#18036: I.parent() should not be the symbolic ring
---------------------------------+------------------------
Reporter: vdelecroix | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
---------------------------------+------------------------
Comment (by vdelecroix):
Replying to [comment:17 mmezzarobba]:
> > > A related question is whether `QQi is NumberField(x^2+1, 'I',
embedding=CC.0)` should be true, or if there should be two separate
parents.
> > >
> > > What do you think?
> >
> > More generally, do we want unique representation for (absolute) number
fields?
>
> I think everyone agrees that absolute number fields should have unique
representation. My question was whether Q[i] should ''be'' an absolute
number field in this sense, or if it should be a “special” object such
that people could work with both Q[i]-as-a-subset-of-complex-numbers and
Q[i]-as-a-number field, possibly at the same time. I'd prefer a single
object as well, but I am sure I have missed some of the implications, so
if anyone has arguments in favor of the other option, I would be
interested in hearing them.
I would be interested in working with '''any''' number field seeing them
as a subfield of the real or complex numbers! Not only `QQi` and it makes
sense to ask whether we need a dedicated class for that. For both parent
and elements.
Note that it is already partly possible to play with element of number
fields as real numbers (especially with quadratic fields)
{{{
sage: K.<sqrt2> = QuadraticField(2)
sage: 1 < sqrt2 < 3/2
True
sage: sqrt2.n()
1.41421356237310
sage: sqrt2 + CC(0,1)
1.41421356237310 + 1.00000000000000*I
sage: sage: cos(sqrt2)
cos(sqrt(2))
sage: sqrt2.continued_fraction()
[1; (2)*]
}}}
About having methods `.cos()`, `.sin()`, `.exp()`, it is already something
which I found dangerous with integers for which the method `.sqrt()` might
return an answer with a different parent
{{{
sage: 4.sqrt() # answer is a Sage integer
2
sage: 2.sqrt() # answer is symbolic
sqrt(2)
}}}
Which is very different from
{{{
sage: R.<x> = ZZ[]
sage: ((x+1)**2 * (x-2)**4).sqrt()
x^3 - 3*x^2 + 4
sage: R(2).sqrt()
Traceback (most recent call last):
...
TypeError: Polynomial is not a square. You must specify
the name of the square root when using the default extend = True
}}}
At the time Sage would support embedding of number fields into p-adic
fields, I think it might be worse to have that dedicated class! But in the
meantime, I have no strong opinion.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/18036#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
