Solutions of systems of algebraic equations and linear maps on residue class rings
The authors present new mathematical results and several new algorithms for solving a system of algebraic equations algebraically. They translate some theoretical arguments for the problem into their counterparts in the theory of linear maps, then they give a new description for the \(U\)- resultant and forms of solutions of systems straighforwardly. New algorithms proposed in the paper apply algorithms of linear algebra to avoid repeated computations of Gröbner bases under lexicographic order, and they require computations of a Gröbner basis, under arbitrary order, only once in principle. The new algorithms improve the efficiency of computation. Among others, the paper contains sections of a new presentation of the theory of solutions of systems and construction of the solutions in simple form. Comparison with other algorithms is given at the end of the paper.
algorithms for solving a system of algebraic equations
scientific article; zbMATH DE number 97806
scientific article