On Mon, Jul 13, 2015 at 10:15 AM, Simon King <
simon...@uni-jena.de> wrote:
> Hi!
>
> On 2015-07-13, Nathann Cohen <
nathan...@gmail.com> wrote:
>> sage: sqrt(2) # a symbolic ring element
>> sqrt(2)
>> sage: QQbar(sqrt(2)) # an algebraic value
>> 1.414213562373095?
>>
>> It is true that this final '?' sounds more like a '...', as if some additional
>> digits were hidden in a value stored as a float/double. Yet it is exact.
>>
>> How could we replace it? Ideally, that would be a 'sqrt(2)' but can we always
>> provide such a representation cheaply? Could we display it as 'sqrt(2)' at least
>> when it is free to do so?
>
> The elements of QQbar are the solutions of algebraic equations. As you
> probably know, the solutions of algebraic equations of degree > 4 can, in
> general, not be expressed that nicely. But it seems like an appealing
> idea to show a nice expression for algebraic numbers of degree up to 4.
>
>> If we cannot get rid totally of this numerical representation, what would you
>> think of replacing this '?' by a 'alg', which would be (slightly) more
>> informative, e.g.:
>
> 1.4142134... looks exact to me: "..." seems to suggest that Sage knows all
> (potentially infinitely many) digits but can't show them all, whereas "?" seems
> to suggest that the last shown digit is questionable (i.e., subject to rounding
> errors), i.e., "?" seems to suggest that Sage doesn't know the exact value.
Yes. Also, with interval arithmetic, that is precisely what it means:
sage: RealIntervalField(53)(sqrt(2))
1.414213562373095?
sage: QQbar(sqrt(2))
1.414213562373095?
It's certainly not good that the above two print in the same way.
The (mysterious [1]) person who made those design choices -- Carl
Witty -- isn't contributing anymore, or I'd ask his opinion.
[1]
http://stackoverflow.com/users/684532/carl-witty
>
> So, I'd prefer to display elements of QQbar as floating point numbers
> (what default precision?), always rounded DOWN to the last digit that is
> displayed, and followed by "..." (not "?") unless the displayed value is
> exact. So, what is displayed is an initial part of the potentially
> infinite sequence of digits.
>
> Best regards,
> Simon
>
>
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--
William (
http://wstein.org)