Buchberger's algorithm

Buchberger's algorithm is a method used in computer algebra to find a simplified, standardized form of a set of polynomial equations called a Gröbner basis. It systematically combines pairs of polynomials to eliminate variables and identify all solutions shared by the original set. By repeatedly performing certain calculations (called S-polynomials) and reducing the results, the algorithm ensures the final basis captures all the solution relationships in a more manageable way. This process is essential in solving systems of polynomial equations and analyzing algebraic structures efficiently.