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today's exercise is to capture the animated gif. Beautiful example from codepen.io

In order to save animaged gif, we need program like Byzanz.

sudo add-apt-repository ppa:fossfreedom/byzanz
sudo apt-get update && sudo apt-get install byzanz
byzanz-record --duration=15 --x=200 --y=300 --width=700 --height=400 out.gif
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The source of all mathematics are integers.
This I understand, not only in your traditional sense that the concept of the continuum is albeitet from consideration of discrete quantities.
Rather, I think these words on results of recent date.
Mastering the exponential function of the number of segments from the acquisition of elliptic functions by means of modular equations can confidently believe that the deepest relationships in the Analysis of arithmetic in nature.
This confidence has already paying off.
http://blog.domini.io/
from sympy import symbols
from sympy.matrices import *
from sympy import collect
x,t = symbols('x a b c d')
V = Matrix([[2*x+a, 1, 0,0], [1, 2*x+b, 1,0], [0, 1, 2*x+c,1], [0,0,1,2*x+d]])
collect(V.det(),a)
"""a*(b*c*d + 2*b*c*x + 2*b*d*x + 4*b*x**2 - b + 2*c*d*x + 4*c*x**2 + 4*d*x**2 - d + 8*x**3 - 4*x) + 2*b*c*d*x + 4*b*c*x**2 + 4*b*d*x**2 + 8*b*x**3 - 2*b*x + 4*c*d*x**2 - c*d + 8*c*x**3 - 2*c*x + 8*d*x**3 - 4*d*x + 16*x**4 - 12*x**2 + 1"""
def S((a,b,c), k=1):
return (a, -2*a*k+b, a*k**2-b*k+c)
def T((a,b,c)):
return (c,b,a)
x = (1,33,-21)
x = (7, 33, -8)
x = (13,13,-22)
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
# http://stackoverflow.com/questions/11175131/code-for-greatest-common-divisor-in-python
def gcd(x, y):
while y != 0:
(x, y) = (y, x % y)
return x
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