Re: Manipulating Equations
- To: mathgroup at smc.vnet.net
- Subject: [mg25153] Re: [mg25064] Manipulating Equations
- From: Laurent CHUSSEAU <chusseau at univ-montp2.fr>
- Date: Tue, 12 Sep 2000 02:58:43 -0400 (EDT)
- Organization: LIRMM
- References: <8pff1n$d7v@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
dans l'article 8pff1n$d7v at smc.vnet.net, BobHanlon at aol.com à BobHanlon at aol.com a écrit le 10/09/2000 9:59 : > > In a message dated 9/7/2000 10:48:48 PM, chusseau at univ-montp2.fr writes: > >> I have to simultaneously solve equations corresponding to a physical >> problem. Therefore most of my variables have a meaning only if they are >> real >> and positive. How can I say to Mathematica that it has to reject solutions >> not corresponding to these cases, and furthermore how to declare these >> variables so that their particular nature is used by Simplify or >> FullSimplify. >> > > var = {x, y, z}; > > eqn = {(x + y)*z^2 == 1, x^2 == 3, y^2 == 3}; > > For real, positive variables the conditions are > > cond = And @@ Join[Im[#] == 0 & /@ var, # > 0 & /@ var]; > > soln = Solve[eqn, var] > > {{x -> -Sqrt[3], y -> -Sqrt[3], > z -> -(I/(Sqrt[2]*3^(1/4)))}, {x -> -Sqrt[3], > y -> -Sqrt[3], z -> I/(Sqrt[2]*3^(1/4))}, > {x -> Sqrt[3], y -> Sqrt[3], z -> -(1/(Sqrt[2]*3^(1/4)))}, > {x -> Sqrt[3], y -> Sqrt[3], z -> 1/(Sqrt[2]*3^(1/4))}} > > Select[soln, cond /. # &] > > {{x -> Sqrt[3], y -> Sqrt[3], z -> 1/(Sqrt[2]*3^(1/4))}} > > Whenever you want to apply the conditions use > > Simplify[expr, cond] > > FullSimplify[expr, cond] > > or define functions > > mySimplify[expr_] := Simplify[expr, cond]; > > myFullSimplify[expr_] := FullSimplify[expr, cond]; > > > Bob Hanlon > Thank you Bob, and thank you Allan Hayes too. I want to point out that both your solutions are valid only with Mathematica 4.0. I miss noting that I am using Mathematica 3.0 that does not include features as Simplify (or FullSimplify) with conditions, and/or InequalitySolve. With Mathematica 3.0, the only possibility I found is to manually choose the right solution among those proposed by Reduce. It rests however that the closest form is not obtained since I can't impose that my variables are real and positive. I still have to do work by hand ... some risky and tedious business with long equations ! I will upgrade soon to Mathematica 4 ...