Vector Multiplication

The aim of this project is to develop a class (object type) for 3-dimensional vectors. The class shall provide typical calculations with vectors as Python operators. Before working through this project you should have read Variables and Operators chapter. For a recap of vector operations see Vectors.

This project consolidates your knowledge on defining custom object types and demonstrates the possibilities of Python’s flexible approach to customization of operator’s behavior.

Class Definition and String Representation

We start with a minimal orking example and then add more functionality step by step.

Task: Create a class Vector representing a vector in 3-dimensional space. The __init__ method takes the 3 components as arguments.

Solution:

# your solution

Task: Add dunder functions __str__ and __repr__ returning human readable representations of a Vector object. Test your code by creating and printing a Vector object.

Solution:

# your test code

Addition

When implementing operations on custom objects we have to decide whether to modify an existing object or to create a new object holding the operation’s result. For vectors, a + b shouldn’t modify a, but return a new object.

Task: Implement vector addition with + operator. The operation should return a new object holding the result. If the second operand is not of type Vector, addition should return NotImplemented. At this point we do not need __radd__ because we only accept Vector objects for addition. So the left-hand side operand will always be a Vector object and Python will call its __add__ method. Test your code!

Solution:

# your test code

Task: Modify your implementation of addition to accept lists of length 3, too. Don’t forget to implement __radd__ now. Else list plus vector won’t work, because the left-hand side list object doesn’t know how to work with Vector objects. Thus, Python tries to call __radd__ on the right-hand side operand. As always: test your code!

Solution:

# your test code

Multiplication by Scalar

Task: Implement multiplication of vectors by scalars via *. Both variants, scalar times vector and vector times scalar, should be supported.

Solution:

# your test code

Inner Products

Now we run out of operators. Of course, we could * again for inner products and check types to decide whether we have to do multiplication by scalars or to compute an inner product. The more readable alternative is implementing inner products without an operator.

Task: Implement a method inner taking a Vector or a list object as argument and returning the inner product with the vector whose inner method has been called. If the argument neither is a vector nor a 3 element list, return NotImplemented although the Python intepreter does not care about (because inner is a usual method, not an operator). If you know about Python’s exception handling mechanism, you should raise NotImplementedError here.

Solution:

# your test code

Outer Products

Task: In analogy to inner implement a method outer returning the outer product of two vectors.

Solution:

# your test code

Equality

At the moment == behaves like is. But we want to make == compare vectors componentwise.

Task: Implement equality test via == between two Vector objects and a vector and a list. If the second operand is of incorrect type both operands are considered unequal.

Solution:

# your test code

List-Like Indexing

There’s a dunder method __getitem__ which is called by the Python interpreter whenever indexing syntax [...] is applied to an object. The index is passed to the method and the method is expected to return the corresponding item.

Task: Implement __getitem__. For invalid indices return None. If you know about Python’s exception handling mechanism, you should raise IndexError here.

Solution:

# your test code

Task: Make the len function work on Vector objects. Return value should be 3.

Solution:

# your test code