Irredundant Decomposition of the Radicals of Polynomial Ideals Based on Rational Univariate Representations

The purpose of this paper is to establish two algorithms for decomposing the radical of a polynomial ideal into an irredundant intersection of prime ideals, which are created by rational univariate representations. In the case of zero-dimensional polynomial sets, the calculation of Gr & ouml;bner bases is not involved. In the case of arbitrary polynomial sets, the times of calculating Gr & ouml;bner bases is less than r if a given set of polynomials is decomposed into r triangular chains.