commit b2257bac8939ee91197d0907f52781f865fff8f4
Author: Ngoc Chung Anh Tran <tranng89494@th-nuernberg.de>
Date:   Tue Oct 13 16:25:37 2026 +0200

    Erster Stand: compute.py

diff --git a/.gitignore b/.gitignore
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+++ b/.gitignore
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+.venv/
+__pycache__/
+.env
diff --git a/AGENTS.md b/AGENTS.md
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+++ b/AGENTS.md
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+# Regeln für dieses Projekt
+
+- Code nach PEP 8, Zeilenlänge maximal 88 Zeichen.
+- Jede Funktion und Methode hat einen Docstring und Type Hints.
+- Vor jedem Commit: `ruff check` und `ruff format`.
diff --git a/compute.py b/compute.py
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+++ b/compute.py
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+import math
+
+
+def matmul(
+    matrix_a: list[list[float]], matrix_b: list[list[float]]
+) -> list[list[float]]:
+
+    # Basic dimensionality checks
+    if not matrix_a:
+        raise ValueError("matrix_a cannot be empty")
+    if not matrix_b:
+        raise ValueError("matrix_b cannot be empty")
+
+    rows_a = len(matrix_a)
+    cols_a = len(matrix_a[0])
+    rows_b = len(matrix_b)
+    cols_b = len(matrix_b[0])
+
+    if cols_a != rows_b:
+        raise ValueError(
+            f"Cannot multiply: matrix_a has {cols_a} columns "
+            f"but matrix_b has {rows_b} rows."
+        )
+
+    # Ensure all rows are rectangular
+    for r in matrix_a:
+        if len(r) != cols_a:
+            raise ValueError("matrix_a is not rectangular")
+    for r in matrix_b:
+        if len(r) != cols_b:
+            raise ValueError("matrix_b is not rectangular")
+
+    # Perform multiplication
+    result: list[list[float]] = [[0.0 for _ in range(cols_b)] for _ in range(rows_a)]
+
+    for i in range(rows_a):
+        for j in range(cols_b):
+            total = 0.0
+            for k in range(cols_a):
+                total += matrix_a[i][k] * matrix_b[k][j]
+            result[i][j] = total
+
+    return result
+
+
+def transpose(matrix: list[list[float]]) -> list[list[float]]:
+    """
+    Transpose a 2D matrix.
+
+    Parameters
+    ----------
+    matrix : list[list[float]]
+        A 2D matrix represented as a list of rows, each containing
+        floating‑point numbers.
+
+    Returns
+    -------
+    list[list[float]]
+        The transposed matrix, where rows become columns.
+
+    Raises
+    ------
+    ValueError
+        If the input matrix is empty or has non‑rectangular rows.
+    """
+    # Check for empty matrix
+    if not matrix:
+        raise ValueError("matrix cannot be empty")
+
+    rows = len(matrix)
+    cols = len(matrix[0])
+
+    # Verify rectangular shape
+    for r in matrix:
+        if len(r) != cols:
+            raise ValueError("matrix is not rectangular")
+
+    # Transpose by column index
+    return [[matrix[r][c] for r in range(rows)] for c in range(cols)]
+
+
+def rot_2D(theta: float) -> list[list[float]]:
+    """
+    Return a 2D rotation matrix for angle ``theta`` in radians.
+
+    Parameters
+    ----------
+    theta : float
+        Rotation angle in radians.
+
+    Returns
+    -------
+    list[list[float]]
+        2 × 2 rotation matrix
+            ``[[cos(theta), -sin(theta)],
+               [sin(theta),  cos(theta)]]``
+
+    Notes
+    -----
+    Uses :func:`math.sin` and :func:`math.cos` from the standard library.
+    """
+    c = math.cos(theta)
+    s = math.sin(theta)
+    return [[c, -s], [s, c]]
+
+
+if __name__ == "__main__":
+    # Test Matmul
+    matrix_a = [
+        [3, 4, -1, 4],
+        [-2, 2, 5, 1],
+    ]
+    matrix_b = [
+        [1, 3, -2],
+        [2, 5, 1],
+        [-1, 4, -4],
+        [2, 3, 6],
+    ]
+    matrix_c = matmul(matrix_a, matrix_b)
+
+    print("Ergebnis C = A * B:")
+    for row in matrix_c:
+        print(row)
+
+    # Test Transpose
+    matrix = [[1, 2, 3], [4, 5, 6]]
+    print("Original matrix:", matrix)
+    print("Transposed matrix:", transpose(matrix))
+
+    # Test Rotate
+    angle = math.pi / 2  # 90 degrees
+    rotation_matrix = rot_2D(angle)
+
+    print("Rotation matrix (90 degrees):")
+    for row in rotation_matrix:
+        print(row)
+
+    # Test rotation of a point using matmul
+    point = [[1], [0]]
+    rotated_point = matmul(rotation_matrix, point)
+    print("Original point:", point)
+    print("Rotated point:", rotated_point)
+
+    # Test invalid matrices
+    print("\nTest invalid matrices:")
+
+    # Test Empty matrix
+    try:
+        transpose([])
+    except ValueError as error:
+        print("Empty matrix:", error)
+
+    # Test Matrix with different row lengths
+    try:
+        transpose([[1, 2, 3], [4, 5]])
+    except ValueError as error:
+        print("Non-rectangular matrix:", error)
+
+    # Test 3 Invalid matrix multiplication
+    try:
+        matmul([[1, 2, 3]], [[1, 2], [3, 4]])
+    except ValueError as error:
+        print("Invalid dimensions:", error)
diff --git a/pyproject.toml b/pyproject.toml
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--- /dev/null
+++ b/pyproject.toml
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+[project]
+name = "matrixmania"
+version = "0.1.0"