by this code $,$ write lecture it contains $(-$

OVERVIEW

$-$BACKGROUND AND MOTIVATION

$-$OBJECTIVES

$-$METHODOLOGY

$-$TOOL DESCRIPTION

$-$IMPLEMENTATIONSPECIFY THENEEDSAREREQUIREDTOPRO

VIDE THE USER WISHES

$-$SPECIFYTHEVARIOUSCOMPONENTSOFTHE

TOOL ARCHITECTURE ACCORDING TO THE

PREVIOUS NEEDS

$-$ANALYZETHEEQUATIONANDFINDTHEPAT

TERN$)$

$-$Python code:

import networkx as nx

import matplotlib. pyplot as plt

# Define the modulus $\text{'}n\text{'}($size of the ring $Zn)$

$n=5$

# Create an empty graph

$)$

# Iterate over all possible combinations of $\text{'}$a$\text{'},$

$\text{'}b\text{'},$ and $\text{'}y\text{'}$ in $Zn$

for a in range $(1,n)$ :

for $b$ in range $(1,n)$ :

for $y$ in range $(1,n)$ :

# calculate the left$-$hand side of the

equation $($ab$)$

$lhs=(a**b)\%n$

# calculate the right$-$hand side of the

equation $y(ab{)}^{{?}^{{?}^{?}}}2$

$rhs=(y**(a**b)****2)\%n$

# check if the equation holds true and

if $\text{'}$a$\text{'}$ and $\text{'}$b$\text{'}$ are different

if lhs $==$ rhs and $ab$ :

# Add an edge between $\text{'}a\text{'}$ and $\text{'}b\text{'}$

if the equation is satisfied by $\text{'}$y$\text{'}-\text{'}$a$\text{'}$ and $\text{'}$a$\text{'}$

$G.ad{d}_e$dge $(a,b)$

# Create a layout for the nodes

layout $=$ nx$.$spring$\_$layout $(G)$

# Draw the graph

$,$ pos$=$layout, with$\_$labels$=$True,

node$\_$size $=300,$ node$\_$color$=$'skyblue', font$\_$size$=10)$

# Display the graph

plt$.$title$($f$\text{'}$Graph for $($ab$)=$y$($ab$)^2$ in Z$\{$n$\}\text{'})$

plt$.$axis $(\text{'}$off$\text{'})$

plt$,$ show $()$