> > I am not sure if this is even related. Does the solver rely on maxima,
> > too!?

Absolutely.

> > The following should yield at least one complex solution... (See also
> > at the end ofhttps://sage.q1cc.net/home/pub/1/)
>
> > a,b = var("a,b")
>
> > solve([a*b==1,a+b==0],a)
> > []
>
> Try solving for both variables (specify both a and b):
>
> sage: solve([a*b==1,a+b==0], a, b)
> [[a == -I, b == I], [a == I, b == -I]]
>

This is documented, I think, that one can use extra variables; it
turns out that in Maxima this also fails with just one variable.
Interestingly, in Maxima just one variable doesn't work, but no
variables do (this is documented in Maxima):


(%i6) solve([a*b=1,a+b=0]);
(%o6)              [[b = - %i, a = %i], [b = %i, a = - %i]]

But this is orthogonal to simplify_radical.

- kcrisman

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