On Tuesday, July 28, 2020 at 9:02:44 PM UTC-4, rjf wrote:
>
> that crashed for me.
>
>   It reminds me of an old joke ..
> <synopsis>
> Man goes to doctor and says, It hurts when I do this <contortion>.
> Doctor says, don't do  <contortion>.
>
>
Well, <contortion> probably shouldn't be in the documentation then :-) 
 See https://trac.sagemath.org/ticket/25636 for an impressive array of 
similar reports, and https://sourceforge.net/p/maxima/bugs/3442/ for at 
least one upstream report.
 

>
> Maxima and Macsyma before it was basically written with real variables in
> mind.  It would be nice to know exactly what behavior Sage expects
> that requires domain:complex.  
>
 
I believe it's primarily the following, according to the Maxima 
documentation.  You may recall this conversation we've had several dozen 
times ;-) but anyway, regardless of that, I am always stumped as to why 
changing this setting messes up integrals.  (As opposed to the 
abs_integrate package we used for a while.)

*Option variable:* *domain*Default value: real

When domain is set to complex, sqrt (x^2) will remain sqrt (x^2) instead of 
returning abs(x).


I don't see what integrate(t,t, 0, 4*a-a^2); has to do with simplifying 
square roots.   If seeing this helps you (or someone else) debug/diagnose 
it, that may be the key to fixing ALL of these discrepancies, for which I 
at least would be profoundly grateful.

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