On the Discriminant Scheme of Homogeneous Polynomials
| Autor: | Laurent Busé, Jean-Pierre Jouanolou |
|---|---|
| Přispěvatelé: | Géométrie , Algèbre, Algorithmes (GALAAD2), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2014 |
| Předmět: |
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Power sum symmetric polynomial [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] Applied Mathematics inertia forms Complete homogeneous symmetric polynomial resultant of homogeneous polynomials Classical orthogonal polynomials Combinatorics Computational Mathematics Elimination theory Computational Theory and Mathematics Discriminant Difference polynomials Homogeneous polynomial discriminant of homogeneous polynomials Orthogonal polynomials Elementary symmetric polynomial [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Mathematics |
| Zdroj: | Mathematics in Computer Science Mathematics in Computer Science, Springer, 2014, Special Issue in Computational Algebraic Geometry, 8 (2), pp.175-234. ⟨10.1007/s11786-014-0188-7⟩ Mathematics in Computer Science, 2014, Special Issue in Computational Algebraic Geometry, 8 (2), pp.175-234. ⟨10.1007/s11786-014-0188-7⟩ |
| ISSN: | 1661-8289 1661-8270 |
| DOI: | 10.1007/s11786-014-0188-7 |
| Popis: | In this paper, the discriminant scheme of homogeneous polynomials is studied in two particular cases: the case of a single homogeneous polynomial and the case of a collection of n − 1 homogeneous polynomials in $${n\geqslant 2}$$ variables. In both situations, a normalized discriminant polynomial is defined over an arbitrary commutative ring of coefficients by means of the resultant theory. An extensive formalism for this discriminant is then developed, including many new properties and computational rules. Finally, it is shown that this discriminant polynomial is faithful to the geometry: it is a defining equation of the discriminant scheme over a general coefficient ring k, typically a domain, if $${2\neq 0}$$ in k. The case where 2 = 0 in k is also analyzed in detail. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink