An Implementation of Faugère's F4 Algorithm for Computing Gröbner Bases
Daniel Cabarcas · OhioLink ETD Center (Ohio Library and Information Network) · 2010
Gröbner bases are an important tool for analyzing systems of polynomial equations.They allow the system of equations to be solved exactly and therefore have gained popularity in many areas of science and technology.However, finding Gröbner bases is a computationally intensive task, thus, several algorithms have been developed for this goal.Faugère invented an elaborate algorithm to compute Gröbner bases in 1999 called F 4 , which has become a benchmark due to its efficiency.We have implemented F 4 from scratch in C++.In this thesis we revisit the theoretical foundation of the algorithm, provide details of our implementation, and compare it with other software that computes Gröbner bases.iii