Book Image

IPython Interactive Computing and Visualization Cookbook - Second Edition

By : Cyrille Rossant
Book Image

IPython Interactive Computing and Visualization Cookbook - Second Edition

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 (19 chapters)
IPython Interactive Computing and Visualization CookbookSecond Edition
Contributors
Preface
Index

Solving equations and inequalities


SymPy offers several ways to solve linear and nonlinear equations and systems of equations. Of course, these functions do not always succeed in finding closed-form exact solutions. In this case, we can fall back to numerical solvers and obtain approximate solutions.

How to do it...

  1. Let's define a few symbols:

    >>> from sympy import *
        init_printing()
    >>> var('x y z a')
  2. We use the solve() function to solve equations (the right-hand side is 0 by default):

    >>> solve(x**2 - a, x)
  3. We can also solve inequalities. Here, we need to use the solve_univariate_inequality() function to solve this univariate inequality in the real domain:

    >>> x = Symbol('x')
        solve_univariate_inequality(x**2 > 4, x)
  4. The solve() function also accepts systems of equations (here, a linear system):

    >>> solve([x + 2*y + 1, x - 3*y - 2], x, y)
  5. Nonlinear systems are also handled:

    >>> solve([x**2 + y**2 - 1, x**2 - y**2 - S(1) / 2], x, y)
  6. Singular...