On 5 September 2012 02:41, Cindy cindy425192...@gmail.com wrote:
Hi, David,
Yes, that's what I mean. Can I find it using sage?
Thanks.
Cindy
sage: K.z = NumberField(x^3 - x + 17)
sage: I = K.primes_above(17)[0]
sage: K.trace_dual_basis(I.basis())
[4/132583*z^2 + 6/7799*z + 2597/132583,
On 5 September 2012 02:56, Cindy cindy425192...@gmail.com wrote:
Hi,
Let K be a number field and O_k denote its ring of integers. For an ideal, J
of O_k, we can have an ideal lattice (I,b_\alpha), where
b_\alpha: J\times J \to Z, b_\alpha(x,y)=Tr(\alpha xy), \forall x,y \in J
and \alpha is
Hi, David,
Could you please explain a little bit about the code?
For the example you use, it seems I is an ideal above 17, what does [0]
mean?
In the end do we get a basis of the dual of I? Why do we need to put
I.basis() in the bracket of trace_dual_basis?
Thanks a lot.
Cindy
On
On 5 September 2012 09:34, Cindy cindy425192...@gmail.com wrote:
Hi, David,
Could you please explain a little bit about the code?
Sure, but you should make a little effort to play with it yourself for
a bit first.
For the example you use, it seems I is an ideal above 17, what does [0]
mean?
Why don't you ask them to install the sage server on a different machine,
and let other people acces it via the notebook? In Leiden they have also
taken this approach and it works fine (see sage.math.leidenuniv.nl).
Thanks Maarten
Le jeudi 30 août 2012 04:34:14 UTC+2, Luis Garcia-Puente a
Hi, David,
Thanks a lot. I tried trace_dual_basis? to find out the meaning. I didn't
realize I should use K.trace_dual_basis?
Thanks. :)
Cindy
On Wednesday, September 5, 2012 5:15:19 PM UTC+8, David Loeffler wrote:
On 5 September 2012 09:34, Cindy cindy42...@gmail.com javascript:
wrote:
Hi, David,
Thanks a lot! It works.^^
Cindy
On Wednesday, September 5, 2012 4:30:40 PM UTC+8, David Loeffler wrote:
On 5 September 2012 02:56, Cindy cindy42...@gmail.com javascript:
wrote:
Hi,
Let K be a number field and O_k denote its ring of integers. For an
ideal, J
of O_k,
Hi,
Let K be a number field and O_k denote its ring of integers. For an ideal,
J of O_k, we can have an ideal lattice (I,b_\alpha), where
b_\alpha: J\times J \to Z, b_\alpha(x,y)=Tr(\alpha xy), \forall x,y \in J
and \alpha is a totally positive element of K\{0}.
Suppose now I know J and
Hi, David,
BTW, do you know how to find the minimum norm of the lattice? I posted a
question regarding this in this group. Do you know which function I should
use?
Thanks.
Cindy
On Wednesday, September 5, 2012 4:30:40 PM UTC+8, David Loeffler wrote:
On 5 September 2012 02:56, Cindy
how can I get the minimum norm for the
ideal lattice (J,\alpha) using sage?
What have you tried so far?
David
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On 9/5/12 4:26 AM, Maarten Derickx wrote:
Why don't you ask them to install the sage server on a different
machine, and let other people acces it via the notebook? In Leiden they
have also taken this approach and it works fine (see
sage.math.leidenuniv.nl).
That's the approach we also take. A
Sorry I am a beginner
I have a function B(t)=(1-t)(t,t)+t*((3-t),t)
There is a way to expand this function in sage?
result expected:
B(t)=(t-t^2,t-t^2)+(t(3-t),t^2)
B(t)=(t-t^2+t(3-t),t-t^2+t^2)
B(t)=(4t-2t^2),t)
and after I should plot this 2d curve.
Thanks in advance.
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You received this
On 9/5/12 9:57 AM, alessio211734 wrote:
Sorry I am a beginner
I have a function B(t)=(1-t)(t,t)+t*((3-t),t)
There is a way to expand this function in sage?
result expected:
B(t)=(t-t^2,t-t^2)+(t(3-t),t^2)
B(t)=(t-t^2+t(3-t),t-t^2+t^2)
B(t)=(4t-2t^2),t)
and after I should plot this 2d curve.
Hi,
I'm trying to compute something using multivariate polynomials, and am
struggling to understand the relation between polynomials of type type
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'
and of type class
Hi,
On Wednesday 05 Sep 2012, Robert Samal wrote:
Hi,
I'm trying to compute something using multivariate polynomials, and am
struggling to understand the relation between polynomials of type type
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular
' and of type
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