On 28 August 2024 16:05:43 BST, Georgi Guninski wrote:
>All of the following return the complex branch:
>pari/gp, mpmath, maxima
>
This is just them lacking functionality specifically for real fields, not
something to copy.
One can always coerse a real field element to an extension containin
This looks like RR should be fixed to match AA here.
On 28 August 2024 12:40:49 BST, Kwankyu Lee wrote:
>sage: ZZ(-1).nth_root(3)
>-1
>sage: _.parent()
>Integer Ring
>sage: QQ(-1).nth_root(3)
>-1
>sage: _.parent()
>Rational Field
>sage: RR(-1).nth_root(3)
>-1.00
>sage: _.parent()
>Rea
On 28 August 2024 12:28:54 BST, Kwankyu Lee wrote:
>
>
>On Wednesday, August 28, 2024 at 7:57:43 PM UTC+9 john.c...@gmail.com wrote:
>
>Surely the output of -1 for AA(-1)^(1/3) is correct: AA is the "Algebraic
>Real Field" and -1 has exactly one cube root in there, namely itself. On
>the ot
All of the following return the complex branch:
pari/gp, mpmath, maxima
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[forwarded from Dima]
This looks like RR should be fixed to match AA here.
On 28 August 2024 12:40:49 BST, Kwankyu Lee wrote:
sage: ZZ(-1).nth_root(3)
-1
sage: _.parent()
Integer Ring
sage: QQ(-1).nth_root(3)
-1
sage: _.parent()
Rational Field
sage: RR(-1).nth_root(3)
-1.00
sage: _.
[fowarded from Dima]
>
>x^(1/n) and x.nth_root(n) do not behave in the same way. All x.nth_root(n)
>gives an n-th root in the same field to which x belongs while all x^(1/n)
>gives the primitive n-th root of unity, with the exception of AA(-1)^(1/n).
the function 1/n : AA->AA is 1-1 on all AA, a
sage: ZZ(-1).nth_root(3)
-1
sage: _.parent()
Integer Ring
sage: QQ(-1).nth_root(3)
-1
sage: _.parent()
Rational Field
sage: RR(-1).nth_root(3)
-1.00
sage: _.parent()
Real Field with 53 bits of precision
sage: CC(-1).nth_root(3)
0.500 + 0.866025403784439*I
sage: _.parent()
Co
On Wednesday, August 28, 2024 at 7:57:43 PM UTC+9 john.c...@gmail.com wrote:
Surely the output of -1 for AA(-1)^(1/3) is correct: AA is the "Algebraic
Real Field" and -1 has exactly one cube root in there, namely itself. On
the other hand, QQbar(-1) has 3 cube roots and one is chosen (in som
It is puzzling, but it does not seem to be so.
If 1/3 would be a python float, (-1)**(1/3) is not defined under the usual
definition of x^y = exp(y*ln(x)) with the standard branch cut for the
logarithmic function.
If Python includes the negative axis in the domain of ln(x), and defines
ln(
Surely the output of -1 for AA(-1)^(1/3) is correct: AA is the "Algebraic
Real Field" and -1 has exactly one cube root in there, namely itself. On
the other hand, QQbar(-1) has 3 cube roots and one is chosen (in some
deterministic way).
I do not think that AA(-1)^(1/3) should return a cubroot
> >>> (-1)**(1/3)
> (0.5001+0.8660254037844386j)
Your example illustrates twice that an operation can lead to a bigger
set : 1/3 is a python float :-)
It is puzzling, but it does not seem to be so.
If 1/3 would be a python float, (-1)**(1/3) is not defined under the usual
defi
On Wed, 28 Aug 2024 at 03:46, Kwankyu Lee wrote:
>
>
> I think it is of doubtful correctness RR not being closed under coercion:
> sage: RR(RR(-1)^(1/3))
> TypeError: unable to convert '0.500+0.866025403784439*I'
> to a real number
>
>
> "closed under coercion" sounds vague to me. I do
I think it is of doubtful correctness RR not being closed under coercion:
sage: RR(RR(-1)^(1/3))
TypeError: unable to convert '0.500+0.866025403784439*I'
to a real number
"closed under coercion" sounds vague to me. I doubt if there is such a
concept in sage.
Fractional powers n
On Tue, Aug 27, 2024 at 3:37 PM Kwankyu Lee wrote:
>
> sage: RR(-1)^(1/3)
> 0.500 + 0.866025403784439*I
I think it is of doubtful correctness RR not being closed under coercion:
sage: RR(RR(-1)^(1/3))
TypeError: unable to convert '0.500+0.866025403784439*I'
to a real numbe
Hi,
I need advice from algebraic fields experts. Currently,
sage: RR(-1)^(1/3)
0.500 + 0.866025403784439*I
sage: CC(-1)^(1/3)
0.500 + 0.866025403784439*I
sage: QQbar(-1)^(1/3)
0.500? + 0.866025403784439?*I
sage: AA(-1)^(1/3) #
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