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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

By : Cyrille Rossant
4.4 (7)
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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

4.4 (7)
By: Cyrille Rossant

Overview of this book

Python is one of the leading open source platforms for data science and numerical computing. IPython and the associated Jupyter Notebook offer efficient interfaces to Python for data analysis and interactive visualization, and they constitute an ideal gateway to the platform. IPython Interactive Computing and Visualization Cookbook, Second Edition contains many ready-to-use, focused recipes for high-performance scientific computing and data analysis, from the latest IPython/Jupyter features to the most advanced tricks, to help you write better and faster code. You will apply these state-of-the-art methods to various real-world examples, illustrating topics in applied mathematics, scientific modeling, and machine learning. The first part of the book covers programming techniques: code quality and reproducibility, code optimization, high-performance computing through just-in-time compilation, parallel computing, and graphics card programming. The second part tackles data science, statistics, machine learning, signal and image processing, dynamical systems, and pure and applied mathematics.
Table of Contents (17 chapters)
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16
Index

A bit of number theory with SymPy

SymPy contains many number-theory-related routines: obtaining prime numbers, integer decompositions, and much more. We will show a few examples here.

Getting ready

To display legends using LaTeX in matplotlib, you will need an installation of LaTeX on your computer (see this chapter's introduction).

How to do it...

  1. Let's import SymPy and the number theory package:
    >>> from sympy import *
        import sympy.ntheory as nt
        init_printing()
  2. We can test whether a number is prime:
    >>> nt.isprime(2017)
    True
  3. We can find the next prime after a given number:
    >>> nt.nextprime(2017)
    How to do it...
  4. What is the 1000th prime number?
    >>> nt.prime(1000)
    How to do it...
  5. How many primes less than 2017 are there?
    >>> nt.primepi(2017)
    How to do it...
  6. We can plot How to do it..., the prime-counting function (the number of prime numbers less than or equal to some number How to do it...). The prime number theorem states that this function is asymptotically equivalent to How to do it.... This expression approximately quantifies...

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