26/11/2023

.idea/misc.xml

@@ -1,4 +1,8 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
+<<<<<<< Updated upstream
   <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.10.6 WSL (Ubuntu): (/home/janniclas/.virtualenvs/Informationssysteme/bin/python)" project-jdk-type="Python SDK" />
+=======
+  <component name="ProjectRootManager" version="2" project-jdk-name="C:\ProgramData\anaconda3 (2)" project-jdk-type="Python SDK" />
+>>>>>>> Stashed changes
 </project>

.idea/python.iml

@@ -5,7 +5,11 @@
       <excludeFolder url="file://$MODULE_DIR$/Virtualenv" />
       <excludeFolder url="file://$MODULE_DIR$/venv" />
     </content>
+<<<<<<< Updated upstream
     <orderEntry type="jdk" jdkName="Python 3.10.6 WSL (Ubuntu): (/home/janniclas/.virtualenvs/Informationssysteme/bin/python)" jdkType="Python SDK" />
+=======
+    <orderEntry type="jdk" jdkName="C:\ProgramData\anaconda3 (2)" jdkType="Python SDK" />
+>>>>>>> Stashed changes
     <orderEntry type="sourceFolder" forTests="false" />
   </component>
 </module>

.idea/rGraphicsSettings.xml

@@ -0,0 +1,9 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="RGraphicsSettings">
+    <option name="height" value="576" />
+    <option name="resolution" value="75" />
+    <option name="version" value="2" />
+    <option name="width" value="2048" />
+  </component>
+</project>

.idea/rSettings.xml

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="RSettings">
+    <option name="interpreterPath" value="C:\Program Files\R\R-4.3.2\bin\R.exe" />
+  </component>
+</project>

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