Book Image

Scientific Computing with Python 3

By : Claus Führer, Jan Erik Solem, Olivier Verdier
Book Image

Scientific Computing with Python 3

By: Claus Führer, Jan Erik Solem, Olivier Verdier

Overview of this book

Python can be used for more than just general-purpose programming. It is a free, open source language and environment that has tremendous potential for use within the domain of scientific computing. This book presents Python in tight connection with mathematical applications and demonstrates how to use various concepts in Python for computing purposes, including examples with the latest version of Python 3. Python is an effective tool to use when coupling scientific computing and mathematics and this book will teach you how to use it for linear algebra, arrays, plotting, iterating, functions, polynomials, and much more.
Table of Contents (23 chapters)
Scientific Computing with Python 3
Credits
About the Authors
About the Reviewer
www.PacktPub.com
Acknowledgement
Preface
References

Elementary Functions


Examples for elementary functions in SymPy are trigonometric functions and their inverses. The following example shows how simplify acts on expression which include elementary function:

x = symbols('x')
simplify(cos(x)**2 + sin(x)**2)  # returns 1

Here is another example for the use of elementary functions:

atan(x).diff(x) - 1./(x**2+1)  # returns 0

If you use SciPy and SymPy together, we strongly recommend that you use them in different namespaces:

import scipy as sp
import sympy as sym
# working with numbers
x=3
y=sp.sin(x)
# working with symbols
x=sym.symbols('x')
y=sym.sin(x)   

Lambda - functions

In section Anonymous functions of Chapter 7, Functions, we saw how to define so-called anonymous functions in Python. The counterpart in SymPy is done by the Lambda command. Note the difference; lambda is a keyword while Lambda is a constructor.

The command Lambda takes two arguments, the symbol of the function's independent variable, and...