Hi Nils,

On 2019-12-02, Nils Bruin <nbr...@sfu.ca> wrote:
> On Monday, December 2, 2019 at 3:18:20 PM UTC-8, Michael Orlitzky wrote:
>>
>> Who do I have to make a campaign donation to if I want this to be the 
>> default? 
>>
>
> The Society for the Prevention of Predictable Performance would be a good 
> place to start.
>
> Trying to find a radical expression for an algebraic number can be pretty 
> expensive and, of course, may fail:
>
> sage: QQbar.options.display_format="radical"
> sage: QQbar['x'](x^5+x+3).roots()
> [(-1.132997565885066?, 1),
>  (-0.4753807566695497? - 1.129701725095409?*I, 1),
>  (-0.4753807566695497? + 1.129701725095409?*I, 1),
>  (1.041879539612083? - 0.822870338109958?*I, 1),
>  (1.041879539612083? + 0.822870338109958?*I, 1)]
>
> so I don't think it will ever be a default.

Hang on, does that mean that with display_format="radical", Sage will
show a radical expression when it finds one, and will show numerical
noise when it finds none (i.e., it does not simply raise an error)?

Indeed:
  sage: QQbar['x'](((x^2+3)*(x^2-3)*(x^2+15)).expand()).roots()
  [(-sqrt(3), 1),
   (sqrt(3), 1),
   (-I*sqrt(15), 1),
   (-I*sqrt(3), 1),
   (I*sqrt(3), 1),
   (I*sqrt(15), 1)]

That's actually quite nice! So, it would be a good default -- if
performance wouldn't be a problem.

Anyway, thank you for pointing to this option, because I wasn't aware
that it exists and would have liked to use it from time to time.

Best regards,
Simon

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