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MathGroup Archive 1997

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system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6383] system of equations
  • From: u632419 <u632419 at csi.uottawa.ca>
  • Date: Sat, 15 Mar 1997 01:21:17 -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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