• Program factoid.py is concerned with shades of primality

• Module primal.py provides three functions to assist

SET UP

PYTHON FILES

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )2

PYTHON FILES

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

3

Program Trace – begins with the program code, traditionally called the main

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

4

Program Trace – execution steps through program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

5

Program Trace – execution steps through program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

6

Program Trace – execution steps through program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

7

Program Trace – execution steps through program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

8

Program Trace – function invocation causes transfer of control

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

9

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x

y

10

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y

11

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y

12

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

13

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

14

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

15

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

16

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

17

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

result True

18

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

result True

19

Program Trace – return expression is the value of the invocation

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

result True

20

Program Trace – return expression is the value of the invocation

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = True

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

result True

21

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 6

y 2

rem 0

result True

22

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

23

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

24

Program Trace – function invocation causes transfers of control

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

25

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

is_factor()

x

y

26

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

is_factor()

x 7

y

27

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

is_factor()

x 7

y

28

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

is_factor()

x 7

y 3

29

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

is_factor()

x 7

y 3

30

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

31

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

32

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

33

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

result False

34

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

result False

35

Program Trace – return expression is the value of the invocation

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

result False

36

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = False

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

result False

37

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 7

y 3

rem 1

result False

38

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

39

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 ???

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

40

Program Trace – function invocation causes transfers of control

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 ???

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

41

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 ???

is_factor()

x

y

42

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 ???

is_factor()

x 4

y

43

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

is_factor()

x 4

y

44

Program Trace – copies of arguments are passed (assigned) to parameters

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 ???

is_factor()

x 4

y 5

45

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 ???

is_factor()

x 4

y 5

46

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 ???

is_factor()

x 4

y 5

47

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

48

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

49

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

50

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

result False

51

Program Trace – function executes

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

result False

52

Program Trace – return expression is the value of the invocation

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = False

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

result False

53

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = False

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

result False

54

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 ???

is_factor()

x 4

y 5

rem 4

result False

55

Program Trace – cpu control is passed back to program

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

56

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

57

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

print()

??? ???

??? True

??? ???

??? ???

58

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 False

59

print()

??? ???

??? True

??? ???

??? ???

True

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 False

60

print()

??? ???

??? True

??? ???

??? ???

True

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

61

True

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

print()

??? ???

??? ???

??? False

??? ???

62

True

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 False

63

print()

??? ???

??? ???

??? False

??? ???

TrueFalse

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 False

64

print()

??? ???

??? ???

??? False

??? ???

TrueFalse

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

65

TrueFalse

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

print()

??? False

??? ???

??? ???

??? ???

66

TrueFalse

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 False

67

print()

??? False

??? ???

??? ???

??? ???

TrueFalseFalse

Program Trace – cpu control is passed to function

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 True

r3 False

68

print()

??? False

??? ???

??? ???

??? ???

TrueFalseFalse

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

main

a1 6

b1 2

a2 7

b2 3

a3 4

b3 5

r1 True

r2 False

r3 False

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

69

TrueFalseFalse

Program Trace – program steps through its code

Program factoid.py

import primal

a1, b1 = 6, 2

a2, b2 = 7, 3

a3, b3 = 4, 5

r1 = primal.is_factor( a1, b1 )

r2 = primal.is_factor( a2, b2 )

r3 = primal.is_factor( a3, b3 )

print( r1 )

print( r2 )

print( r3 )

Module primal.py

def is_factor( x, y ) :

rem = x % y

if ( rem == 0 ) :

result = True

else:

result = False

return result

def are_relative_primes( x, y ) :

...

70

TrueFalseFalse

Program Trace – program steps through its code

71

TrueFalseFalse