Sha's profile - activity

Hi I have the following:

E=EllipticCurve(Qp,[0,0,0,-3267,45630])
P=E([-21,324])

Is there some coding I can use to get the 4-torsion point of this elliptic curve. I reckon it might have something to do with the nth divisional polynomial but I couldn't find it.

@johnpalmieri thank you for the feedback John. I really appreciate it.

@dsejas Hi diego. thank you for your reply. I am actually trying to figure out the formula too.. just to check if there's anything wrong with it. I don't have a deadline with this. Thank you for your help. Let me too re check the calculation manually.

Hi. I am quite new to using phyton is SAGE, but what I did here is that I have tried my best to come up with the code based on reading multiple notes on SAGE.

The values of alpha, n, eta, lambda, h, T, t, kappa, k(x-s) and gamma values are given.

I have tried to do the coding from scratch and this is what I have obtained:

from __future__ import print_function
alpha = 1.2
n = 2
eta = 1.3
lamda = 1
h = 1
T = 1
t = 0.1

h, t, x, s = var('h t x s')
U[t] = 1/3*t^3+1
P[t] = 2*t-lamda*(-t^4/24+t^5/15-t^7/126+t^8/72)
b[k] = 1

def X(m):
    if m <= 1:
        return 0
    else:
        return 1

k[x,s]=s-x
gamma[z]=integrate(x^(z-1)*e^(-x),x, 0, infinity)
u[0]=1

for m in range(1,4):
    u[m] = sum(b[k]/factorial(k)*t^k,k,0,n-1) + X[m]*u[m-1]-X[m]*sum(𝚍𝚎𝚛𝚒𝚟𝚊𝚝𝚒𝚟𝚎(u[m-1][0],t,k)/factorial(k)*t^k,k,0,n-1)+h/gamma[eta-alpha]*integrate((t-tau)^(eta-alpha-1)*u[m-1].subs(t=tau)*P[t].subs(t=tau),tau, 0, t); print(u[m].full_simplify())

UU=u[1]+u[2]+u[3]+u[4]:

What I am trying to achieve here is the values of u_1, u_2, u_3, u_4. Then calculate UU = u_1 + u_2 + u_3 + u_4.

At the moment, I am not getting the answer. Not sure what is causing the error. It took me so much time and effort to come up with this from scratch, hope someone can help me indicate what's wrong with this coding. Thank you in advance.

oh sorry... it was giving an error code every time I ran the code.

the answers I am planning to obtain is the list of numbers for x, y, z that satisfies the equation x^4+y^4=z^3.

thank you! this is great!

Hi. I have the following code that I want to integrate and differentiate, but I am stuck at the expression of M, where it is unable to integrate. Is my coding wrong?

c,t = var('c t')
Pi = RR.pi()
G=integrate(sqrt(1-t^2)*(t+c),t,-0.9,0.9);G
H=G.diff(c);H
L=integrate(-(t+c)/(sqrt(1-t^2)),t,-0.9,0.9);L
M=integrate(1/(sqrt(1-t^2)*(t-c)),t,-0.9,0.9);M #cannot seem to integrate this wrt to t
I=(c^2-1)*(L+(1-c^2)*M);I #equation I that involves M
P=I.diff(c);P #differentiate I wrt to c to obtain equation P

I have tried integrating M by hand which gives me a closed-form involving log function, but I can't seem to integrate it here using Sage.

Hi, I have the equation x^4+y^4=z^3. I want to run each variable from -100 till 100 to see which numbers satisfy this equation. Here is what I have done:

x,y,z= var('x y z')
for x in range(-100, 100):
     for y in range(-100, 100):
           for z in range(-100, 100):
x^4+y^4==z^3
print(x,y,z)

There is definitely something wrong with the coding that's not giving me the desired answer. Can someone enlighten me, please.