Solutions of systems of algebraic equations and linear maps on residue class rings. (English) Zbl 0757.13013

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.
Reviewer: Y.Kuo (Knoxville)


13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
12E12 Equations in general fields
Full Text: DOI


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