       # Re: Parametric & nonlinear equations system

• To: mathgroup@smc.vnet.net
• Subject: [mg10310] Re: Parametric & nonlinear equations system
• From: Paul Abbott <paul@physics.uwa.edu.au>
• Date: Mon, 5 Jan 1998 03:47:26 -0500
• Organization: University of Western Australia
• References: <68crp7\$a5h@smc.vnet.net>

```Anna Elisabetta Ziri wrote:

> I have to solve or reduce a nonlinear parametric system of equations:
> after three days Mathematica is still elaborating. How can I simplify
> or implement it in t, a & v to have a result in a reasonable time?
>
> X1[t,a,v] = r (1+ a^2) ((1-t^2) xi + 2 t xj) - s ((1 + t^2) (1- a^2) xl
> + 2 a xm) - v xk + c1;
>
> Y1[t,a,v] = r (1+ a^2) ((1-t^2) yi + 2 t yj) - s
> ((1 + t^2) (1- a^2) yl + 2 a ym) - v yk + c2;
>
> Z1[t,a,v] = r (1+ a^2) *
> ((1-t^2) zi + 2 t zj) - s ((1 + t^2) (1- a^2) zl + 2 a zm) - v zk + c3
>
> eqns={ X1[t,a,v] ==0, Y1[t,a,v] ==0,  Z1[t,a,v] ==0}

One attack (output omitted).  Since you are not interested in r and s we
eliminate these variables:

In:= Subtract @@ Eliminate[eqns,{r,s}]

(Applying Subtract to turns the equation into an expression that
vanishes and makes it easier to collect terms)

In:= Collect[%,{t,a},Factor]

You obtain a 6th order equation in t.  I think you cannot expect to get
much further for general parameters.

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul@physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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