Lee's profile - activity

Thank you very much, Max!

Thanks a lot for the anwser ! So there is no program or command in Sage or Pari to do that directly, right?

Thanks a lot for the anwser ! So this no program or command in Sage or Pari to do that, right?

Thanks a lot for the anwser !

For example, given a basis [1.4752770112052821796 - 0.6182637476411826238i, 1.6774834051116878106 - 2.20502299078472825

compute the equation for elliptic curves from lattices Given a lattice in $\mathbb{C}$, is there commands in Sage or Par

For example, given a basis [0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851i, 0.2

For example, given a basis $[0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851i, 0.

For example, given a basis [0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851i, 0.2

For example, given a basis [0.098399731571614359624741719123619532184 + 0.234797628763158122884319861656265970851I, 0.2

compute the equation for elliptic curves from lattices Given a lattice in $C$, is there commands in Sage or Pari to comp

compute the equation for elliptic curves from lattices Given a lattice in $C$, is there commands in Sage or Pari that co

compute the equation for elliptic curves from lattices Given a lattice in $C$, is there command in Sage or Pari that com

compute the equation for elliptic curves from lattices Given a lattice in $C$, is the command in Sage or Pari that compu

Thanks a lot ! I find that the .mfsymbol() can set precision in Sage. For example, I use pari.mfsymbol(S,L[0],256) can i

Thanks a lot ! But this seem not effect when I use Sage. Please see the example I give in the comment below.

For example, I run the following code in sage from cypari2 import Pari pari = Pari() print(R) K.<a>=CyclotomicFie

For example, I run the following code in sage from cypari2 import Pari pari = Pari() print(R) K.<a>=CyclotomicFie

For example, I run the following code in sage from cypari2 import Pari pari = Pari() print(R) K.=CyclotomicField(3) E=p

Thanks a lot! I tried this command pari.set_real_precision(), but when I use mfsymboleval, the precision does not chang

set precision for pari in Sage In the pari program, we can use \pb 256 to set the precision. For the pari in Sage, how t

Thank you very much, John.

everyone! Let $E:y^2+y=x^3-61$ be the minimal model of the elliptic curve 243b. How can I find the CM point $\tau$ in $X_0(243)$ such that $\tau$ maps to the point $(3\sqrt[3]{3},4)$ under the modular parametrization? Can anyone tell me the answer or how to use sagemath to find it?

I use the sagemath code

EllipticCurve([0,0,1,0,-61])
phi = EllipticCurve([0,0,1,0,-61]).modular_parametrization()
f=phi.power_series(prec = 10000)[1]
f.truncate(20000)

to get the parametrization of y coordinate, then I use

q=var('q')
f(q)=
df=diff(f,q)              
NewtonIt(q)=q-(f/df)(q)
xn=e^(2*pi*I*a/20.031)                      
for i in range(1000):
    xn=N(NewtonIt(xn),digits=2000)
print xn

to get the numerical $e^{2\pi i \tau}$. After taking log and dividing by $2 \pi i$, I get the numerical $\tau$. But if I use

z=
p=z.algebraic_dependency(100)

I get the wrong polynomial. Why?

Thank you very much! I modified the code into following

@parallel(ncpus=47)

def P(i,j):

if sqrt(i*i+i*j+j*j) in QQ:
    for k in [0,1,2]:
        L=Q(i,j)*W*Q(i,j)^(-1)*W^(-1)*B^k
        if Gamma(L):
            for l in [0,1,2]:
                M=Q(i,j)*B*Q(i,j)^(-1)*B^l
                if Gamma(M):
                    return i,j

I=[1..1000]

for i,j in itertools.product([1..100],I): P(i,j)

but seems no effect. What is the reason?

There is an server with 48 cpus in my office. I want to use all of them to compute the following codes in sage. How can I do that?

%time

import itertools

def is_matrix_integral(M):

    for i,j in itertools.product(range(2),range(2)):
        if M[i][j] not in ZZ:
            return False
    return True

def Gamma(M):

    if is_matrix_integral(M) and M[1][0]%243==0 and M.det()==1:
        return True
    return False


p=4

T=Matrix([[2,-1],[9,-4]])*Matrix([[4,0],[0,9]])

W=Matrix([[0,1],[-243,0]])

S=Matrix([[1,1/3],[0,1]])

A=Matrix([[1,0],[81,1]])

B=-1/(243)*W*A^(-1)*W*A

C=Matrix([[1,1/9],[-27,-2]])

e=Matrix([[1,0],[0,-1]])


def Q(a,c):

    return T*Matrix([[a,a+c],[c,-a]])*T^(-1)*e   

I=[-100000..-1]+[1..100000]

for i,j in itertools.product([1..100000],I):

    if sqrt(i*i+i*j+j*j) in QQ:
        for k in [0,1,2]:
            L=Q(i,j)*W*Q(i,j)^(-1)*W^(-1)*B^k
            if Gamma(L):
                print x,Q(i,j),Q(i,j).det(),i,j
                for l in [0,1,2]:
                    M=Q(i,j)*B*Q(i,j)^(-1)*B^l
                    if Gamma(M):
                        print x,x,M,M.det(),i,j,k,l
                        break