Overview

This program computes the multiplication table for the finite field extension $\mathbb{F}_{3^2}$. The field $\mathbb{F}_{3^2}$ is constructed using the relation $x^2 = 2$ over $\mathbb{F}_3$. Elements in this field are of the form $a + bx$, where $a, b \in$ {0, 1, 2}, and $x$ is the indeterminate.

Field Elements in $\mathbb{F}_{3^2}$

The nine elements of the field $\mathbb{F}_{3^2}$ are: [ { 0, 1, 2, x, 1 + x, 2 + x, 2x, 1 + 2x, 2 + 2x } ] These elements are used to construct the multiplication table.

Program Description

The program defines a struct F3x2 to represent elements in $\mathbb{F}_{3^2}$ with two fields:

• a: Coefficient of the constant term.
• b: Coefficient of the $x$ term.

Multiplication of two elements is implemented in the multiply function, taking into account the relation $x^2 = 2$ in the field.

Usage

To run the program, ensure you have Rust installed on your machine. (If Rust is not installed, follow the instructions on the official Rust website to install it). Then, use the following commands:

cargo build --release
cargo run

The program will display the elements of the field and output the multiplication table in the console.

Multiplication Table

The multiplication table for $\mathbb{F}_{3^2}$ is computed and printed, with each element in the rows and columns being multiplied according to the rules of field multiplication.

Contributing

• If you intend to contribute to this project, fork the repository and make a pull request.

Acknowledgments

• Rust

Clone the repository:

git clone /~https://github.com/cypriansakwa/Multiplication_Table_for_Field_Extension_F_9.git
cd Multiplication_Table_for_Field_Extension_F_9