Variables, Expressions, and Standard Functions

1
Variables, Expressions, and Standard Functions
2
Topics

• Basic calculation
• Expressions, variables, and operator precedence
• Data types
• Input / Output
• Examples

3
A calculator

• We can use a computer as a calculator.
• Just type expressions into the Python Shell

Python Shell in Wing IDE
4
A calculator

• Try this.

Type it into Python Shell
gtgtgt 10 5 50 gtgtgt 1 2 3 4 10 gtgtgt
1234 10 gtgtgt 1 4 5 2 29
The answer
Spaces are irrelevant
is for exponentiation
5
Expression

• What we have just typed into the Python Shell is
  called expressions.
• After the shell reads each expression, the shell
  evaluate it and reports the result.

6
Easy calculation

• An object moves with the starting speed of 10 m/s
  with an acceleration of 2 m/s2. After 5 seconds,
  how far is the object from its starting position?

s ut at2/2
10 5 2 (55) / 2
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Operators (1)

• In previous examples, we use many operators such
  as , -, or /, to tell Python to perform various
  computations with the data.
• An operator tells Python what operation to
  perform with its operands.

operands
10 5
operator
8
Operators (2)

• Operators can be
• Binary operators that work with two operands,
  e.g., , -, or .5 3 10 2
  157
• Unary operators that work with a single operand,
  e.g, .-3 2 -5 7

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Operators (2)

• Basic mathematical operators are shown in the
  table below

Operator Meaning Examples
addition 35
- subtraction 4-2
multiplication 4.510
/ division see next page
modulo see next page
exponentiation 34
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Division in Python

• There are two operators related to division

division
modulo find the remainder
expression result
4/2 2.0
3/2 1.5
10/7 4286
3.0/2 1.5
10/7.0 1.4286
expression result
42 0
32 1
107 3
3.02 1.0
107.0 3.0
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Numbers in Python

• There are two types for numbers in Python
  integer (type int) and floating points (type
  float)

Integer expression Value Floating-point expr. Values
10 10 10.0 10.0
3-2 1 3.0-2 1.0
195 95 195.2 98.8
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Quick test
Expressions Values
2 3 6 20
(23) 6 30
3/52 1.2
35.0/2 7.5
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Integers v.s. Floating-points

• If you write a number without a "dot", it will be
  treated as an integer.
• Results
• Every mathematical operation between integer and
  integer returns an integer, except for division.
• Division returns floating-point numbers.
• Any operations with floating-point numbers return
  floating-point numbers.

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3/52

• Evaluation is usually done from left to right

((3/5)2)
( 0.6 2)
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Operator precedence

• But operators have different precedence, e.g.,
  or / have higher precedence over or -.

236
2(36)
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This is just.

• High-school math!

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Operator precedence
Operators Examples
1 () (34)
2 (expo.) 23
3 -, (unary) -5, 10
4 ,/, 34, 72
5 -, 27, 3-4

• Evaluation order is from left-to-right for
  operators with the same precedence, except .

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Try this (1)
256/3(7-23)
What is the result?
13.0
19
Try this (2)
2 2 3
What is the result?
2 (2 3)
28 256
20
Reusing values

• A force of 2.5 newton pushes a rock with mass 1
  kg to the left. Where is the rock after 1
  second, 5 second and 15 second?

(1.0/2.5)11/2
Redundant
(1.0/2.5)55/2
(1.0/2.5)1515/2
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Variables

• We can use variables to refer to result from
  previous computation.

a 1.0/2.5
a11/2
a55/2
a1515/2
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Variables
a 1.0/2.5
0.4

• A variable is used to refer to various data.
• Use "" to assign a value to a variable.
• When we refer to that variable, we get the value
  that the variable is referring to.

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Variables can be "modified" (1)
a 10a 5b 3a ba 7a ba b
5aa b
50
13
10
8
11
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Variables can be "modified" (2)
a 10a a 1
11
25
Variables can be "modified" (3)
x 10x x 2
20
26
Variables can be "modified" (4)
x 10x x 2 5
25
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Working on Wing IDE
Shell or Console After you type commands or
expressions, the Python Interpreter evaluates
them and prints out the output
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Typing programs in WingIDE
Editing area Any commands here are executed after
you hit the "run" button.
29
A program

• A program is a sequence of commands (or
  statements)

a 10b a 5a - bc 12b a cc aba
b c1 a - c
Try totype this intoWing IDE
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Result
Empty

• Because the program does not have statements that
  output anything.

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Printing

• We can use function
• print
• to display results

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A program

• A program is a sequence of commands (or
  statements)

Add"print"to display the valueof the required
expressions
a 10b a 5print(a b)c 12b a cc
abprint(a b c)print(1 a c)
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See the output after hitting "Run"
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Function calls
print(10)
Function name
Arguments
35
What's going on?
print(a b 2)
20
Assume that a 5 b 10
25
print(25)

• The expressions on the parameter list are
  evaluated before sending the result to the
  function.

36
A simple calculation program

• We have the following coins
• 5 one-baht coins
• 7 ten-baht coins
• 2 twenty-baht notes
• 3 hundred-baht notes

How muchmoney do wehave ?
sum1 1 5sum10 10 7sum20 20 2sum100
100 3sum sum1sum5sum20sum100print(sum)
37
A simple program (2)

• Or we can even remove variable sum

sum1 1 5sum10 10 7sum20 20 2sum100
100 3print(sum1sum5sum20sum100)
38
Meaningful names
Comparethese twoprograms
a 1 5b 10 7c 20 2d 100 3e a
b c dprint(e)
Theyperform thesame task
sum1 1 5sum10 10 7sum20 20 2sum100
100 3sum sum1sum5sum20sum100print(sum)
Which oneis easier to understand?
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Suggestions

• Write programs for people to read
• At the very least, one of the audience is
  yourself.

