system of equations
- To: mathgroup at smc.vnet.net
- Subject: [mg6383] system of equations
- From: u632419 <u632419 at csi.uottawa.ca>
- Date: Sun, 16 Mar 1997 19:24:47 -0500 (EST)
- Organization: University of Ottawa
- Sender: owner-wri-mathgroup at wolfram.com
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.
- 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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