A modular method to compute the rational univariate representation of zero-dimensional ideals

zbMath0945.13010MaRDI QIDQ1808670

Kazuhiro Yokoyama, Masayuki Noro

Publication date: 4 October 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

zbMATH Keywords

Gröbner basisrational univariate representationmodular methodsHensel liftingshape lemmazeros of ideals

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Relevant commutative algebra (14A05)

Related Items (14)

Computing PUR of zero-dimensional ideals of breadth at most one ⋮ An improvement of the rational representation for high-dimensional systems ⋮ A simplified rational representation for positive-dimensional polynomial systems and SHEPWM equations solving ⋮ A new Gröbner basis conversion method based on stabilization techniques ⋮ Computer algebra for guaranteed accuracy. How does it help? ⋮ Implementation of prime decomposition of polynomial ideals over small finite fields ⋮ Computing polynomial univariate representations of zero-dimensional ideals by Gröbner basis ⋮ Gröbner bases of symmetric ideals ⋮ Usage of modular techniques for efficient computation of ideal operations ⋮ Stratification associated with local \(b\)-functions ⋮ Computing and using minimal polynomials ⋮ Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem ⋮ Modular Algorithms for Computing a Generating Set of the Syzygy Module ⋮ Ideals Modulo a Prime

Cites Work

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• Interpolating polynomials from their values
• Solutions of systems of algebraic equations and linear maps on residue class rings
• On lucky primes
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• P-adic reconstruction of rational numbers

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