The problem of solving polynomial equations over finite fields has many applications in cryptography and coding theory. In this paper, we consider polynomial equations over a “large” finite field with a “small” characteristic. We introduce a new algorithm for solving this type of equations, called the Successive Resultants Algorithm (SRA) in the sequel. SRA is radically different from previous ...

The hierarchy of integrable equations are considered. The dynamical approach to theory of nonlinear waves is proposed. The special solutions (nonlinear waves) of considered equations are derived. We use powerful methods of computer algebra such as differential resultant and others.

Given two curves in P 3 , either implicitly or by a param-eterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.

The behavior of the Cayley-Dixon resultant construction and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substituted by a univariate polynomial in a distinct variable. It is shown that a Dixon projection operator (a multiple of the resultant) of the composed system can be expressed as a power of the...