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 -------------------------