tp_14.py

from math import *

import scipy.integrate as integrate

import numpy as np
import matplotlib.pyplot as plt

## exercice 1
def getPrimes(limit):
    L = []
    a = [True] * limit
    a[0] = a[1] = False
    count = 0
    for (i, isPrime) in enumerate(a):
        if isPrime:
            L.append(i)
            for n in range(i*i, limit, i):
                a[n] = False
    return L

def plotPrimes(n):
    primes = getPrimes(n+1)[2:]
    x = []
    y = []
    # add additionals points
    count = 0
    for i in primes:
        # ajout de deux points
        x += [i]*2
        y.append(count)
        count += 1
        y.append(count)
    plt.plot(x, y, 'b')

# a is const, b is x
def customInt(f, a, b, w = 0.0001):
    L = np.arange(a, b, w)
    area = 0
    for i in L:
        area += w*f(i)
    return area

def drawAccu(n):
    plotPrimes(n)

    w = 0.01
    x = np.arange(2, n, w)

    g = lambda x: x/log(x)
    plt.plot(x, np.vectorize(g)(x), 'r--')
    
    #Li = lambda x: (integrate(lambda t: 1/log(t), 2, x))
    #Li = lambda x: integrate.quad(lambda t: 1/log(t), 2, x)[0]
    f = lambda t: 1/log(t)
    Li = [0]
    for i in x:
        Li.append(Li[-1] + w*f(i))
    Li = Li[1:]

    plt.plot(x, Li, 'g--')
    plt.legend(['pi(n)', 'x \mapsto x/log(x)', 'integral'])

#drawAccu(10000)

## Exercice 2

def plotSquarePrime(n = 100):
    primes = getPrimes((n*n)+1)[2:]
    for i in range(n+1):
        for j in range(n+1):
            if (i*n+j) in primes:
                # dessin du carré
                x = [j, j+1, j+1, j, j]
                y = [i, i, i+1, i+1, i]
                plt.fill(y, x, 'black')
    plt.xlim(0, n)
    plt.ylim(0, n)

# plotSquarePrime()

## Bonus, Yin Yung

# size of the whole figure 2 unit of diameter
# (0, 0) is the center of the design
# (0, 0.5) is the center of the black circle
# (0, -0.5) is the center of the white circle

def drawBonus():
    # first draw the big circle
    t = np.arange(0, 2*pi, 0.01)
    x = list(np.cos(t))
    y = list(np.sin(t))
    plt.plot(x, y, 'k', lw=0.5)
    
    getRange = lambda a, b, s=1: np.arange(a, b, s*0.01)
    
    # draw the upper circle
    t = getRange(pi/2, 3*pi/2)
    x = [cos(k)*0.5 for k in t]
    y = [sin(k)*0.5+0.5 for k in t]
    
    # draw the lower circle
    t = getRange(pi/2, -pi/2, -1)
    x += [cos(k)*0.5 for k in t]
    y += [sin(k)*0.5-0.5 for k in t]
    
    # draw the return to the first points
    t = getRange(-pi/2, pi/2)
    x += list(np.cos(t))
    y += list(np.sin(t))
    
    plt.fill(x, y, 'k')
    
    innerWidth = 0.15
    # draw the inner smaller lower circle
    t = getRange(0, 2*pi)
    x = [cos(k)*innerWidth for k in t]
    y = [sin(k)*innerWidth-0.5 for k in t]
    plt.fill(x, y, 'k')
    
    t = getRange(0, 2*pi)
    x = [cos(k)*innerWidth for k in t]
    y = [sin(k)*innerWidth+0.5 for k in t]
    plt.fill(x, y, 'w')
    
    plt.axis('scaled')

drawBonus()

plt.show()