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Feedback and general discussion on this video. How do you do this?Â .Q:

Finding the direction of the twist of a curve

Let $x^\prime=t_0 + t_1 X$ and $y^\prime=t_0 + t_1 Y$ be a basis for the tangent space to a given curve. Consider the parametrization of the curve which is the intersection of the curves $t_0 + t_1 X = y^\prime$ and $t_0 + t_1 Y = t_0^2 + t_1 t_0 + t_1^2 Y$.
I need to show that this parametrization (the image of the curve) is twisted once when going around the origin, once when going around the point $(t_0, t_0^2)$ and once around the point $(t_0, t_1t_0 + t_1^2Y)$ (please see the picture).
I got the idea of considering the curve as a function $f(t_0,t_1)$ and showing the first twist of the curve is $\left(x^\prime \frac{\partial f}{\partial t_1},y^\prime \frac{\partial f}{\partial t_1}\right)$ and the other two twists by taking the first derivative wrt $t_0$ and using the so called “extended sum property”. Is this a good idea? Should I just simply differentiate the original parametrization?
How can I show that?

A:

The tangent vectors are:
v_1 = \frac{\partial}{\partial t_1} = \left(\frac{\partial t_1}{\partial x}, \frac{\partial t_1}{\partial y} \right) = (t_0+t_1 X

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I have a csv file that contains millions of lines. I need to read each line of the file and do some operations and save the output (e.g., file1, file2) file. There is a small number of lines that will be changed (e.g., will be removed or added, etc). I am having trouble with the code below: the main process doesn’t wait for all of the child processes to finish. I am using multiprocessing to achieve the desired parallelisation, but the processing time takes forever. Below is my code.
import csv
import multiprocessing

class BatchFileWriter(object):
def __init__(self, file_name):
self.file_name = file_name
self.output_file = open(file_name, ‘w’)

def write(self, item):
# write the item to the output file
self.output_file.write(item)

def close(self):
self.output_file.close()

if __name__ == ‘__main__’:
if multiprocessing.cpu_count() > 1:
import csv
from multiprocessing.dummy import Pool
# here is my list with millions of lines
lines_list = sorted(open(file_path)) # sort the file by line numbers
lines_list = list(lines_list)