Erster Stand: compute.py

.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/matrixmania.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="jdk" jdkName="Python 3.13" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.13" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.13" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/matrixmania.iml" filepath="$PROJECT_DIR$/.idea/matrixmania.iml" />
+    </modules>
+  </component>
+</project>

.idea/vcs.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$" vcs="Git" />
+  </component>
+</project>

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`.

compute.py

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+import math
+
+def matmul(a: list[list[float]], b: list[list[float]]) -> list[list[float]]:
+    """Multiply two non-empty rectangular matrices.
+
+    Args:
+        a: The left matrix.
+        b: The right matrix.
+
+    Returns:
+        The matrix product a * b.
+
+    Raises:
+        ValueError: If either matrix is empty or ragged, or if their
+            dimensions are incompatible.
+    """
+    _validate_matrix(a, "a")
+    _validate_matrix(b, "b")
+
+    if len(a[0]) != len(b):
+        raise ValueError(
+            "Matrix dimensions are incompatible: the number of columns in a "
+            "must equal the number of rows in b."
+        )
+
+    return [
+        [
+            sum(a_row[index] * b[index][column] for index in range(len(b)))
+            for column in range(len(b[0]))
+        ]
+        for a_row in a
+    ]
+
+def transpose(matrix: list[list[float]]) -> list[list[float]]:
+    """Return the transpose of a non-empty rectangular matrix.
+
+    Args:
+        matrix: A matrix represented as rows of numbers.
+
+    Returns:
+        A new matrix whose rows are the columns of matrix.
+
+    Raises:
+        ValueError: If the matrix is empty or its rows have different lengths.
+    """
+    _validate_matrix(matrix, "matrix")
+    return [list(column) for column in zip(*matrix)]
+
+def rot_2D(angle: float) -> list[list[float]]:
+    """Return the 2D rotation matrix for a given angle in radians.
+
+    Args:
+        angle: The rotation angle in radians.
+
+    Returns:
+        The rotation matrix for rotating points counterclockwise.
+    """
+    return [
+        [math.cos(angle), -math.sin(angle)],
+        [math.sin(angle), math.cos(angle)]
+    ]
+
+def _validate_matrix(matrix: list[list[float]], name: str) -> None:
+    """Raise ValueError unless matrix is non-empty and rectangular."""
+    if not matrix:
+        raise ValueError(f"Matrix {name} must be non-empty.")
+
+    column_count = len(matrix[0])
+
+    if column_count == 0:
+        raise ValueError(f"Matrix {name} must have at least one column.")
+
+    if any(len(row) != column_count for row in matrix):
+        raise ValueError(f"Matrix {name} must have rows of equal length.")
+
+if __name__ == "__main__":
+    first = [[1, 2, 3], [4, 5, 6]]
+    second = [[7, 8], [9, 10], [11.0, 12.0]]
+
+    assert matmul(first, second) == [
+        [58.0, 64.0],
+        [139.0, 154.0]
+    ]
+    print("Matrix product:", matmul(first, second))
+
+    try:
+        matmul([[1, 2]], [[1, 2]])
+    except ValueError as error:
+        print("Expected error:", error)
+    else:
+        raise AssertionError(
+            "Expected a ValueError for incompatible dimensions."
+        )
+
+    assert transpose_matrix(first) == [
+        [1, 4],
+        [2, 5],
+        [3, 6]
+    ]
+    print("Transpose:", transpose_matrix(first))
+

pyproject.toml

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+[project]
+name = "matrixmania"
+version = "0.1.0"