Thoughts on Python numerics

---

• Today we build upon our pythonic problem solving skills by introducing the notion of type

• A type is a collection of values along with operators and functions that can manipulate those values.

• There are three basic types in Python

• int: provides support for integer arithmetic

• float: provides support for decimal arithmetic

• str: provides support for string production and manipulation

• The important arithmetic operators are described below, in there variables a are b are numeric values. Except for the decimal division operator, if both operands are integer, the value of the operation is integer; otherwise, the value of the operation is decimal. For the decimal division operator, the result is always decimal.

a + b	The sum of a and b
a - b	The difference of b from a
a * b	The product of a and b
a / b	The decimal quotient a divided by b
a // b	The truncated quotient of of a divided by b
a ** b	The remainder when b does not evenly divide b
a % b	The remainder when b does not evenly divide a

• The two important string operators are described below, in there value s is a string and n is an integer.

s + t	The contatenation (gluing) of strings s and t
n * s	If n is positive, it is the concatenation of s with itself n-1 times; otherwise it is the ''
s * n	Equals n * s

• Typos are maddening. When you write and read code, do it mindfully,

• A module is a library (collection) of Python resources. They are typically functins.

• An import statement gives its code file access to an external Python resource. For example, The statement

import math

gives its code access to the standard Python math library.

• An invocation of a function f() from a module m requires m. in front of the invoked function f(). For example, math.sin( 45 ) invokes the math module’s function sin() to determine the sine of 45 degrees.

• All values in Python are stored in base 2. An individual binary digit is called a bit. A bit is either 0 or 1.

• Most Python implementations use 64 bits to represent a decimal number, where 1 bit keeps track of the sign of the number, 10 bits keep track of the power of 2 being represented. and 53 bits to store the number itself.

• Why 64 bits for a decimal number — modern computers have 64-bit operating systems.

• With only 64 bits to represent a decimal value, the best approximation of π in Python is kept track by math.pi, which equals 3.141592653589793.

 

---

 

 

 
   
   
   
 

© 2019 Jim Cohoon

Resources from previous semesters are available.