Field.py contains classes and functions related to mathematical fields.
gcd(a, b): This function calculates the greatest common divisor (GCD) of two integers a and b using the Euclidean algorithm.Rational class: This class represents rational numbers and provides various arithmetic operations for rational numbers.PolynomialRing.py contains classes and functions related to polynomial rings and operations on polynomials.
lex_ord(v1, v2): This function defines the lexicographic order for vectors v1 and v2.grlex_ord(v1, v2): This function defines the graded lexicographic order for vectors v1 and v2.grelex_ord(v1, v2): This function defines the graded reverse lexicographic order for vectors v1 and v2.monomial_ordering(order_type='lex'): This function returns a monomial ordering function based on the specified order type.Monomial class: This class represents a monomial and provides various operations on monomials, including multiplication, division, comparison, etc.Term class: This class represents a term, which is a monomial multiplied by a coefficient. It inherits from the Monomial class and provides additional operations such as addition, subtraction, etc.Polynomial class: This class represents a polynomial and provides operations such as addition, subtraction, multiplication, division, etc.