There are algorithms in the literature, as well as
in commercial macsyma, for denesting square roots.
Authors include Richard Zippel and Susan Landau.
The flag is called GCD, and it is probably set to ezgcd or
sparsemod.
There are a few other possibilities,though, like subres.
Andrei Zorine wrote:
> Hello, Richard.
>
> Finally I found, that
>
>> 1. "Quotient is not exact" is always the result of a bug. It
>> comes from computing the GCD G of two polynomials P, Q, and reducing
>> the fraction P/Q to P/G / Q/G. But it finds that G does
>> not divide P or Q. So it is a GCD bug. Try changing the GCDSWITCH
>> to use a different GCD algorithm.
>
>
>
> no GCDSWITCH is defined anywhere in Maxima-5.9.0/* subdirectories. Maybe
> something's missing in the distribution? The switches are only mentioned
> in one .dem file :(
>
>>
>> 3. Try, after substitution, to use ratsimp or radcan.
>>
> it doesn't help. Maxima doesn't see that sqrt(2*sqrt(11)+12) =
> 1+sqrt(11). I wish I could teach it handle nested radicals if I only
> knew the proper algorithm.
>
> --
> Andrei Zorine
>
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