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Scientific Computing with Python - Second Edition

By Claus Führer , Jan Erik Solem , Olivier Verdier
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  1. Free Chapter
    Variables and Basic Types
About this book
Python has tremendous potential within the scientific computing domain. This updated edition of Scientific Computing with Python features new chapters on graphical user interfaces, efficient data processing, and parallel computing to help you perform mathematical and scientific computing efficiently using Python. This book will help you to explore new Python syntax features and create different models using scientific computing principles. The book presents Python alongside mathematical applications and demonstrates how to apply Python concepts in computing with the help of examples involving Python 3.8. You'll use pandas for basic data analysis to understand the modern needs of scientific computing, and cover data module improvements and built-in features. You'll also explore numerical computation modules such as NumPy and SciPy, which enable fast access to highly efficient numerical algorithms. By learning to use the plotting module Matplotlib, you will be able to represent your computational results in talks and publications. A special chapter is devoted to SymPy, a tool for bridging symbolic and numerical computations. By the end of this Python book, you'll have gained a solid understanding of task automation and how to implement and test mathematical algorithms within the realm of scientific computing.
Publication date:
July 2021
Publisher
Packt
Pages
392
ISBN
9781838822323

 
Variables and Basic Types

In this chapter, we will present the most important and basic types in Python. What is a type? It is a set consisting of data content, its representation, and all possible operations. Later in this book, we will make this definition much more precise when we introduce the concepts of a class in Chapter 8: Classes.

In this chapter, we'll cover the following topics:

  • Variables
  • Numeric types
  • Booleans
  • Strings
 

2.1 Variables

Variables are references to Python objects. They are created by assignments, for example:

a = 1
diameter = 3.
height = 5.
cylinder = [diameter, height] # reference to a list

Variables take names that consist of any combination of capital and small letters, the underscore _, and digits. A variable name must not start with a digit. Note that variable names are case sensitive. A good naming of variables is an essential part of documenting your work, so we recommend that you use descriptive variable names.

Python has 33 reserved keywords, which cannot be used as variable names (see Table 2.1). Any attempt to use such a keyword as a variable name would raise a syntax error:

Table 2.1: Reserved Python keywords

As opposed to other programming languages, variables require no type declaration in Python. The type is automatically deduced:

x = 3 # integer (int)
y = 'sunny' # string (str)

You can create several variables with a multiple assignment statement:

a = b = c = 1 # a, b and c get the same value 1

Variables can also be altered after their definition:

a = 1 
a = a + 1 # a gets the value 2 
a = 3 * a # a gets the value 6

The last two statements can be written by combining the two operations with an assignment directly by using increment operators:

a += 1 # same as a = a + 1 
a *= 3 # same as a = 3 * a
 

2.2 Numeric types

At some point, you will have to work with numbers, so we start by considering different forms of numeric types in Python. In mathematics, we distinguish between natural numbers (ℕ), integers (ℤ), rational numbers (ℚ), real numbers (ℝ), and complex numbers (ℂ). These are infinite sets of numbers. Operations differ between these sets and may even not be defined. For example, the usual division of two numbers in ℤ might not result in an integer — it is not defined on ℤ.

In Python, like many other computer languages, we have numeric types:

  • The numeric type, int, which is at least theoretically the entire ℤ
  • The numeric type, float, which is a finite subset of ℝ
  • The numeric type, complex, which is a finite subset of ℂ

Finite sets have a smallest and a largest number and there is a minimum spacing between two numbers; see Section 2.2.2Floating-point numbersfor further details.

                                             
About the Authors
  • Claus Führer

    Claus Führer is a professor of scientific computations at Lund University, Sweden. He has an extensive teaching record that includes intensive programming courses in numerical analysis and engineering mathematics across various levels in many different countries and teaching environments. Claus also develops numerical software in research collaboration with industry and received Lund University’s Faculty of Engineering Best Teacher Award in 2016.

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  • Jan Erik Solem

    Jan Erik Solem is a Python enthusiast, former associate professor, and computer vision entrepreneur. He co-founded several computer vision startups, most recently Mapillary, a street imagery computer vision company, and has worked in the tech industry for two decades. Jan Erik is a World Economic Forum technology pioneer and won the Best Nordic Thesis Award 2005-2006 for his dissertation on image analysis and pattern recognition. He is also the author of "Programming Computer Vision with Python" (O'Reilly 2012).

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  • Olivier Verdier

    Olivier Verdier began using Python for scientific computing back in 2007 and received a PhD in mathematics from Lund University in 2009. He has held post-doctoral positions in Cologne, Trondheim, Bergen, and Ume and is now an associate professor of mathematics at Bergen University College, Norway.

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Scientific Computing with Python - Second Edition
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