Thirty years of polynomial system solving, and now?

DOI10.1016/j.jsc.2008.03.004zbMath1158.13314OpenAlexW2093230301WikidataQ55879445 ScholiaQ55879445MaRDI QIDQ1006651

Daniel Lazard

Publication date: 25 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.03.004

zbMATH Keywords

connected componentscylindrical algebraic decompositionpolynomial system solvingalgebraic optimizationeffective algebraic geometryparametric systemradical equidimensional decompositiontopology of semi-algebraic sets

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Real algebraic and real-analytic geometry (14P99) Computational aspects in algebraic geometry (14Q99)

Related Items (9)

Counting solutions of a polynomial system locally and exactly ⋮ Parallel computation of real solving bivariate polynomial systems by zero-matching method ⋮ Random arithmetic formulas can be reconstructed efficiently ⋮ On the family of cubical multivariate cryptosystems based on the algebraic graph over finite commutative rings of characteristic 2 ⋮ Computation of moderate-degree fully-symmetric cubature rules on the triangle using symmetric polynomials and algebraic solving ⋮ \( \mathcal{H}_\infty\) consensus for nonlinear stochastic multi-agent systems with time delay ⋮ A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection ⋮ The Approach of Moments for Polynomial Equations ⋮ On Dynamical Systems of Large Girth or Cycle Indicator and Their Applications to Multivariate Cryptography

Uses Software

• FGb
• RAGlib
• ISOLATE

Cites Work

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• Résolution des systèmes d'équations algébriques
• Solving zero-dimensional algebraic systems
• Symbolic and algebraic computation. EUROSAM '79, an international symposium on symbolic and algebraic manipulation, Marseille, France, June 1979
• Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen
• A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
• Solving zero-dimensional systems through the rational univariate representation
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Efficient isolation of polynomial's real roots.
• Injectivity of real rational mappings: the case of a mixture of two Gaussian laws
• Solving parametric polynomial systems
• Testing sign conditions on a multivariate polynomial and applications
• Using computer algebra to certify the global convergence of a numerical optimization process
• Algèbre linéaire sur $K[X_1,\dots,X_n$ et élimination]
• Automated Deduction in Geometry
• Projective modules over polynomial rings

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