In this paper, an original reduction algorithm for solving simultaneous multivariate polynomial equations is presented. The exponential in complexity, but the well-known algorithms, such as extended Euclidean and Buchberger's algorithm, are superexponential. superexponential complexity of algorithms due to their not being "minimal" a certain sense. produces Groebner basis. proposed achieves req...

Let AN (K̄) denote the affine space of homogeneous polynomials of degree d in n + 1 variables with coefficients from the algebraic closure K̄ of a field K of arbitrary characteristic; so N = (n+d n ) . It is proved that the variety of all reducible polynomials in this affine space can be given by a system of polynomial equations of degree less than 56d7 in N variables. This result makes it possib...