164 lines
5.0 KiB
Python
164 lines
5.0 KiB
Python
# Author: Jan-Niclas Loosen
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# Matrikelnummer: 1540907
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import numpy as np
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import matplotlib.pyplot as plt
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# EXERCISE 1
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class Rational:
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numerator = 0
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divisor = 1
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def __str__(self):
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return "%d/%d" % (self.numerator, self.divisor)
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def __init__(self, a=0, b=1):
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if isinstance(a, Rational):
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self.numerator = a.numerator
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self.divisor = a.divisor
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self.shorten()
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elif isinstance(a, int) and isinstance(b, int):
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if b == 0:
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print("Divisor cannot be zero!")
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exit(1)
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if b < 0:
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b = -b
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a = -a
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self.numerator = a
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self.divisor = b
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self.shorten()
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else:
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print("Numerator and divisor must be integer.")
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exit(1)
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def gcd(self, a, b):
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while b != 0:
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(a, b) = (b, a % b)
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return a
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def lcm(self, a, b):
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return abs(a * b) // self.gcd(a, b)
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def lcd(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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return self.lcm(self.divisor, other.divisor)
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def shorten(self):
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d = self.gcd(self.numerator, self.divisor)
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self.numerator = self.numerator // d
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self.divisor = self.divisor // d
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# addition
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def __add__(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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lcm = self.lcm(self.divisor, other.divisor)
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fac1 = lcm // self.divisor
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fac2 = lcm // other.divisor
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new_divisor = lcm
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new_nominator = self.numerator * fac1 + other.numerator * fac2
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return Rational(new_nominator, new_divisor)
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def __radd__(self, other):
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return self.__add__(other)
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# subtraction
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def __sub__(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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divisor_lcm = self.lcm(self.divisor, other.divisor)
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new_nominator = (self.numerator * divisor_lcm / self.divisor) - (other.numerator * divisor_lcm / other.divisor)
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return Rational(int(new_nominator), int(divisor_lcm))
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def __rsub__(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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divisor_lcm = self.lcm(self.divisor, other.divisor)
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new_nominator = (other.numerator * divisor_lcm / other.divisor) - (self.numerator * divisor_lcm / self.divisor)
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return Rational(int(new_nominator), int(divisor_lcm))
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# multiplication
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def __mul__(self, other):
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if isinstance(other, Rational):
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return Rational(self.numerator * other.numerator, self.divisor * other.divisor)
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else:
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return Rational(self.numerator * other, self.divisor)
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def __rmul__(self, other):
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return self.__mul__(other)
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# division
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def __truediv__(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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new_numerator = self.numerator * other.divisor
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new_divisor = self.divisor * other.numerator
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return Rational(new_numerator, new_divisor)
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def __rtruediv__(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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new_numerator = self.divisor * other.numerator
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new_divisor = self.numerator * other.divisor
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return Rational(new_numerator, new_divisor)
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def __lt__(self, other):
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divisor_lcm = self.lcd(other)
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return (self.numerator * divisor_lcm / self.divisor) < (other.numerator * divisor_lcm / other.divisor)
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def __gt__(self, other):
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divisor_lcm = self.lcd(other)
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return (self.numerator * divisor_lcm / self.divisor) > (other.numerator * divisor_lcm / other.divisor)
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def __le__(self, other):
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divisor_lcm = self.lcd(other)
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return (self.numerator * divisor_lcm / self.divisor) <= (other.numerator * divisor_lcm / other.divisor)
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def __ge__(self, other):
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divisor_lcm = self.lcd(other)
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return (self.numerator * divisor_lcm / self.divisor) >= (other.numerator * divisor_lcm / other.divisor)
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def __eq__(self, other):
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if not isinstance(other, Rational):
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other = Rational(other)
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# all constructed Rationals are already shortened
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return self.divisor == other.divisor and self.numerator == other.numerator
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def __ne__(self, other):
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return not self.__eq__(other)
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# EXERCISE 2
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def heron(a, x, run):
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for i in range(run):
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x = x - (x ** 2 - a) / (2 * x)
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return x
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# Generate x values
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x_values = [x for x in range(10)]
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# Calculate the difference between heron and sqrt functions
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a = 2
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b = 1.9
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x0 = 1.5
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y_values_a = [abs(heron(a, x0, run) - np.sqrt(a)) for run in x_values]
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y_values_b = [abs(heron(b, x0, run) - np.sqrt(b)) for run in x_values]
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# Plot the difference
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plt.plot(x_values, y_values_a, label='a = 2, x0 = 1.5', color="blue")
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plt.plot(x_values, y_values_b, label='b = 0.5, x0 = 1.5', color="red")
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# Add labels and a legend
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plt.xlabel('Iterations')
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plt.ylabel('Difference')
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plt.legend()
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# Show the plot
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plt.show()
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