I've been calculating some sequence of rational functions associated with a
combinatorial problem. I'm doing the following:
sage: K. = PolynomialRing()
sage: R = FractionField(K)
I then do some calculations in for elements in R. When I get back the
answer (say in f), and I look at
f.numerat
The cartesian product of two polyhedra doesn't work if their dimensions are
different:
Consider the following (just run on sagenb.org):
sage: B1 = Polyhedron(vertice=[(0,),(1,)])
sage: B1
A 1-dimensional polyhedron in ZZ^1 defined as the convex hull of 2
vertices
sage: B2 = B1*B1
sage: B1
uld be to enlarge the set of j-invariants for
> which the group order was computed by formula, say to include the other
> class number 1 j-invariants. A project for someone!
>
> Victor, feel free to open a ticket with my first suggestion, which would
> be very easy to implement.
&
olve some Weil pairings, etc --
> then finding point orders after that will be faster.
>
> I think what this means is that as soon as you find the order of a point
> on a curve whose group order has not yet been computed and cached, that
> information should be cached.
>
> I
this means is that as soon as you find the order of a point
> on a curve whose group order has not yet been computed and cached, that
> information should be cached.
>
> I hope this makes some sense!
>
> John
>
>
> On 15 August 2013 02:24, Victor Miller >wrote:
>
>
Consider the following:
def NextProgression(n,a,q):
p = next_prime(n)
while (p%q) != a:
p = next_prime(p+1)
return p
def Test(n,compute=False):
p = NextProgression(n,2,3)
print "found prime=",p
F. = GF(p^2)
print "Found field"
E = EllipticCurve(F,[0,1])
i
In the latest version of sage (at least what cloud.sagemath.org is
running), there is a problem with substituting constants into the formal
integrals of formal functions. See the examples below.
Victor
sage: var('a'); function('f',a)
sage: g = f(a).integrate(a,0,a^2)
sage: g
integrate(f(a),0,a
it. But if you are able
> to download and apply the patch there then that's an alternative.
>
> John
>
>
> On 24 April 2013 13:39, Volker Braun >wrote:
>
>> I'm pretty sure I removed that in #3416
>>
>>
>> On Wednesday, April 24, 20
One more thing: it would be really nice (required?) if
Elliptic_curve_from_cubic would return the morphism that it found (and
perhaps an inverse).
Victor
On Wednesday, April 24, 2013 8:22:33 AM UTC-4, Victor Miller wrote:
>
> In Sage 5.8 on a mac. I have a functioning (and licensed) ma
Ah, I just found that I should specify the point as a list and not a tuple.
Now it works. However, the error is sure weird and indecipherable!
Victor
On Wednesday, April 24, 2013 8:22:33 AM UTC-4, Victor Miller wrote:
>
> In Sage 5.8 on a mac. I have a functioning (and licensed) magma
In Sage 5.8 on a mac. I have a functioning (and licensed) magma on my
computer, and apparently sage is trying to call it.
Victor
R. = QQ[]
F = x^3 + 2*x*(y^2 + y*z + z^2) + y*z*(y + z)
F(0,0,1)
> 0
E = EllipticCurve_from_cubic(F,(0,0,1))
Traceback (most recent call last):
File "", l
be overkill!
>
> John
>
> On 3 April 2013 09:09, Jeroen Demeyer >
> wrote:
> > On 2013-04-02 21:13, Victor Miller wrote:
> >> I have a bunch of ideals in number fields whose orders in the class
> >> group I want to calculate. If K is the nu
I've found that if l is a list of points with float coordinates, then
Polyhedron(vertices=l)
gives a long trace back error message (see below for example). At the very
least it should give something short like asking the user to specify a
base_ring argument. Even better, would be to infer a b
I have a bunch of ideals in number fields whose orders in the class group I
want to calculate. If K is the number field and a is the ideal, I had been
doing something like
H = K.class_group()
print H(a).order()
But if K is a big number field this seems wasteful (and takes a long time),
since
Aha, I found the nvals= option to magma commands. So for now I'll use
that. I would like to ask that LLL optionally return the transition matrix
(and also BKZ if that's possible).
Victor
On Tuesday, March 19, 2013 2:38:02 PM UTC-4, Victor Miller wrote:
>
> Suppose that A is a
ed
matrix. Is there a way of getting the entire tuple of returned values from
magma?
Victor
B,U,rk = magma.LLL(A)
I get a message from sage (it's pretty obscure) saying that it
On Tuesday, March 19, 2013 2:38:02 PM UTC-4, Victor Miller wrote:
>
> Suppose that A is an m by n integ
Suppose that A is an m by n integer matrix. Its Gram matrix is G = A*A^t.
If A is not full rank, then G has some eigenvalues of 0. If I do
G.LLL_gram() I get a somewhat uniformative error message like:
Value Error: ma matrix from Full MatrixSpace of 10 by 2 dense matrices over
Integer Ring c
There are times when I've added a bunch of cells to a notebook, and then I
realize that I'd like to make those cells into a separate notebook. Is
there a straightforward way of doing this? I know that I can cut and paste
individual cells, but that gets rather tedious.
Victor
--
You received
Since the OP's problem has no inequalities (such as requiring that all
integers in question are non-negative), it is solved by using Hermite
normal form.
If A is an m by n integer matrix, the Hermite normal form of A is an upper
triangular integer matrix H (also m by n), along with an m by m in
There's a real bug in Cython. It looks like it's some sort of parsing bug.
Consider the following program:
def Check(P,x):
Q = 2**(1+len(x))*P
R = P
for _ in range(1+len(x)):
R = 2*R
if Q != R:
print "Check: Got it!, Q=",Q," R=",R
else:
print "Ok"
def
Good news (so far) -- I tracked down the source of the bug. I had a long
calculation (the details of which are irrelevant) which produced a pair of
points on an elliptic curve, say P1 and P2, over a finite field of the form
GF(2^n). In order to check the calculation I needed to check
Q1 == 2**(
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