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```{raw} html

<div id="qe-notebook-header" align="right" style="text-align:right;">

<a href="https://quantecon.org/" title="quantecon.org">

For example, let's build some arrays

```{code-block} python3

```{code-cell} python3

import numpy as np # Load the library

a = np.linspace(-np.pi, np.pi, 100) # Create even grid from -π to π

Now let's take the inner product

```{code-block} python3

```{code-cell} python3

b @ c

```

For example, let's calculate $\int_{-2}^2 \phi(z) dz$ where $\phi$ is the standard normal density.

```{code-block} python3

```{code-cell} python3

from scipy.stats import norm

from scipy.integrate import quad

The [SymPy](http://www.sympy.org/) library provides this functionality from within the Python shell.

```{code-block} python3

```{code-cell} python3

from sympy import Symbol

x, y = Symbol('x'), Symbol('y') # Treat 'x' and 'y' as algebraic symbols

We can manipulate expressions

```{code-block} python3

```{code-cell} python3

expression = (x + y)**2

expression.expand()

```

solve polynomials

```{code-block} python3

```{code-cell} python3

from sympy import solve

solve(x**2 + x + 2)

```

and calculate limits, derivatives and integrals

```{code-block} python3

```{code-cell} python3

from sympy import limit, sin, diff

limit(1 / x, x, 0)

```

```{code-block} python3

```{code-cell} python3

limit(sin(x) / x, x, 0)

```

```{code-block} python3

```{code-cell} python3

diff(sin(x), x)

```

Here's a simple example, using some dummy data generated with Numpy's excellent

`random` functionality.

```{code-block} python3

```{code-cell} python3

import pandas as pd

np.random.seed(1234)

print(df)

```

```{code-block} python3

```{code-cell} python3

df.mean()

```

Here's some example code that generates and plots a random graph, with node color determined by shortest path length from a central node.

```{code-block} ipython

```{code-cell} ipython

import networkx as nx

import matplotlib.pyplot as plt

%matplotlib inline