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<p>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 Gröbner bases is not involved. In the case of arbitrary polynomial sets, the times of calculating Gröbner bases is less than <i>r</i> if a given set of polynomials is decomposed into <i>r</i> triangular chains.</p>

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

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Shuijing Xiao,
  • Guangxing Zeng

摘要

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 Gröbner bases is not involved. In the case of arbitrary polynomial sets, the times of calculating Gröbner bases is less than r if a given set of polynomials is decomposed into r triangular chains.