Lecture 2 — Python as a Calculator

Overview

Most of this is covered in Chapter 2 of both Practical Programming and Think Python

• Part 1:
  • Basic operations, including some surprises
  • Types
• Part 2:
  • Variables and the assignment operator
  • Syntax and semantic errors
  • Variable names and Python keywords
• Part 3:
  • Expressions
  • Precedence

Throughout we will pay attention to problems and mistakes, both real and potential.

Aside: Lectures, Note Taking and Exercises

• Lecture notes are outlines.
  • Therefore, you should hand-write details as we cover them in class.
• We will create and run examples in class.
  • You should write down the shorter ones
  • We will post the longer ones on-line, but you should write down as much as you can, especially about the results of running the examples.

Python As a Calculator

We will start class by using Python as an interactive calculator, working through a number of examples.

• The area of a square, rectangle or circle
• The number of minutes in a year.
• What about the volume of a sphere? We’ll calculate the volume of the earth in cubic kilometers.
• Is this right? How do we know?
• Lesson: we need to be careful to check our calculations, doing so as much as possible through calculations that we can check by hand!

Python Types

• A type is a set of possible values — also called a “representation” — and a set of operations on those values, such as +, -, *, / and **
• Common Python types we are working with initially include integer, float and string

Integers

• Values include

  

• The operators on integers include +, -, *, /, **, %.

• The biggest surprise is division. The best way to think about integer / and % is in terms of the old “dividend” and “remainder” calculation from grade school:

  

• This integer division rule, common to many programming languages, has been changed in Python 3.

• What happens with negative numbers? We’ll try it out in class and then figure out what is happening.

Aside: Lots of Integers

• Unlike many other language such as C, C++ and Java, any integer you wish to represent can be represented in Python, provided you are patient enough.
  • Using the Python interpreter, we will look at the examples of 1**1**1, 2**2**2, 3**3**3, etc.
• We will soon see that this is not true for real numbers.

Floats

• Floats are the Python types most like real numbers and most like what we see when we use a calculator.

• Playing around with calculations like

  • 5.0 / 9.0 and then subtracting off 0.55555555, and
  • 1.0**1.0**1.0, 2.0**2.0**2.0, 3.0**3.0**3.0, etc.

  will help illustrate float numbers and operators.

• The ’e’ notation we will see in these examples is Python’s version of scientific notation.

• Python can store a limited range of possible values, both in decimals and in the exponent.

Mixing Integer and Float

• In an expression that mixes integers and floats, the conversion is made to float, but this is not done until Python applies an operation that needs to combine an integer and a float
• Examples
  • 9.0 / 5.0 is the same as both 9 / 5.0 and 9.0 / 5
• What is 9 / 5 * 5.0?

Exercise Set 1

1. Fix our formula for computing the volume of the earth. What is the correct value?
2. Write a formula to convert the temperature 80 from Fahrenheit to Celsius. You must first subtract 32, then multiply by . Use your intuition to figure out where to put parentheses.
3. Write a version of this expression that uses as few floats as possible, but is still correct, and write a version that is not correct even though it might be on a calculator.
4. Write a formula to convert the temperature 80 from Celsius to Fahrenheit.

On to Part 2: Variables and Assignment

• Most calculators have one or several memory keys. Python, and all other programming languages, use “variables” as their memory.

• We’ll start with a simple example of the area of a circle, typed in class. You will notice as we go through this that there is no output until we use a print statement.

• Here is a more extensive example of computing the volume and surface area of a cylinder:

  >>> pi = 3.14159
  >>> radius = 2
  >>> height = 10
  >>> base_area = pi * radius ** 2
  >>> volume = base_area * height
  >>> surface_area = 2 * base_area + 2 * pi * radius * height
  >>> print "volume is", volume, ", surface area is", surface_area
  volume is 125.6636 , surface area is 150.79632
  

• A variable is a name that has a value “associated” with it.

  • There are six variables in the above code.

• The value is substituted in for the variable when the variable appears on the right hand side of the =.

• The value is assigned to the variable when the variable name appears on the left hand side of the =.

More on Variable Assignment

• The operator = is an assignment of a value (calculated on the right side) to a variable (on the left). Thus, in the line

  >>>  base_area = pi * radius ** 2
  

  • Python accesses the values associated with the variables pi and radius
  • Multiplies them, and multiplies the result by 2
  • Associates the resulting value with the variable base_area
  • Later, Python accesses the value of base_area when calculating the values to assign to volume and surface_area.

