The New is the Well-Forgotten Old—F4 Algorithm Optimization

The Gröbner basis is a fundamental concept in computational algebra. F4 is one of the fastest algorithms for computing Gröbner basis. In this paper, we will discuss the process of writing effective F4. Despite the fact that this work focuses on algorithms from computational algebra, some of the results and ideas presented here may have broader applications beyond this specific subject area. In general, the theory described below can be regarded as an abstraction, as it progresses through the text. This is because the text is not actually about the F4 algorithm itself, but rather about the power of profiling, unconventional techniques, and selecting the appropriate memory model. We will provide examples of inefficient usage of the standard library, recall the fundamental principles of optimization in order to apply them as efficiently as possible to obtain the fastest F4 algorithm, using non-traditional approaches.