Vektorübungen, Serie 1 Übungen 26 und 27

vektoren/serie_1_26.py

@@ -0,0 +1,17 @@
+# %%
+# Determinante mit Python berechnen
+import numpy as np
+
+a = [1, 1, 1, 0]  # a Vektor
+b = [1, 0, -1, 1]  # b Vektor
+c = [2, 1, 1, 0]  # c Vektor
+d = [0, 0, -1, 1]  # d Vektor
+e = [-3, -2, -3, -1]  # e Vektor
+
+abcd = [a, b, c, d]
+abde = [a, b, d, e]
+abce = [a, b, c, e]
+
+print(f"Determinante abcd: {np.linalg.det(abcd)}")  # Determinante abcd
+print(f"Determinante abde: {np.linalg.det(abde)}")  # Determinante abde
+print(f"Determinante abce: {np.linalg.det(abce)}")  # Determinante abce

vektoren/serie_1_27.py

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+# %%
+# Ausdrücke berechnen
+import numpy as np
+
+
+# Vector Klasse um fehler abzufangen wie Vektor + Skalar. Numpy führt das aus, ist aber mathematisch nicht definiert.
+class Vector:
+    def __init__(self, values):
+        self._values = np.asarray(values)
+
+    def __add__(self, other):
+        if not isinstance(other, Vector):
+            raise TypeError("Can only add vectors")
+        if self._values.shape != other._values.shape:
+            raise ValueError("Vectors must have the same dimension")
+        return Vector(self._values + other._values)
+
+    def __sub__(self, other):
+        if not isinstance(other, Vector):
+            raise TypeError("Can only subtract vectors")
+        return Vector(self._values - other._values)
+
+    def __mul__(self, other):
+        if isinstance(other, Vector):
+            # Vector * Vector = dot product
+            return np.dot(self._values, other._values)
+
+        if np.isscalar(other):
+            # Vector * scalar = scaled vector
+            return Vector(self._values * other)
+
+        return NotImplemented
+
+    def __rmul__(self, scalar):
+        return self * scalar
+
+    def cross(self, other):
+        if not isinstance(other, Vector):
+            raise TypeError("Cross product requires two vectors")
+        return Vector(np.cross(self._values, other._values))
+
+    def __abs__(self):
+        return np.linalg.norm(self._values)
+
+    def __repr__(self):
+        return f"Vector({self._values})"
+
+
+a = Vector([3.8, 2.12, -4.01])
+b = Vector([0.01, -0.02, 2.341])
+c = Vector([-5.1, 1.0, 4.5])
+d = Vector([1.0, 0.32])
+
+
+operations = [
+    lambda: 4 * a + 2.1 * (b * c),
+    lambda: -8.35 * (a.cross(c) * b - abs(d) ** 2),
+    lambda: (3.1 * d).cross(a) - (a * 2 * c) * b,
+    lambda: a * (1 / abs(d)) - (2 * b - 9.33 * c),
+]
+
+for operation in operations:
+    try:
+        print(operation())
+    except Exception as e:
+        print(f"Error: {e}")