11 V21 + V12 V22 + V13 V23 + V14 V24 = 0

V11^2 + V21^2 = 2Q1^2 / (Q1^2 + Q2^2 + Q3^2 + Q4^2)

V12^2 + V22^2 = 2Q2^2 / (Q1^2 + Q2^2 + Q3^2 + Q4^2)

V13^2 + V23^2 = 2Q3^2 / (Q1^2 + Q2^2 + Q3^2 + Q4^2)

V14^2 + V24^2 = 2Q4^2 / (Q1^2 + Q2^2 + Q3^2 + Q4^2)

* 7 Equations and 8 Variables, may be fix one of them e.g. V12 = 0 ?

Special Case Q1 = Q2 = Q3 = Q4 (This case was solved)

----------- End of problem -------------------------

```

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