-
1
-
-
0031097237
-
Polar varieties, real equation solving, and data structures: The hypersurface case
-
B. Bank, M. Giusti, J. Heintz, G.M. Mbakop, Polar varieties, real equation solving, and data structures: the hypersurface case, J. Complexity 13 (1997) 5-27.
-
(1997)
J. Complexity
, vol.13
, pp. 5-27
-
-
Bank, B.1
Giusti, M.2
Heintz, J.3
Mbakop, G.M.4
-
2
-
-
0035465565
-
Polar varieties and efficient real elimination
-
B. Bank, M. Giusti, J. Heintz, G.M. Mbakop, Polar varieties and efficient real elimination, Math. Z. 238 (2001) 115-144.
-
(2001)
Math. Z.
, vol.238
, pp. 115-144
-
-
Bank, B.1
Giusti, M.2
Heintz, J.3
Mbakop, G.M.4
-
3
-
-
0030291482
-
On the combinatorial and algebraic complexity of quantifier elimination
-
S. Basu, R. Pollack, M.F. Roy, On the combinatorial and algebraic complexity of quantifier elimination, J. ACM 43 (1996) 1002-1045.
-
(1996)
J. ACM
, vol.43
, pp. 1002-1045
-
-
Basu, S.1
Pollack, R.2
Roy, M.F.3
-
5
-
-
0003615227
-
-
Springer, New York
-
L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation, Springer, New York, 1998.
-
(1998)
Complexity and Real Computation
-
-
Blum, L.1
Cucker, F.2
Shub, M.3
Smale, S.4
-
6
-
-
0040277331
-
-
Ergebnisse der Math., 3. Folge, Band 12, Springer, Berlin
-
J. Bochnak, M. Coste, M.-F. Roy, Géométrie Algébrique Réelle, Ergebnisse der Math., 3. Folge, Band 12, Springer, Berlin, 1987.
-
(1987)
Géométrie Algébrique Réelle
-
-
Bochnak, J.1
Coste, M.2
Roy, M.-F.3
-
7
-
-
0015143623
-
On Euclid's algorithm and the computation of polynomial greatest common divisors
-
W.S. Brown, On Euclid's algorithm and the computation of polynomial greatest common divisors, J. ACM 18 (1971) 478-504.
-
(1971)
J. ACM
, vol.18
, pp. 478-504
-
-
Brown, W.S.1
-
8
-
-
0018014720
-
The subresultant PSR algorithm
-
W.S. Brown, The subresultant PSR algorithm, ACM Trans. Math. Software 4 (1978) 237-249.
-
(1978)
ACM Trans. Math. Software
, vol.4
, pp. 237-249
-
-
Brown, W.S.1
-
9
-
-
0015141743
-
On Euclid's algorithm and the theory of subresultants
-
W.S. Brown, J.F. Traub, On Euclid's algorithm and the theory of subresultants, J. ACM 18 (1971) 505-514.
-
(1971)
J. ACM
, vol.18
, pp. 505-514
-
-
Brown, W.S.1
Traub, J.F.2
-
10
-
-
0042461761
-
On the hardness of polynomial equation solving
-
submitted
-
D. Castro, M. Giusti, J. Heintz, G. Matera, L.M. Pardo, On the hardness of polynomial equation solving, Found. Comput. Math (2003), submitted.
-
(2003)
Found. Comput. Math
-
-
Castro, D.1
Giusti, M.2
Heintz, J.3
Matera, G.4
Pardo, L.M.5
-
11
-
-
0035294748
-
Kronecker's and Newton's approaches to solving: A first comparison
-
D. Castro, K. Hägele, J.E. Morais, L.M. Pardo, Kronecker's and Newton's approaches to solving: a first comparison, J. Complexity 17 (2001) 212-303.
-
(2001)
J. Complexity
, vol.17
, pp. 212-303
-
-
Castro, D.1
Hägele, K.2
Morais, J.E.3
Pardo, L.M.4
-
12
-
-
0013026624
-
The distribution of condition numbers of rational data of bounded bit length
-
D. Castro, J.L. Montaña, L.M. Pardo, J. San Martín, The distribution of condition numbers of rational data of bounded bit length, Found. Comput. Math. 1 (1) (2002) 1-52.
-
(2002)
Found. Comput. Math.
, vol.1
, Issue.1
, pp. 1-52
-
-
Castro, D.1
Montaña, J.L.2
Pardo, L.M.3
San Martín, J.4
-
13
-
-
22844453744
-
On the distribution of points in projective space of bounded height
-
K.K.S. Choi, On the distribution of points in projective space of bounded height, Trans. Amer. Math. Soc. 352 (2000) 1071-1111.
-
(2000)
Trans. Amer. Math. Soc.
, vol.352
, pp. 1071-1111
-
-
Choi, K.K.S.1
-
14
-
-
84945709818
-
Subresultants and reduced polynomial remainder sequence
-
G.E. Collins, Subresultants and reduced polynomial remainder sequence, J. ACM 14 (1967) 128-142.
-
(1967)
J. ACM
, vol.14
, pp. 128-142
-
-
Collins, G.E.1
-
15
-
-
84962995474
-
On a principle of Lipschitz
-
H. Davenport, On a principle of Lipschitz, J. London Math. Soc. 26 (1951) 179-183.
-
(1951)
J. London Math. Soc.
, vol.26
, pp. 179-183
-
-
Davenport, H.1
-
16
-
-
0001625611
-
On a problem in the theory of uniform distribution. I
-
P. Erdös, P. Turán, On a problem in the theory of uniform distribution. I, Indagagtiones. Math. 10 (1948) 370-378.
-
(1948)
Indagagtiones. Math.
, vol.10
, pp. 370-378
-
-
Erdös, P.1
Turán, P.2
-
17
-
-
0012995936
-
On a problem in the theory of uniform distribution. II
-
P. Erdös, P. Turán, On a problem in the theory of uniform distribution. II, Indag. Math. 10 (1948) 406-413.
-
(1948)
Indag. Math.
, vol.10
, pp. 406-413
-
-
Erdös, P.1
Turán, P.2
-
18
-
-
0000936391
-
La Détermination des Points Isolés et de la Dimension d'une Varieté Algébrique Peut se Faire en Temps Polynomial
-
D. Eisenbud, L. Robbiano (Eds.), Proceedings of the Cortona Conference on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica, Cambridge University Press, Cambridge
-
M. Giusti, J. Heintz, La Détermination des Points Isolés et de la Dimension d'une Varieté Algébrique Peut se Faire en Temps Polynomial, in: D. Eisenbud, L. Robbiano (Eds.), Computational Algebraic Geometry and Commutative Algebra, Proceedings of the Cortona Conference on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica, Vol. XXXIV, Cambridge University Press, Cambridge, 1993, pp. 216-256.
-
(1993)
Computational Algebraic Geometry and Commutative Algebra
, vol.34
, pp. 216-256
-
-
Giusti, M.1
Heintz, J.2
-
19
-
-
0031142051
-
Lower bounds for diophantine approximations
-
M. Giusti, K. Hägele, J. Heintz, J.E. Morais, J.L. Montaña, L.M. Pardo, Lower bounds for diophantine approximations, J. Pure Appl. Algebra 117 & 118 (1997) 277-317.
-
(1997)
J. Pure Appl. Algebra
, vol.117-118
, pp. 277-317
-
-
Giusti, M.1
Hägele, K.2
Heintz, J.3
Morais, J.E.4
Montaña, J.L.5
Pardo, L.M.6
-
20
-
-
84955611783
-
When polynomial equation systems can be "Solved" fast?
-
G. Cohen, M. Giusti, T. Mora (Eds.), AAECC-11, Paris, Lecture Notes in Computer Science, Springer, Berlin
-
M. Giusti, J. Heintz, J.E. Morais, L.M. Pardo, When polynomial equation systems can be "Solved" fast?, in: G. Cohen, M. Giusti, T. Mora (Eds.), Proceedings of the 11th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris, Lecture Notes in Computer Science, Vol. 948, Springer, Berlin, 1995, pp. 205-231.
