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Elimination Methods

The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions...

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Bibliographic Details
Main Author: Wang, D.
Format: eBook
Language:English
Published: Vienna Springer Vienna 2001, 2001
Edition:1st ed. 2001
Series:Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria
Subjects:
Computer Science—mathematics
Complex Manifolds
Symbolic And Algebraic Manipulation
Convex And Discrete Geometry
Topology
Convex Geometry 
Manifolds And Cell Complexes (incl. Diff.topology)
Algebra
Geometry
Manifolds (mathematics)
Discrete Geometry
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Polynomial arithmetic and zeros
  • 1.1 Polynomials
  • 1.2 Greatest common divisor, pseudo-division, and polynomial remainder sequences
  • 1.3 Resultants and subresultants
  • 1.4 Field extension and factorization
  • 1.5 Zeros and ideals
  • 1.6 Hilbert’s Nullstellensatz
  • Zero decomposition of polynomial systems
  • 2.1 Triangular systems
  • 2.2 Characteristic-set-based algorithm
  • 2.3 Seidenberg’s algorithm refined
  • 2.4 Subresultant-based algorithm
  • Projection and simple systems
  • 3.1 Projection
  • 3.2 Zero decomposition with projection
  • 3.3 Decomposition into simple systems
  • 3.4 Properties of simple systems
  • Irreducible zero decomposition
  • 4.1 Irreducibility of triangular sets
  • 4.2 Decomposition into irreducible triangular systems
  • 4.3 Properties of irreducible triangular systems
  • 4.4 Irreducible simple systems
  • Various elimination algorithms
  • 5.1 Regular systems
  • 5.2 Canonical triangular sets
  • 5.3 Gröbner bases
  • 5.4 Resultant elimination
  • Computational algebraic geometry and polynomial-ideal theory
  • 6.1 Dimension
  • 6.2 Decomposition of algebraic varieties
  • 6.3 Ideal and radical ideal membership
  • 6.4 Primary decomposition of ideals
  • Applications
  • 7.1 Solving polynomial systems
  • 7.2 Automated geometry theorem proving
  • 7.3 Automatic derivation of unknown relations
  • 7.4 Other geometric applications
  • 7.5 Algebraic factorization
  • 7.6 Center conditions for certain differential systems
  • Bibliographic notes
  • References

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