Elimination Methods (Paperback)

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 Grobner 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.