-
(1995)
Proceedings of the 11th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
, vol.948
, pp. 205-231
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Pardo, L.M.4
-
21
-
-
0031539424
-
Le Rôle des Structures de Données dans les Problèmes d'Élimination
-
M. Giusti, J. Heintz, J.E. Morais, L.M. Pardo, Le Rôle des Structures de Données dans les Problèmes d'Élimination, C. R. Acad. Sci. Paris Série I 325 (1997) 1223-1228.
-
(1997)
C. R. Acad. Sci. Paris Série I
, vol.325
, pp. 1223-1228
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Pardo, L.M.4
-
22
-
-
0031992346
-
Straight-line programs in geometric elimination theory
-
M. Giusti, J. Heintz, J.E. Morais, J. Morgenstern, L.M. Pardo, Straight-line programs in geometric elimination theory, J. Pure Appl. Algebra 124 (1998) 101-146.
-
(1998)
J. Pure Appl. Algebra
, vol.124
, pp. 101-146
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Morgenstern, J.4
Pardo, L.M.5
-
23
-
-
0035294718
-
A Gröbner free alternative for polynomial system solving
-
M. Giusti, G. Lecerf, B. Salvy, A Gröbner free alternative for polynomial system solving, J. Complexity 17 (2001) 154-211.
-
(2001)
J. Complexity
, vol.17
, pp. 154-211
-
-
Giusti, M.1
Lecerf, G.2
Salvy, B.3
-
24
-
-
51249194297
-
Eine Verallgemeirung des Sturmschen Wurzelzählverfahrens
-
W. Habicht, Eine Verallgemeirung des Sturmschen Wurzelzählverfahrens, Comment. Math. Helv. 21 (1948) 99-116.
-
(1948)
Comment. Math. Helv.
, vol.21
, pp. 99-116
-
-
Habicht, W.1
-
25
-
-
0034695774
-
On the intrinsic complexity of the arithmetic nullstellensatz
-
K. Hägele, J.E. Morais, L.M. Pardo, M. Sombra, On the intrinsic complexity of the arithmetic nullstellensatz, J. Pure Appl. Algebra 146 (2) (2000) 103-183.
-
(2000)
J. Pure Appl. Algebra
, vol.146
, Issue.2
, pp. 103-183
-
-
Hägele, K.1
Morais, J.E.2
Pardo, L.M.3
Sombra, M.4
-
27
-
-
0000627865
-
Definability and fast quantifier elimination in algebraically closed fields
-
J. Heintz, Definability and fast quantifier elimination in algebraically closed fields, Theor. Comput. Sci. 24 (1983) 239-277.
-
(1983)
Theor. Comput. Sci.
, vol.24
, pp. 239-277
-
-
Heintz, J.1
-
28
-
-
0002174190
-
Wachenchauzer, The intrinsic complexity of parametric elimination methods
-
J. Heintz, G. Matera, Luis M. Pardo, R. Wachenchauzer, The intrinsic complexity of parametric elimination methods, Electron. J. SADIO 1 (1) (1998) 37-51.
-
(1998)
Electron. J. SADIO
, vol.1
, Issue.1
, pp. 37-51
-
-
Heintz, J.1
Matera, G.2
Luis, M.3
Pardo, R.4
-
30
-
-
0001404855
-
Testing polynomials which are easy to compute
-
(an International Symposium in Honour of Ernst Specker), Monographie n. 30 de l'Enseignement Mathématique, (A preliminary version appeared in Proceedings of the 12th Annual ACM Symposium on Computing, 1980, pp. 262-268)
-
J. Heintz, C.P. Schnorr, Testing polynomials which are easy to compute, in: Logic and Algorithmic (an International Symposium in Honour of Ernst Specker), Monographie n. 30 de l'Enseignement Mathématique, 1982, pp. 237-254 (A preliminary version appeared in Proceedings of the 12th Annual ACM Symposium on Computing, 1980, pp. 262-268).
-
(1982)
Logic and Algorithmic
, pp. 237-254
-
-
Heintz, J.1
Schnorr, C.P.2
-
31
-
-
0029487224
-
Approximating the volume of definable sets
-
36th Annual IEEE Symposium FOCS
-
P. