$"""$

Sample code for ADA topic $1$

Date: $20-10-2022$

Following should be inside "ratNum.py$"$

$"""$

# find greatest common divisor

# using the fact that gcd$($a$,$b$)=$ gcd$($b$,$c$)$ where c $=$ a $\%$ b

# if b is zero, gcd$($a$,$b$)=$ gcd$($a$,0)=$ a

def gcd$($a$,$b$)$:

while b $!=0$:

r $=$ a $\%$ b

a $=$ b

b $=$ r

return a

# find least common multiple using gcd$()$ function

def lcm$($a$,$ b$)$:

return a$*$b $//$ gcd$($a$,$b$)$

# ratNum representing rational numbers $($a$/$b$)$

class ratNum:

# constructor for creating a rational number, default is zero

def $\_\_$init$\_\_($self$,$ a$=0,$ b$=1)$:

self.a $=$ a

if b $>0$: self.b $=$ b

else:

print$("$b shound be greater than zero!"$)$

self.b $=1$

def input$($self$)$: # input a rational number from keyboard

while True:

a$,$ b $=$ input$("$input a$/$b $($b$>0)$: $").$split$("/")$

a$,$ b $=$ int$($a$),$ int$($b$)$

if b $>0$: break

print$("$b shound be greater than zero!"$)$

self.a $=$ a

self.b $=$ b

def $\_\_$str$\_\_($self$)$: # convert to str for display

return f$"\{$self$.$a$\}/\{$self$.$b$\}"$

def $\_\_$add$\_\_($self$,$ y$)$: # rational number addition

b $=$ lcm$($self$.$b$,$ y$.$b$)$

a $=$ self.a $*$ b $//$ self.b $+$ y$.$a $*$ b $//$ y$.$b

return ratNum$($a$,$b$)$

def $\_\_$sub$\_\_($self$,$ y$)$: # rational number subtraction

b $=$ lcm$($self$.$b$,$ y$.$b$)$

a $=$ self.a $*$ b $//$ self.b $-$ y$.$a $*$ b $//$ y$.$b

return ratNum$($a$,$b$)$

def $\_\_$mul$\_\_($self$,$ y$)$: # rational number multiplication

a $=$ self.a $*$ y$.$a

b $=$ self.b $*$ y$.$b

g $=$ gcd$($a$,$ b$)$;

a $=$ a $//$ g

b $=$ b $//$ g

return ratNum$($a$,$b$)$

def $\_\_$truediv$\_\_($self$,$ y$)$: # rational number division

if $($y$.$a $==0)$: print$("$Division by zero!"$)$

else:

a $=$ self.a $*$ y$.$b

b $=$ self.b $*$ y$.$a

g $=$ gcd$($a$,$ b$)$

a $=$ a $//$ g

b $=$ b $//$ g

return ratNum$($a$,$b$)$

def $\_\_$eq$\_\_($self$,$ y$)$: # comparing two rational numbers

diff $=($self $-$ y$).$a

if diff $>0$: return $1$

elif diff $<mtext\; id="EditorElement\_3184475"></mtext><mn\; id="EditorElement\_3184476">0</mn>$: return $-1$

return $0$

# end of "ratNum.py$"$

# Following should be inside "main.py$"$

# from ratNum import $*$

z$1=$ ratNum$()$; z$1.$input$()$

z$2=$ ratNum$()$; z$2.$input$()$

print$($z$1,"+",$ z$2,"=",$ z$1+$z$2)$ # Task $0$

print$($z$1,"-",$ z$2,"=",$ z$1-$z$2)$ # Task $1$

print$($z$1,"$x$",$ z$2,"=",$ z$1*$z$2)$ # Task $2$

print$($z$1,"/",$ z$2,"=",$ z$1/$z$2)$ # Task $3$

print$($z$1,"==",$ z$2,"=",$ z$1==$z$2)$ # Task $4$