diff --git a/.idea/misc.xml b/.idea/misc.xml
index 46ad6d9..7489572 100644
--- a/.idea/misc.xml
+++ b/.idea/misc.xml
@@ -1,4 +1,8 @@
+<<<<<<< Updated upstream
+=======
+
+>>>>>>> Stashed changes
\ No newline at end of file
diff --git a/.idea/python.iml b/.idea/python.iml
index ca820fc..64b45c5 100644
--- a/.idea/python.iml
+++ b/.idea/python.iml
@@ -5,7 +5,11 @@
+<<<<<<< Updated upstream
+=======
+
+>>>>>>> Stashed changes
\ No newline at end of file
diff --git a/.idea/rGraphicsSettings.xml b/.idea/rGraphicsSettings.xml
new file mode 100644
index 0000000..b5b9c2e
--- /dev/null
+++ b/.idea/rGraphicsSettings.xml
@@ -0,0 +1,9 @@
+
+
+
+
+
+
+
+
+
\ No newline at end of file
diff --git a/.idea/rSettings.xml b/.idea/rSettings.xml
new file mode 100644
index 0000000..ca29c32
--- /dev/null
+++ b/.idea/rSettings.xml
@@ -0,0 +1,6 @@
+
+
+
+
+
+
\ No newline at end of file
diff --git a/ha_03/loosen_janniclas_1540907_04.py b/ha_03/loosen_janniclas_1540907_04.py
index 9db67f6..a311ea7 100644
--- a/ha_03/loosen_janniclas_1540907_04.py
+++ b/ha_03/loosen_janniclas_1540907_04.py
@@ -1,3 +1,4 @@
+<<<<<<< Updated upstream
# Jan-Niclas Loosen
# 1540907
@@ -32,3 +33,169 @@ if num < 0 :
print("invalid input")
else:
print(prime_factorization(num))
+=======
+# Author: Jan-Niclas Loosen
+# Matrikelnummer: 1540907
+import math
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+# EXERCISE 1
+class Rational:
+ numerator = 0
+ divisor = 1
+
+ def __str__(self):
+ return "%d/%d" % (self.numerator, self.divisor)
+
+ def __init__(self, a=0, b=1):
+ if isinstance(a, Rational):
+ self.numerator = a.numerator
+ self.divisor = a.divisor
+ self.shorten()
+ elif isinstance(a, int) and isinstance(b, int):
+ if b == 0:
+ print("Divisor cannot be zero!")
+ exit(1)
+ if b < 0:
+ b = -b
+ a = -a
+ self.numerator = a
+ self.divisor = b
+ self.shorten()
+ else:
+ print("Numerator and divisor must be integer.")
+ exit(1)
+
+ def gcd(self, a, b):
+ while b != 0:
+ (a, b) = (b, a % b)
+ return a
+
+ def lcm(self, a, b):
+ return abs(a * b) // self.gcd(a, b)
+
+ def lcd(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+ return self.lcm(self.divisor, other.divisor)
+
+ def shorten(self):
+ d = self.gcd(self.numerator, self.divisor)
+ self.numerator = self.numerator // d
+ self.divisor = self.divisor // d
+
+ # addition
+ def __add__(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+
+ lcm = self.lcm(self.divisor, other.divisor)
+
+ fac1 = lcm // self.divisor
+ fac2 = lcm // other.divisor
+
+ new_divisor = lcm
+ new_nominator = self.numerator * fac1 + other.numerator * fac2
+ return Rational(new_nominator, new_divisor)
+
+ def __radd__(self, other):
+ return self.__add__(other)
+
+ # subtraction
+ def __sub__(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+ divisor_lcm = self.lcm(self.divisor, other.divisor)
+ new_nominator = (self.numerator * divisor_lcm / self.divisor) - (other.numerator * divisor_lcm / other.divisor)
+ return Rational(int(new_nominator), int(divisor_lcm))
+
+ def __rsub__(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+ divisor_lcm = self.lcm(self.divisor, other.divisor)
+ new_nominator = (other.numerator * divisor_lcm / other.divisor) - (self.numerator * divisor_lcm / self.divisor)
+ return Rational(int(new_nominator), int(divisor_lcm))
+
+ # multiplication
+ def __mul__(self, other):
+ if isinstance(other, Rational):
+ return Rational(self.numerator * other.numerator, self.divisor * other.divisor)
+ else:
+ return Rational(self.numerator * other, self.divisor)
+
+ def __rmul__(self, other):
+ return self.__mul__(other)
+
+ # division
+ def __truediv__(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+ new_numerator = self.numerator * other.divisor
+ new_divisor = self.divisor * other.numerator
+ return Rational(new_numerator, new_divisor)
+
+ def __rtruediv__(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+ new_numerator = self.divisor * other.numerator
+ new_divisor = self.numerator * other.divisor
+ return Rational(new_numerator, new_divisor)
+
+ def __lt__(self, other):
+ divisor_lcm = self.lcd(other)
+ return (self.numerator * divisor_lcm / self.divisor) < (other.numerator * divisor_lcm / other.divisor)
+
+ def __gt__(self, other):
+ divisor_lcm = self.lcd(other)
+ return (self.numerator * divisor_lcm / self.divisor) > (other.numerator * divisor_lcm / other.divisor)
+
+ def __le__(self, other):
+ divisor_lcm = self.lcd(other)
+ return (self.numerator * divisor_lcm / self.divisor) <= (other.numerator * divisor_lcm / other.divisor)
+
+ def __ge__(self, other):
+ divisor_lcm = self.lcd(other)
+ return (self.numerator * divisor_lcm / self.divisor) >= (other.numerator * divisor_lcm / other.divisor)
+
+ def __eq__(self, other):
+ if not isinstance(other, Rational):
+ other = Rational(other)
+ # all constructed Rationals are already shortened
+ return self.divisor == other.divisor and self.numerator == other.numerator
+
+ def __ne__(self, other):
+ return not self.__eq__(other)
+
+
+# EXERCISE 2
+def heron(a, x, run):
+ for i in range(run):
+ x = x - (x ** 2 - a) / (2 * x)
+ return x
+
+
+# Generate x values
+x_values = [x for x in range(10)]
+
+# Calculate the difference between heron and sqrt functions
+a = 2
+b = 1.9
+x0 = 1.5
+
+y_values_a = [abs(heron(a, x0, run) - np.sqrt(a)) for run in x_values]
+y_values_b = [abs(heron(b, x0, run) - np.sqrt(b)) for run in x_values]
+
+# Plot the difference
+plt.plot(x_values, y_values_a, label='a = 2, x0 = 1.5', color="blue")
+plt.plot(x_values, y_values_b, label='b = 0.5, x0 = 1.5', color="red")
+
+# Add labels and a legend
+plt.xlabel('Iterations')
+plt.ylabel('Difference')
+plt.legend()
+
+# Show the plot
+plt.show()
+>>>>>>> Stashed changes