A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
From MaRDI portal
Publication:1260758
DOI10.1006/jsco.1993.1011zbMath0783.14039OpenAlexW1975442862MaRDI QIDQ1260758
Publication date: 25 August 1993
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/bae99681eadbe82fab25b8cddd83be93e4cdd246
polynomial ideal theorydecomposition of an algebraic varietygreatest common divisors of univariate polynomials
Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials, factorization in commutative rings (13P05) Varieties and morphisms (14A10) Computational aspects in algebraic geometry (14Q99)
Related Items (62)
Characteristic sets verses generalized characteristic sets ⋮ Chordality Preserving Incremental Triangular Decomposition and Its Implementation ⋮ Automatic constructibility checking of a corpus of geometric construction problems ⋮ The algebro-geometric method: Solving algebraic differential equations by parametrizations ⋮ Applications of the theory of weakly nondegenerate conditions to zero decomposition for polynomial systems ⋮ Modular composition modulo triangular sets and applications ⋮ A generalized Euclidean algorithm for geometry theorem proving ⋮ A characteristic set method for solving Boolean equations and applications in cryptanalysis of stream ciphers ⋮ Rational general solutions of higher order algebraic ODEs ⋮ Chordal Networks of Polynomial Ideals ⋮ A Direttissimo Algorithm for Equidimensional Decomposition ⋮ An improved algorithm for deciding semi-definite polynomials ⋮ Analyzing the dual space of the saturated ideal of a regular set and the local multiplicities of its zeros ⋮ Bifurcation analysis and complex dynamics of a Kopel triopoly model ⋮ Algorithms for computing triangular decomposition of polynomial systems ⋮ Characteristic set algorithms for equation solving in finite fields ⋮ Methodologies of Symbolic Computation ⋮ Decomposing polynomial sets into simple sets over finite fields: the zero-dimensional case ⋮ Squarefree normal representation of zeros of zero-dimensional polynomial systems ⋮ Chordal graphs in triangular decomposition in top-down style ⋮ Generic regular decompositions for parametric polynomial systems ⋮ Rational general solutions of trivariate rational differential systems ⋮ On solving parametric polynomial systems ⋮ Parametric equation solving and quantifier elimination in finite fields with the characteristic set method ⋮ On the efficiency of solving Boolean polynomial systems with the characteristic set method ⋮ When does \(\langle T \rangle\) equal \(\text{sat}(T)\)? ⋮ Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification ⋮ Characteristic decomposition: from regular sets to normal sets ⋮ On the mechanization of straightedge and compass constructions ⋮ Elimination theory in differential and difference algebra ⋮ Relaxed Hensel lifting of triangular sets ⋮ An equivalence theorem for regular differential chains ⋮ Computing strong regular characteristic pairs with Gröbner bases ⋮ Real solution isolation using interval arithmetic ⋮ On computer-assisted classification of coupled integrable equations ⋮ An algorithm for decomposing a polynomial system into normal ascending sets ⋮ Mechanical geometry theorem proving based on Gröbner bases ⋮ Bounding the number of limit cycles for a polynomial Liénard system by using regular chains ⋮ On approximate triangular decompositions in dimension zero ⋮ Change of order for regular chains in positive dimension ⋮ A systematic framework for solving geometric constraints analytically ⋮ Unmixed-dimensional decomposition of a finitely generated perfect differential ideal ⋮ An alternative algorithm for computing the pseudo-remainder of multivariate polynomials ⋮ An Algorithm for Transforming Regular Chain into Normal Chain ⋮ Algebraic, rational and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one ⋮ Decomposition of polynomial sets into characteristic pairs ⋮ Thirty years of polynomial system solving, and now? ⋮ A characteristic set method for ordinary difference polynomial systems ⋮ On the theories of triangular sets ⋮ Triangular sets for solving polynomial systems: a comparative implementation of four methods ⋮ Computing representations for radicals of finitely generated differential ideals ⋮ On the complexity of counting components of algebraic varieties ⋮ Factorization-free decomposition algorithms in differential algebra ⋮ Computing differential characteristic sets by change of ordering ⋮ Whitney's theorem, triangular sets, and probabilistic descent on manifolds ⋮ Computing triangular systems and regular systems ⋮ Generic regular decompositions for generic zero-dimensional systems ⋮ Accelerated tower arithmetic ⋮ Multiplicity-preserving triangular set decomposition of two polynomials ⋮ On the Chordality of Simple Decomposition in Top-Down Style ⋮ Analyses and implementations of chordality-preserving top-down algorithms for triangular decomposition ⋮ An algorithm for isolating the real solutions of semi-algebraic systems
Uses Software
This page was built for publication: A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
