On 2017-01-05 13:17, Erick Knight wrote:
Thanks for both of your replies. Just to double check so that I don't
have any misunderstanding, PARI is correctly determining whether my
ideal is principal, and if it is, it is attempting to produce a
generator. It may fail at that, but, since I never a
On Thursday, January 5, 2017 at 11:27:05 AM UTC-8, John Cremona wrote:
>
> > I'm tempted to say: beware of memory leaks. Caching an extension on the
> base
> > field would probably imply that both fields are now participating in a
> > reference cycle, anchored in the global UniqueRepresentation
On 5 January 2017 at 18:15, Nils Bruin wrote:
> On Thursday, January 5, 2017 at 2:27:06 AM UTC-8, John Cremona wrote:
>>
>> I have a degree 5 polynomial whose Galois group is large (S_5):
>>
>> sage: x = polygen(QQ)
>> sage: f = x^5 - 6*x^3 - x^2 + 6*x - 1
>>
>> I can compute its splitting field e
On Thursday, January 5, 2017 at 2:27:06 AM UTC-8, John Cremona wrote:
>
> I have a degree 5 polynomial whose Galois group is large (S_5):
>
> sage: x = polygen(QQ)
> sage: f = x^5 - 6*x^3 - x^2 + 6*x - 1
>
> I can compute its splitting field easily, thanks to code written by
> Jeroen Demeyer I
Thanks for both of your replies. Just to double check so that I don't have
any misunderstanding, PARI is correctly determining whether my ideal is
principal, and if it is, it is attempting to produce a generator. It may
fail at that, but, since I never ask it for a generator, this produces no
to me this looks an unimplemented feature of SR; basically, you want SR to
be able to manipulate
algebraic numbers with a specified embedding in the same ring with
transcendental functions.
(perhaps Mathematica does support this, although I'm not 100% sure)
On Thursday, January 5, 2017 at 10:29
On 2017-01-05 11:29, Daniel Krenn wrote:
> On 2017-01-05 10:55, Daniel Krenn wrote:
>> as there is no *canonical* coercion as no embedding of the number field
>> is specified.
>>
>> How can I specify this embedding such that it is used e.g. for the
>> symbolic I?
>
> This looks weird: I is defined
On 2017-01-05 10:55, Daniel Krenn wrote:
> as there is no *canonical* coercion as no embedding of the number field
> is specified.
>
> How can I specify this embedding such that it is used e.g. for the
> symbolic I?
This looks weird: I is defined in sage.libs.pynac.pynac via
K = QuadraticFiel
I have a degree 5 polynomial whose Galois group is large (S_5):
sage: x = polygen(QQ)
sage: f = x^5 - 6*x^3 - x^2 + 6*x - 1
I can compute its splitting field easily, thanks to code written by
Jeroen Demeyer I believe:
sage: %time L = f.splitting_field(names='b')
CPU times: user 1min 1s, sys: 272
I want to take an number field element embedded in the symbolic ring
like the imaginary I and add it to an algebraic number:
sage: I.pyobject() + QQbar(sqrt(2))
This results in
TypeError: unsupported operand parent(s) for '+': 'Number Field in I
with defining polynomial x^2 + 1' and 'Algebrai
On 5 January 2017 at 09:27, Jeroen Demeyer wrote:
> Sorry, I was wrong. I actually looked at the PARI source code this time and
> the warning comes from the bnfisprincipal() function to determine the class
> of a given ideal in the class group (so, in particular, it can be used to
> check whether
Sorry, I was wrong. I actually looked at the PARI source code this time
and the warning comes from the bnfisprincipal() function to determine
the class of a given ideal in the class group (so, in particular, it can
be used to check whether an ideal is principal). This function can also
compute
Strange, did you use the commas instead of the dots on the squareroots?
I tried with the others suggestions and it worked out.
onsdag 4. januar 2017 17.24.03 UTC+1 skrev Dima Pasechnik følgende:
>
> This works for me after I defined cmsel as you did in your previous posts.
>
> On Wednesday, Janu
On 4 January 2017 at 20:31, Jeroen Demeyer wrote:
> I think it means that PARI didn't compute the unit group for certain number
> fields. Since you don't need the unit group, I see no issue.
>From what I know of the algorithm used -- and one should ask the pari
list to be certain -- it computed h
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