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Comments ()

• To make a program easier to read, we can add
  comments to the program
• Everything after the symbol is a comment.

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A program with comments
this program calculates total money from the
amount of each type of coins or bank notes that
you havesum1 1 5 value of 1-baht
coinssum10 10 7sum20 20 2sum100 100
3print(sum1sum5sum20sum100)
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Strings

• A computer can work with many types of data.
• A string is another data type which is very
  important. It is a type for texts or messages.
• Formally, a string is a sequence of characters.

Hello
Hello, world
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String constants

• We can either use single or double quotes to
  specify strings, e.g.,
• Hello
• World
• However, the starting quotes and the ending
  quotes must match.
• We can also have special characters inside a
  string. They will start with backslash " \ ".

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Examples (1)
print("hello")
hello
print('hello')
hello
print("I'm 9")
I'm 9
print('I'm 9')
ERROR
print('I\'m 9')
I'm 9
print("I\'m 9")
I'm 9
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Examples (2)
print("123")
123
print(123)
123
print("12" "3")
123
print(12 3)
15
print("12" '3')
123
print("12" 3)
ERROR
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A slightly better program
sum1 1 5sum10 10 7sum20 20 2sum100
100 3sum sum1sum5sum20sum100print("The
total is",sum)
The total is 415
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A slightly even better program
sum1 1 5sum10 10 7sum20 20 2sum100
100 3sum sum1sum5sum20sum100print("The
total is",sum,"bath.")
The total is 415 bath.
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Sidenote printing and new lines

• We can display data using function print.
• It will always add a new line at the end.
• If we want to avoid the new line, we can add an
  additional option "end" to print.

print(10)print(20)print(10,end'')print(20)
10201020
This tells print to end this output with an empty
string, instead of a new line.
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Reading inputs

• We can use function input to read data from the
  user
• input
• The function returns a string that the user types
  into the shell.

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Examples in the Python Shell

• gtgtgt name input()
• Somchai
• gtgtgt print("Hello", name)
• Hello Somchai
• gtgtgt a input()
• 10
• gtgtgt b input()
• 100
• gtgtgt print(ab)
• 10100

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Remarks

• Consider this statement
• print(ab)
• Since both variables a and b are strings from
  function input. When we add two strings, we only
  get the concatenation of them.

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?????

• How are we going to do calculations when we can
  only read strings from the user?

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Conversion

• We can use function int, float, and str to
  convert between various data types

int("10")
10
float("10")
10.0
float(10)
10.0
int(10.6)
10
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Type conversion
int("10")10
20
float("10")10
20.0
float(10)int(5)
15.0
str(10)str(5)
105
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Conversion between float and int (1)
int(10.2)
10
int(10.9)
10
int(-10.1)
-10
Always return the integers without the fractional
parts.
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Conversion between float and int (2)
We can also use function round that returns the
closest integers.
round(10.2)
10
round(10.9)
11
round(-10.1)
-10
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Adding two numbers
This program adds two numbersastr input()a
int(astr)bstr input()b int(bstr)print("Th
e result is",ab)
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Nested function calls (1)

• Consider this part of the program
• We use variable astr to refer to an input string.
  We then convert it to an integer and assign the
  result to variable a.
• We can avoid using variable astr

astr input()a int(astr)
a int(input())
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Nested function calls (2)

• This is how it works.

a int(input())
input()
"12345"
int
12345
a 12345
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Two additional important functions
Functions Return values
abs(x) Returns the absolute value of x
pow(x,y) Returns the value of xy
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Money calculation (improved)
This program calculates total amount of money
from numbers of bank notesp1 int(input())sum1
1 p1p5 int(input())sum5 10 p5p20
int(input())sum20 20 p20p100
int(input())sum100 100 p100sum
sum1sum5sum20sum100print("The total
is",sum,"bath.")
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A prompt

• We can tell function input to display a prompt
  before reading input by providing a string
  argument to input

x int(input("Enter X "))print(x10)

Enter X
100
110
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Thinking corner

• An object, initially sitting still, starts moving
  with an acceleration of a m/s2 for t seconds.
• Write a program that reads the acceleration and
  the duration and computes the displacement.

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Solution
a float(input("Enter a "))t
float(input("Enter t "))print("Total distance
", att/2)
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Thinking corner
Enter length in inch 320It is 26 feet, 8 inch.
x int(input("Enter length in inch"))xf
int(x/12)xi x xf 12print("It is", xf,
"feet,",xf,"inch.")
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Volume Calculation

• Compute the volume of a cylinder

r
?r2 x h
h
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?

• We can use 22/7 (which is quite inaccurate).
• We can use a closer estimation, in module math.

3.141592653589793
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The math module

• In Python, functions are categorized into various
  groups, called modules. To use functions from a
  module, we have to declare that by using the
  import statement.
• Then all functions can be referred to by
  prefixing with the module name.

import math print("Pi is", math.pi)
3.141592653589793
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Thinking corner

• Write a program that reads r and h and compute
  the volume of a cylinder.

r
?r2 x h
h
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Solution
import mathr float(input("Enter r "))h
float(input("Enter h "))print("Volume ",
math.pirrh)
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Important functions in math module
Functions Goals
fabs(x) The absolute value of x
sin(x), cos(x), tan(x) Trigonometric functions of x (the angles are specified in radian)
pi Constant Pi
e Constant e
log(x),log10(x) Natural logarithm, logarithm base 10
exp(x) The value of ex
sqrt(x) Square root of x
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Another example

• Projection

don't forget to import math recall that the
angle must be in radianr t math.pi/180fy
f math.sin(r)fx f math.cos(r)
import math radian anglesfy f
math.sin(t)fx f math.cos(t)