Degeneracy Loci and Polynomial Equation Solving

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Let (Formula presented.) be a smooth, equidimensional, quasi-affine variety of dimension (Formula presented.) over (Formula presented.), and let (Formula presented.) be a (Formula presented.) matrix of coordinate functions of (Formula presented.), where (Formula presented.). The pair (Formula presen...

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Autor principal: Bank, B.
Otros Autores: Giusti, M., Heintz, J., Lecerf, G., Matera, G., Solernó, P.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Springer New York LLC 2014
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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024 7 |2 scopus  |a 2-s2.0-84925511394 
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100 1 |a Bank, B. 
245 1 0 |a Degeneracy Loci and Polynomial Equation Solving 
260 |b Springer New York LLC  |c 2014 
270 1 0 |m Heintz, J.; Departamento de Computación, Universidad de Buenos Aires, Ciudad Univ., Pab.I, Argentina 
506 |2 openaire  |e Política editorial 
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504 |a Bank, B., Giusti, M., Heintz, J., Mbakop, G.M., Polar varieties and efficient real elimination (2001) Math. Z, 238 (1), pp. 115-144 
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504 |a Giusti, M., Heintz, J., Morais, J.E., Morgenstern, J., Pardo, L.M., Straight-line programs in geometric elimination theory (1998) J. Pure Appl. Algebra, 124 (1-3), pp. 101-146 
504 |a Giusti, M., Lecerf, G., Salvy, B., A Gröbner free alternative for polynomial system solving (2001) J. Complexity, 17 (1), pp. 154-211 
504 |a Heintz, J., Definability and fast quantifier elimination in algebraically closed fields, Theoret (1983) Comput. Sci, 24 (3), pp. 239-277 
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504 |a Heintz and C.-P. Schnorr, Testing polynomials which are easy to compute, International Symposium on Logic and Algorithmic (Zurich, 1980) (Geneva), Monograph. Enseign. Math. vol. 30, Univ (1982) Genève, pp. 237-254 
504 |a E. Kaltofen and B. D. Saunders, On Wiedemann’s method of solving sparse linear systems, Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991), Lecture Notes in Comput. Sci., vol. 539, Springer, Berlin, 1991, pp. 29–38; Matsumura, H., (1986) Cambridge Studies in Advanced Mathematics, 8. , Cambridge University Press, Cambridge, Translated from the Japanese by M. Reid 
504 |a Mumford, D., Springer-Verlag Berlin, p. 1988 
504 |a Piene, R., Polar classes of singular varieties (1978) Ann. Sci. École Norm. Sup. (4), 11 (2), pp. 247-276 
504 |a http://www-polsys.lip6.fr/~safey/RAGLib, M. Safey El Din, RAGLib (Real Algebraic Geometry Library), Maple (TM) package, from 2007; Safey El Din, M., Trébuchet, P., Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry, Tech. Report 6001 (2006) INRIA, , http://hal.inria.fr/inria-00105204 
504 |a Schwartz, J.T., Fast probabilistic algorithms for verification of polynomial identities (1980) J. Assoc. Comput. Mach, 27 (4), pp. 701-717 
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504 |a Zippel, R., Probabilistic algorithms for sparse polynomials, Symbolic and algebraic computation (EUROSAM ’79, Internat. Sympos. Marseille (1979) Lecture Notes in Comput. Sci., vol. 72, Springer, Berlin, 1979, pp. 216-226 
520 3 |a Let (Formula presented.) be a smooth, equidimensional, quasi-affine variety of dimension (Formula presented.) over (Formula presented.), and let (Formula presented.) be a (Formula presented.) matrix of coordinate functions of (Formula presented.), where (Formula presented.). The pair (Formula presented.) determines a vector bundle (Formula presented.) of rank (Formula presented.) over (Formula presented.). We associate with (Formula presented.) a descending chain of degeneracy loci of (Formula presented.) (the generic polar varieties of (Formula presented.) represent a typical example of this situation). The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded-error probabilistic pseudo-polynomial-time algorithm that we will design and that solves a series of computational elimination problems that can be formulated in this framework. We describe applications to polynomial equation solving over the reals and to the computation of a generic fiber of a dominant endomorphism of an affine space. © 2014, SFoCM.  |l eng 
593 |a Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, 10099, Germany 
593 |a Laboratoire d’informatique, LIX, UMR 7161 CNRS, Campus de l’École Polytechnique, Palaiseau Cedex, 91128, France 
593 |a Departamento de Computación, Universidad de Buenos Aires, Ciudad Univ., Pab.I, Buenos Aires, 1428, Argentina 
593 |a CONICET, Ciudad Univ., Pab.I, Buenos Aires, 1428, Argentina 
593 |a Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, 39071, Spain 
593 |a Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, Los Polvorines, Buenos Aires, B1613GSX, Argentina 
593 |a CONICET, J. M. Gutierrez 1150, Los Polvorines, Buenos Aires, B1613GSX, Argentina 
593 |a Instituto Matemático Luis Santaló, CONICET, Buenos Aires, 1428, Argentina 
593 |a Departamento de Matemáticas, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina 
690 1 0 |a DEGENERACY LOCUS 
690 1 0 |a DEGREE OF VARIETIES 
690 1 0 |a POLYNOMIAL EQUATION SOLVING 
690 1 0 |a PSEUDO-POLYNOMIAL COMPLEXITY 
690 1 0 |a ALGORITHMS 
690 1 0 |a COORDINATE FUNCTIONS 
690 1 0 |a DEGENERACY LOCI 
690 1 0 |a DEGREE OF VARIETIES 
690 1 0 |a DESCENDING CHAIN 
690 1 0 |a ELIMINATION PROBLEM 
690 1 0 |a POLYNOMIAL COMPLEXITY 
690 1 0 |a POLYNOMIAL EQUATION SOLVING 
690 1 0 |a POLYNOMIAL-TIME ALGORITHMS 
690 1 0 |a POLYNOMIAL APPROXIMATION 
700 1 |a Giusti, M. 
700 1 |a Heintz, J. 
700 1 |a Lecerf, G. 
700 1 |a Matera, G. 
700 1 |a Solernó, P. 
773 0 |d Springer New York LLC, 2014  |g v. 15  |h pp. 159-184  |k n. 1  |p Found. Comput. Math.  |x 16153375  |t Foundations of Computational Mathematics 
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856 4 0 |u https://doi.org/10.1007/s10208-014-9214-z  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_16153375_v15_n1_p159_Bank  |y Handle 
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999 |c 84901 

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