On Thu, Dec 4, 2008 at 3:52 PM, Francois Maltey wrote:
>
> Bill Page wrote:
>>> I find quite important to get a right reponse to
>>> solve (a^2*x+1=x+a, x) with 3 cases a=1, a=-1 and else.
>>>
>>> Usual cas reponse x=(a-1)/(a^2-1)=1/(a+1) is irrelavant, but
>>> mupad (now scilab) could do it.
>>>
> Mupad get directly theses 3 lines,
> I don't have any mupad at home, only at work...
>
> {1/(a+1)} for a <> 1 and a <> -1
> emptyset for a=-1
> C for a=1
>
> This reponse illustrates the difference between the only one
> algebraic solve in Q(a) and the not-so-algebraic-but-elementry
> -mathematics solves for all the possible a. The trap of this
> example is around the unseen case a=1 in the simplified
> reponse. The axiom/maple solve gives x=1/(a+1), and
> x=1/2 only if a=1.
>
> Today only? mupad gives the right solution.
>Ok, thank you for the explanation. So you would expect a piecewise result to explicitly include the a=-1 and a=1 cases. But isn't it equally correct to give x=(a-1)/(a^2-1) (unsimplified) as the correct and complete answer? Here the cases a=-1 and a=1 are implicit, i.e. -2/0 = emptyset and 0/0 = C. The "error" is in the simplification of the result. If the simplification is accepted then it might be desirable that the process of "simplification" also returned the zeros of the denominator. Maybe this is difficult for some complex (> degree 4) cases. In any case I do not see this as a problem with "solve" and I am not sure that I would consider a piecewise expression as necessarily "simpler" than the unsimplified result. Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
