The F5 algorithm is presented by Faugère in 2002. However, Faugère have not provide the rigorous proofs so far. In this paper, we will give a new complete proof and hence reveal the essence of this algorithm. The proof consists of the correctness and termination of the algorithm and the correctness of two criteria in it.

We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection strategies for non-multiplicative prolongations. By using the standard data base of polynomial benchmarks for Gröbner bases software we compare the modifications and confront them with Magma that implements Faugère’s F4...

abstract background: understanding the electrophysiological effects of toxins, may facilitate new drugs discovery. buthotusschach (bs) has been shown to be one of the most dangerous scorpions in tropical part of iran. present study was aimed to investigate the electrophysiological effects of two active fractions (f4 and f6) isolated from bs scorpion toxin on action potential (ap) characteristic...

Faugère’s criterion used in the F5 algorithm is still not understand and thus there are not many implementations of this algorithm. We state its proof using syzygies to explain the normalization condition of a polynomial. This gives a new insight in the way the F5 criterion works.

In this paper, we present an improved approach to the “breaking the F5 algorithm”. The key idea is to search for an “optimal” value of β (the probability that a non-zero AC coefficient will be modified) for the image under consideration. Rather than averaging the values of β for 64 shifting steps worked on an image, an optimal β is determined that corresponds to the shift having minimal distanc...

It has previously been reported that azalomycin F could induce permeability changes in Candida albicans causing loss of cell constituents and inhibition of substrate uptake which resulted in the death of the organism1). The present report is concerned with the effect of the antibiotic on bacteria. Methods and Results Azalomycin F inhibited the growth of Bacillus subtilis PCI 219 at concentratio...

Team matches for two-person games / sports, e.g. chess are considered. In a competition between two teams A and B each player of team A has to play against exactly one player of team B. To arrange this assignment each team chooses a line-up. For the line-up the playing strength is the most common criterion. The best player of A should be the rst and so on. Assuming that team A has lined up its ...

Faugère's F5 algorithm computes a Gröbner basis incrementally, by computing a sequence of (non-reduced) Gröbner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Gröbner basis with its reduced Gröbner basis. As a result, F5C considers fewer polynomials and performs substantially fewer polynomial reductions, so that it terminates more quickly. We also provi...

MutantXL is an algorithm for solving systems of polynomial equations that was proposed at SCC 2008 and improved in PQC 2008. This article gives an overview over the MutantXL algorithm. It also presents experimental results comparing the behavior of the MutantXL algorithm to the F4 algorithm on HFE and randomly generated multivariate systems. In both cases MutantXL is faster and uses less memory...