ninho's profile - activity

I have written a Sage code that performs some calculations with elliptic curves, and I want to get how much time it took to finish the calculations. I saw that there is already a function called timeit, but what I see is that it basically times the given command. Instead what I need is that I want to time the execution of certain code block (for example, a loop). Assuming, I have a code segment as this:

for i in range(0, 100):
     # Do some calculations...

How can I get how much time it took to execute the code block (in this case the whole loop)?

I want to create a quadratic extension of a finite field via x^2 + 1, and for that purpose I have the following Sage code:

proof.arithmetic(False)

# Parameters
f = 1
lA = 2
lB = 3
eA = 372
eB = 239

# Define the prime p
p = f*lA**eA*lB**eB-1
assert p.is_prime()

# Prime field of order p
Fp = GF(p)
# The quadratic extension via x^2 + 1 since p = 3 mod 4 
Fp2.<i> = Fp.extension(x^2+1)

Though, the above code throws a rather cryptic error UnboundLocalError: local variable 'E' referenced before assignment. Any ideas how to solve the problem and create a quadratic extension field.

I have a PARI/GP script which I want to load and run locally on my laptop inside a Sage notebook. I tried to open a new notebook in the same directory where my script is located, and run this:

%default_mode gp

But, it throws the following error:

UsageError: Line magic function '%default_mode` not found.

Please note that I'm using Sage 8.3. How can I run a PARI/GP script locally?

@j.c. Yes, expected and simulated correspond to the values in the y-axis, and there are some integer values that are input to the simulation and theoretical calculations that is used to populate the x-axis. What I mean the values double is that you can see in the examples, the values for both expected and simulated are quite close to each other, but every value keeps doubling, so it was 48, then 96, then 191, then 383, then 767, and so on. And the values on the x-axis also increase exponentially, so you can guess that all these smaller values correspond to smaller values of x, as the values of x increase exponentially, so on the right size we will have a point or to on the top right corner, and all the other points on the lower left corner.

I'm performing some simulations, and at the end I have a CSV file with three columns. One column holds the values for the x-axis, which was also input to the simulation and theoretical calculations, second one holds theoretically expected values, and the other column holds the values obtained by the simulation. I was planning to plot something like this:

But that does not look good in my case, as the values in y-axis normally double, and the values for the x-axis exponentially increase, so most of the points end up getting collected at the lower left part, near the intersection of x-axis and y-axis of the plot. Therefore, I need a different way to plot such data, which will be more visually appealing and inform how close the simulation results are to the theoretical expected ones. For example, some of my values can be seen below:

x         = [2, 4, 8, 16, 32, 64] # partially removed for brevity
expected  = [47.9995, 95.9783, 191.9127, 383.9708, 767.8831] # partially removed for brevity 
simulated = [48, 96, 191.8, 383.8, 767.4] # partially removed for brevity

What is a good way to plot such a data that doubles in the y-axis and exponentially increases on the x-axis all the time, and to view how similar the two datasets actually are?

So, I have three lists in Sage, and I want to combine two list plots, where in one of them I have the expected values, and in the other one I have the simulation results, and the third one is the x-axis values that corresponds to these points. So my lists (all same size), look like this:

# all lists removed partially for brevity
expected  = [47.4246, 47.9955, 95.9383]
simulated = [47.2, 48, 96]
primes    = [23327, 3009311, 886463]

# plotting
p = list_plot(expected, color='blue', marker='o') + list_plot(simulated, color='red', marker='x')
p.save('plot.svg')

Now, this creates a plot, and the y-axis corresponds to the values in expected and simulated lists, but I do not know how to incorporate the values in primes to the x-axis. So that I have 47.4246 for expected and 47.2 for simulated in the y-axis when I have 23327 in x-axis, and so on. Any ideas how to do this in Sage?