[Maxima] algsys and real solutions

Michel Gosse michel.gosse at free.fr
Sat Aug 19 03:13:39 CDT 2006

```Great thanks for all the answers to this problem.
Obviously, it seems that Maxima does a good job, but this problem is very hard
to solve and we can't expect to find easyly the solutions.

Best regards

Le vendredi 18 Août 2006 13:56, Barton Willis a écrit :
> -----Michel Gosse  wrote: -----
>
> >Solving the above system with algsys, i obtain
> >only complex solutions. How can
> >i obtain the real solutions of this system ?
> >
> >eq1: alpha * beta * teta / ( (alpha-1)*(beta+1)) - 1.5
> >eq2: alpha * beta * teta^2 / ( (alpha-2)*(beta+2)) - 3
> >eq3: alpha * beta * teta^3 / ( (alpha-3)*(beta+3)) - 4.5
>
> To find only the real solutions, set the option variable
> 'realonly' to true. Also, the user documentation says that
> algsys solves polynomial equations, so I mapped ratnumer
> over your equations to covert them to polynomial form:
>
> (%i33) algsys(map('ratnumer, [eq1,eq2,eq3]),[alpha,beta,teta]), realonly :
> true;
> `rat' replaced -1.5 by -3//2 = -1.5
> `rat' replaced -4.5 by -9//2 = -4.5
> (%o33) []
>
> The fact that algsys returns the empty list doesn't prove that there
> are no real solutions. Maxima might be correct, but it might be wrong.
> Do you have some reason to think that there is a real solution?
>
> Barton
>
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