Simultaneous elimination by using several tools from real algebraic geometry

DOI10.1006/jsco.1998.0268zbMath0952.14043OpenAlexW2152080657MaRDI QIDQ1808663

Laureano Gonzalez-Vega, Neila Gonzalez-Campos

Publication date: 10 January 2001

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

Full work available at URL: https://doi.org/10.1006/jsco.1998.0268

zbMATH Keywords

computer aided geometric designeliminationreal algebraic geometrygreatest common divisor of polynomialsHermite's method

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computer science aspects of computer-aided design (68U07) Numerical computation of solutions to systems of equations (65H10) 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) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Real algebraic and real-analytic geometry (14P99)

Related Items (3)

Improving root separation bounds ⋮ Squarefree decomposition of univariate polynomials depending on a parameter. Application to the integration of parametric rational functions ⋮ Barnett's theorems about the greatest common divisor of several univariate polynomials through Bezout-like matrices

Cites Work

• Multidimensional analogues of Newton's formulas for systems of nonlinear algebraic equations and some of their applications
• Inertia characteristics of self-adjoint matrix polynomials
• Solutions of systems of algebraic equations and linear maps on residue class rings
• Radical computations of zero-dimensional ideals and real root counting.
• An elementary proof of Barnett's theorem about the greatest common divisor of several univariate polynomials
• On the combinatorial and algebraic complexity of quantifier elimination
• On the complexity of computing the greatest common divisor of several univariate polynomials
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