On 13/07/15 19:15, Simon King wrote:
Hi!
On 2015-07-13, Nathann Cohen <nathann.co...@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.
+1
It is consistent with
sage: words.FibonacciWord([0,1])
word: 0100101001001010010100100101001001010010...
sage: continued_fraction(pi)
[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ...]
sage: IntegerRange(0,+Infinity,2)
{0, 2, ...}
Vincent
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