solution of system of quadratic eqns



On 06/23/2012 10:23 AM, Richard Fateman wrote:
> On 6/23/2012 8:19 AM, Richard Fateman wrote:
> ....
>
>> For what it is worth, the commercial Macsyma does this without 
>> difficulty. It seems to use
>> a grobner basis algorithm, but the default is a triangularization 
>> method.
> ....
> It turns out that if I set use_grobner: false, then it uses a 
> resultant method and algsys returns
> empty, same as Maxima.
>
> So I was wrong in thinking this could not have been a bug in old systems.
>
> I still think that resultants should work if some bug were removed, 
> but so can Grobner bases; the fastest should
> be triangularization, if it is applicable.
>
> RJF
>
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>


Yes, I confirm that the resultant method works as follows:


(%i14) solve(resultant(lhs(e1)-1,lhs(e2)-1,x),y);

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced -0.5 by -1/2 = -0.5
                             sqrt(7) - 1      sqrt(7) + 1
(%o14)               [y = - -----------, y = -----------]
                                  4                4


Krishna