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Bank, B.; Giusti, M.; Heintz, J.; Safey El Din, M.; Schost, E. "On the geometry of polar varieties" (2010) Applicable Algebra in Engineering, Communications and Computing. 21(1):33-83
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Abstract:

We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are necessary to prove the correctness and complexity estimates of these algorithms. Our results form also the geometrical main ingredients for the computational treatment of singular hypersurfaces. In particular, we show the non-emptiness of suitable generic dual polar varieties of (possibly singular) real varieties, show that generic polar varieties may become singular at smooth points of the original variety and exhibit a sufficient criterion when this is not the case. Further, we introduce the new concept of meagerly generic polar varieties and give a degree estimate for them in terms of the degrees of generic polar varieties. The statements are illustrated by examples and a computer experiment. © 2009 Springer-Verlag.

Registro:

Documento: Artículo
Título:On the geometry of polar varieties
Autor:Bank, B.; Giusti, M.; Heintz, J.; Safey El Din, M.; Schost, E.
Filiación:Humboldt-Universität zu Berlin, Institut für Mathematik, Berlin 10099, Germany
CNRS, École Polytechnique, Laboratoire LIX, Palaiseau Cedex 91228, France
Departamento de Computación, Universidad de Buenos Aires and CONICET, Ciudad Univ., Pab.I, 1428 Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Santander 39071, Spain
UPMC, Univ Paris 06, INRIA, Case 169, 4, Place Jussieu, Paris 75252, France
Computer Science Department, Middlesex College, University of Western Ontario, London, ON, Canada
Palabras clave:Real polynomial equation solving, Singularities, Classic polar varieties, Dual polar varieties, Generic polar varieties, Meagerly generic polar varieties; Computational complexity; Polynomials; Algebraic varieties; Complexity bounds; Complexity estimates; Computer experiment; Hyper-surfaces; Real polynomial equation solving; Sufficient criterion; Geometry
Año:2010
Volumen:21
Número:1
Página de inicio:33
Página de fin:83
DOI: http://dx.doi.org/10.1007/s00200-009-0117-1
Título revista:Applicable Algebra in Engineering, Communications and Computing
Título revista abreviado:Appl Algebra Eng Commun Comput
ISSN:09381279
CODEN:AAECE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09381279_v21_n1_p33_Bank

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Citas:

---------- APA ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M. & Schost, E. (2010) . On the geometry of polar varieties. Applicable Algebra in Engineering, Communications and Computing, 21(1), 33-83.
http://dx.doi.org/10.1007/s00200-009-0117-1
---------- CHICAGO ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M., Schost, E. "On the geometry of polar varieties" . Applicable Algebra in Engineering, Communications and Computing 21, no. 1 (2010) : 33-83.
http://dx.doi.org/10.1007/s00200-009-0117-1
---------- MLA ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M., Schost, E. "On the geometry of polar varieties" . Applicable Algebra in Engineering, Communications and Computing, vol. 21, no. 1, 2010, pp. 33-83.
http://dx.doi.org/10.1007/s00200-009-0117-1
---------- VANCOUVER ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M., Schost, E. On the geometry of polar varieties. Appl Algebra Eng Commun Comput. 2010;21(1):33-83.
http://dx.doi.org/10.1007/s00200-009-0117-1