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# A simple application

Imagine that we want to add two vectors called `a` and `b`. The word vector is used here in the mathematical sense, which means a one-dimensional array. We will learn in Chapter 3, Statistics and Linear Algebra, about specialized NumPy arrays that represent matrices. The vector `a` holds the squares of integers `0` to n; for instance, if `n` is equal to `3`, `a` contains `0`, `1`, or `4`. The vector `b` holds the cubes of integers `0` to n, so if `n` is equal to `3`, then the vector `b` is equal to `0`, `1`, or `8`. How would you do that using plain Python? After we come up with a solution, we will compare it with the NumPy equivalent.

The following function solves the vector addition problem using pure Python without NumPy:

`def pythonsum(n): a = range(n) b = ...`

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