On 8 May 2014 08:18, Nils Bruin wrote:
> On Wednesday, April 30, 2014 1:07:55 AM UTC-7, John Cremona wrote:
>
>> NO! If f1 and f2 define the same extension field then will
>> not be prime, e.g. f1=x^2-2 and f2=x^2-8 over QQ.
>>
>
> you probably mean f1=x^2-2 and f2=y^2-8 in QQ[x,y] . =<1> is
>
On Wednesday, April 30, 2014 1:07:55 AM UTC-7, John Cremona wrote:
> NO! If f1 and f2 define the same extension field then will
> not be prime, e.g. f1=x^2-2 and f2=x^2-8 over QQ.
>
you probably mean f1=x^2-2 and f2=y^2-8 in QQ[x,y] . =<1> is
also not prime but that doesn't have much to do
On 30 April 2014 10:09, François Colas wrote:
> What I am trying to do is to use the prime factorisation of m to compute in
> another field than Q(zeta_m) (i.e. Q(zeta_m1, zeta_m2, ..., zeta_ml)) or
> Q[x]/ (i.e. Q[x1, ..., xl] / ) because I need m
> between 1000 and 1 and actually sage is not
What I am trying to do is to use the prime factorisation of m to compute in
another field than Q(zeta_m) (i.e. Q(zeta_m1, zeta_m2, ..., zeta_ml)) or
Q[x]/ (i.e. Q[x1, ..., xl] / ) because I need m
between 1000 and 1 and actually sage is not able to do this. The idea
is to have a faster arit
On 29 April 2014 19:23, Martin Albrecht wrote:
> On Monday 28 Apr 2014 14:57:59 François Colas wrote:
>> Hi Martin,
>>
>> Here is two examples using multivariate quotients and extension fields
>> which should be faster than computing CyclotomicField(m) or
>> NumberField(cyclotomic(m), 'r') :
>>
>>
On Monday 28 Apr 2014 14:57:59 François Colas wrote:
> Hi Martin,
>
> Here is two examples using multivariate quotients and extension fields
> which should be faster than computing CyclotomicField(m) or
> NumberField(cyclotomic(m), 'r') :
>
> m = 3*5*7
> pi = prime_factors(m)
> Qi = PolynomialRin
Hi Martin,
Here is two examples using multivariate quotients and extension fields
which should be faster than computing CyclotomicField(m) or
NumberField(cyclotomic(m), 'r') :
m = 3*5*7
pi = prime_factors(m)
Qi = PolynomialRing(QQ, len(pi), 'q')
Idl = [cyclotomic_polynomial(p, 'q'+str(i)) for (
I just tried to run:
sage: m = random_prime(10^5)
sage: K. = CyclotomicField(m)
and I ran out of RAM! Doing a smaller example:
sage: m = random_prime(10^4)
sage: %prun K. = CyclotomicField(m)
puts
sage.rings.number_field.number_field_morphisms.create_embedding_from_approx
as the most expensi
Hi Vincent,
In fact that's exactly what I want to do!
But I am using morphisms:
m = ZZ(int(random()*10^5+1))
R. = NumberField(cyclotomic_polynomial(m))
Idl = []
for (p, e) in factor(m):
Idl.append(cyclotomic_polynomial(p))
K = NumberField(Idl, 'k')
F = Hom(R, K)
f = F([...])
Unfortuna
I wa going to write: "Is there any reason not to do
sage: m=random_prime(10^5)
sage: K. = CyclotomicField(m)
sage: R = K.ring_of_integers()
"
but I tried it and the last line is (much too) slow, which probably
means that a generic algorithm is being used even though one knows
that R = Z[r].
John
Hi François,
Might be related to the ticket #16116 on trac
(http://trac.sagemath.org/ticket/16116). Note that for performance, it
is possible to use multivariate polynomials as described in the
ticket.
Best
Vincent
2014-04-15 18:30 UTC+02:00, François Colas :
> Hello group,
>
> I am playing with
Hello group,
I am playing with quotient ring of Z over cyclotomic polynomial but it is
strangely slow:
sage: m = random_prime(10^4); m
2437
sage: %time R. = ZZ['z'].quotient(cyclotomic_polynomial(m))
CPU times: user 2.50 s, sys: 0.00 s, total: 2.50 s
Wall time: 2.50 s
cyclotomic_polynomial(m) i
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