Re: [maxima:bugs] #2123 radcan not idempotent

Yes, you mentioned this issue in the comments on the bug in 2011-01-06 (!).

Comments there <https://sourceforge.net/p/maxima/bugs/2123/#6ec5>.

Binding *radexpand:false* or *domain:complex* sounds reasonable. Any
objections?

On Sun, Apr 19, 2026 at 1:28 PM Richard Fateman <[email protected]> wrote:

> I'm trying this on maxima 5.46.0.
> This is peculiar in another way, in that it produces abs(x), which is not
> an algebraic function, which radcan should
> not return.  Some program has been called internally (simplification) that
> converts sqrt(x^2) to abs(x), which
> is not a legitimate radcan result.
>
> consider
> sqrt(x^2+2*x+1)
>
> radcan(%)   produces x+1    correct.   NOT abs(x+1), which is incorrect,
> but consistent with the incorrect abs(x).
>
> RJF
>
>
> On Sun, Apr 19, 2026 at 9:31 AM David Scherfgen <
> [email protected]> wrote:
>
>>
>>    - *status*: open --> closed
>>    - *Group*: --> None
>>    - *Comment*:
>>
>> This seems to have been fixed at some point.
>> ------------------------------
>>
>> *[bugs:#2123] <https://sourceforge.net/p/maxima/bugs/2123/> radcan not
>> idempotent*
>>
>> *Status:* closed
>> *Group:* None
>> *Labels:* Lisp Core - Polynomials
>> *Created:* Wed Jan 05, 2011 10:01 PM UTC by Stavros Macrakis
>> *Last Updated:* Sun Nov 18, 2012 07:53 PM UTC
>> *Owner:* nobody
>>
>> ex: (1-1/x^2)^(3/2)*x$
>> radcan(ex) =>
>> sqrt(x-1)*sqrt(x+1)*(x^3-x)/(x^2*abs(x))
>> Note the factor of x in the numerator and denominator that hasn't been
>> factored out.
>> radcan(radcan(ex)) =>
>> sqrt(x-1)*sqrt(x+1)*(x^2-1)/(x*abs(x))
>> The common factor is factored out.
>>
>> Workaround: A rat or ratsimp before or after the radcan gets rid of the
>> problem.
>> ------------------------------
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