• Thus, the meaning of = in Python is quite different from the meaning of = in mathematics.

• The statement

  >>>  base_area * height = volume
  

  is not legal Python code. Try it!

• It takes a while to get accustomed to the meaning of an assignment statement in Python.

Variable Names

• Notice that our example variable names include letters and the _ (underscore) character.

• Legal variable names in Python must

  • Start with a letter or a _, and
  • Be followed by any number of letters, underscores or digits.

  Characters that are none of these, including spaces, signal the end of a variable name.

• Capital letters and small letters are different

• We will look at many examples in class.

Syntax and Semantic Errors

• Python tells us about the errors we make in writing the names of variables and in reversing the left and right side of the = operator.
• These are examples of syntax errors — errors in the form of the code.
• Programs with syntax errors will not run; the Python interpreter inspects the code and tells us about these errors before it tries to execute them. We can then fix the errors and try again
• More difficult to find and fix are semantic errors — errors in the logical meaning of our programs resulting in an incorrect result.
  • We have already seen an example of a semantic error. Can you think where?
  • Throughout the semester we will discuss strategies for finding and fixing semantic errors.

Python Keywords

• Not all variable names that follow the above rules are legal Python names.

• The (only) exception is the set of “keywords” that have special meaning to Python and allow use to write more complicated operations — involving logic and repetition — than just calculating.

• print is the first keyword we used in this lecture

  • What happens when you try to assign a value to print?

• You can get a list of Python keywords by typing

  >>> import keyword
  >>> print keyword.kwlist
  

• Over the next few lectures, we will soon understand the detailed meaning of the . in the above statement.

Do Variables Exist Before They Are Assigned a Value?

• Suppose we forgot to assign pi a value? What would happen?
  • Try it out!
• Variables do not exist until they are assigned a value.
• This leads to a simple form of semantic error.

Exercise Set 2

1. Which of these are legal variable names?

   import
   56abc
   abc56
   car-talk
   car_talk
   car talk

2. Create 2 invalid variable names and 4 valid variable names from the _ character, the digit 0, and the letter a.

3. Which of these lines of code contain syntax errors?

   pi = 3.14159
   area = pi * r * r
   r = 6.5
   r + 5 = r_new
   

4. Write Python code that computes and prints the surface area and volume of a rectangular solid that has length 5, width 16.5, and height 12, all in inches. Convert the result to cubic feet. Use variables as appropriate. Test it by typing it into the Python interpreter.

On to Part 3: Expressions

• In our volume and surface area calculation, the right hand side of the = in the line

  >>> surface_area = 2 * base_area + 2 * pi * radius * height
  

  is what’s known as an expression.

• Expressions are formed from syntactically-legal combinations of values (the number 2), operators (+ and *), and variables (base_area, radius and height)

• Expressions can be as simple as a single value, but Python allows them to be arbitrarily complicated.

Precedence

• The order in which operations are applied is important.
• Among the basic operations in Python the order is
  1. Parentheses
  2. **, right to left
  3. Unary + and -
  4. * and /, left to right
  5. + and -, left to right
• We will play with many examples in class
• When in doubt
  • Try it out and see!
  • Insert parentheses to make sure

Mixed Operators

• Assignments of the form

  >>> i = i + 1
  

  are commonly seen in Python. We will take a careful look at what is happening here.

• Python contains a short-hand for these:

  >>> i += 1
  

  These two statements are exactly equivalent.

• Other mixed operators include

  -=     *=    /=

  but += is used most commonly for reasons that will gradually become clear.

Exercise Set 3

1. Assuming you start with $100 and earn 5% interest each year, how much much will you have at the end of one year, two years and three years? Write Python expressions to calculate these, using variables as appropriate.

2. What is the output of the following Python code? Try to figure it out by hand before typing the statements into the Python interpreter.

   x = 12
   y = 7.4
   x -= y
   print x, y
   y = y-x +7
   z = 1
   x *= 2 + z
   print x, y
   x += x*y
   print x, y
   

3. What is the output of the following?

   z = 2
   z = z**2**3
   print z
   x = 4
   x = (x**2)**3 + 6 - z / 4 * 2
   print x
   

Summary — Important Points to Remember

• Values in Python are one of several different types — integers and floats for now.
• Variables are Python’s form of memory
• Python keywords can not be used as variables.
• = is Python’s means of assigning a value to a variable
• Variables do not exist in Python until they are given a value
• Expressions are formed from combinations values, variables and operators
• Make sure you have the precedence correct in your Python expressions.