On Euclid's Algorithm and the Theory of Subresultants
From MaRDI portal
Publication:5633584
DOI10.1145/321662.321665zbMath0226.65041OpenAlexW2008957088MaRDI QIDQ5633584
Publication date: 1971
Published in: Journal of the ACM (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1145/321662.321665
Related Items
Theory of multiple polynomial remainder sequence ⋮ A superfast solver for Sylvester's resultant linear systems generated by a stable and an anti-stable polynomial ⋮ Computing sparse GCD of multivariate polynomials via polynomial interpolation ⋮ Primitive polynomial remainder sequences in elimination theory ⋮ The complexity of elementary algebra and geometry ⋮ A study of approximate polynomials. I: Representation and arithmetic ⋮ Computer algebra: Past and future ⋮ Bounds for resultants of univariate and bivariate polynomials ⋮ An algorithm for generalized point location and its applications ⋮ Multivariate subresultants in roots ⋮ An improved projection operation for cylindrical algebraic decomposition of three-dimensional space ⋮ Exact computation of the medial axis of a polyhedron ⋮ Deterministic distinct-degree factorization of polynomials over finite fields ⋮ Algebraic phase unwrapping along the real axis: extensions and stabilizations ⋮ Parallel computation of polynomial GCD and some related parallel computations over abstract fields ⋮ A new approach for constructing subresultants ⋮ Bernstein-Bézoutian matrices ⋮ Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander ⋮ On the complexity of computing the greatest common divisor of several univariate polynomials ⋮ Double Sylvester sums for subresultants and multi-Schur functions. ⋮ A Bridge between Euclid and Buchberger: (An Attempt to Enhance Gröbner Basis Algorithm by PRSs and GCDs) ⋮ An elementary approach to subresultants theory. ⋮ Subresultants revisited. ⋮ A fraction free matrix Berlekamp/Massey algorithm ⋮ Improved polynomial remainder sequences for Ore polynomials ⋮ A Fast Schur–Euclid-Type Algorithm for Quasiseparable Polynomials ⋮ Analysis of Euclidean algorithms for polynomials over finite fields ⋮ Singular points of algebraic curves ⋮ A fraction-free unit-circle zero location test for a polynomial with any singularity profile ⋮ Computing the polynomial remainder sequence via Bézout matrices ⋮ Subresultants and locally nilpotent derivations. ⋮ A singly exponential stratification scheme for real semi-algebraic varieties and its applications ⋮ Subresultants, Sylvester sums and the rational interpolation problem ⋮ Quantifier elimination for a class of exponential polynomial formulas ⋮ Birational properties of the gap subresultant varieties ⋮ An elementary proof of Sylvester's double sums for subresultants ⋮ Approximate GCD and its application to ill-conditioned algebraic equations ⋮ On the computational complexity and geometry of the first-order theory of the reals. III: Quantifier elimination ⋮ Recursive polynomial remainder sequence and its subresultants ⋮ Three new algorithms for multivariate polynomial GCD ⋮ A fast parallel sparse polynomial GCD algorithm ⋮ Blind image deconvolution via Hankel based method for computing the GCD of polynomials ⋮ Improvements of the power-series coefficient polynomial remainder sequence GCD algorithm ⋮ On the complexity of the Lickteig-Roy subresultant algorithm ⋮ Sylvester-Habicht sequences and fast Cauchy index computation ⋮ Global minimization of rational functions and the nearest GCDs ⋮ Computing high precision matrix Padé approximants ⋮ Various new expressions for subresultants and their applications ⋮ Solving a congruence on a graded algebra by a subresultant sequence and its application ⋮ Efficient parallel factorization and solution of structured and unstructured linear systems ⋮ Another polynomial homomorphism ⋮ D-resultant and subresultants ⋮ Computational aspects of deciding if all roots of a polynomial lie within the unit circle ⋮ A parametric representation of totally mixed Nash equilibria ⋮ Subresultants of two Hermite-Laurent series ⋮ The computation of polynomial greatest common divisors over an algebraic number field ⋮ Spécialisation de la suite de Sturm et sous-résultants (I) ⋮ Exact, efficient, and complete arrangement computation for cubic curves ⋮ Zero-Equivalence in Function Fields Defined by Algebraic Differential Equations ⋮ An improved EZ-GCD algorithm for multivariate polynomials ⋮ Fraction-free computation of the unit-circle resultant with any singularity profile ⋮ Power series remainder sequences and Padé fractions over an integral domain ⋮ A verified implementation of algebraic numbers in Isabelle/HOL ⋮ On the Piano Movers problem. II: General techniques for computing topological properties of real algebraic manifolds ⋮ New structure theorem for subresultants ⋮ Fp is locally like ℂ ⋮ Zur Charakterisierung und Berechnung von symmetrischen Kubaturformeln ⋮ Challenges of symbolic computation: My favorite open problems. With an additional open problem by Robert M. Corless and David J. Jeffrey ⋮ Congruence arithmetic algorithms for polynomial real zero determination ⋮ Algorithme de Bareiss, algorithme des sous-résultants ⋮ An exact and efficient approach for computing a cell in an arrangement of quadrics ⋮ Systems of rational polynomial equations have polynomial size approximate zeros on the average
