README.md

This program implements two classes to handle algebraic operations over the $\mathbb{Z}_2$ field and on polynomials with coefficients in $\mathbb{Z}_2$.

The Z2 class represents elements in the field $\mathbb{Z}_2\ = \{0, 1\}$ and supports:

1. Constructors: default and from short int
2. Conversion operator: converts a Z2 element to short int
3. Operators:

• +=, *=, /=
• +, /, * as global functions returning a new Z2 object
• << outputting the Z2 element as an integer to std::ostream

The Polynomial class implements operations on polynomials with coefficients in $\mathbb{Z}_2$, allowing for any degree, and supports:

1. Constructors: default and from an array of Z2 coefficients
2. Operators:

• +=, *=
• [] returning the coefficient of the given power

3. Degree: returns the polynomial's non-degenerated degree
4. toString: outputs the polynomial in text format, ignoring zero terms

Additional global functions include:

• operator+ and operator* for polynomial addition and multiplication
• mod for computing the quotient and remainder for polynomial division
• operator/ and operator% for division and modulus
• operator<< and operator>> for outputting and inputting polynomials in a custom format