This is one of the 100 recipes of the IPython Cookbook, the definitive guide to high-performance scientific computing and data science in Python.

In [ ]:

```
from sympy import *
init_printing()
```

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```
var('x z')
```

We define a new function depending on x.

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```
f = 1/(1+x**2)
```

Let's evaluate this function in 1.

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```
f.subs(x, 1)
```

We can compute the derivative of this function...

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```
diff(f, x)
```

limits...

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```
limit(f, x, oo)
```

Taylor series...

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```
series(f, x0=0, n=9)
```

Definite integrals...

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```
integrate(f, (x, -oo, oo))
```

indefinite integrals...

In [ ]:

```
integrate(f, x)
```

and even Fourier transforms!

In [ ]:

```
fourier_transform(f, x, z)
```

You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).

IPython Cookbook, by Cyrille Rossant, Packt Publishing, 2014 (500 pages).