*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[5]:= Subtract @@ Eliminate[eqns,{r,s}] (Applying Subtract to turns the equation into an expression that vanishes and makes it easier to collect terms) In[6]:= 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 ____________________________________________________________________