Partial solution for bug 1452341: solve(x^(5/2)+1,x)

rather than change ratsimp so that it works harder (sometimes MUCH harder),
I suggest trying to prove the solutions by using radcan, under control of
a flag.

I think the idea of a list of solutions that you are "pretty sure of"  is 
unappealing.
How about solutions that "you have proven"?  and "others"

[caveat: I wrote solve, ratsimp, and radcan, at least the versions that
existed before 1971. My opinions may be colored by false pride. I'm
sure that the programs can be improved, especially solve.  I'm much more 
skeptical
about changing ratsimp though.]


----- Original Message ----- 
From: "Stavros Macrakis" <macrakis at gmail.com>
To: "Richard Fateman" <fateman at cs.berkeley.edu>
Cc: "Raymond Toy" <raymond.toy at ericsson.com>; <maxima at math.utexas.edu>
Sent: Thursday, May 25, 2006 8:32 AM
Subject: Re: [Maxima] Partial solution for bug 1452341: solve(x^(5/2)+1,x)


On 5/25/06, Richard Fateman <fateman at cs.berkeley.edu> wrote:
>
> I'm pretty sure that you will not be able to confirm all the roots
> that are produced by solve, by using ratsimp.
>

Here's an example where ratsimp fails.

eq: (x^5-1)^5-1$
sols: solve(eq,x)$
ratsimp(subst(sols[6],eq));

In this case, expand, radcan, and factor all do simplify it to 0, and it's
unfortunate that ratsimp does not.  Perhaps ratsimp should be improved....

          -s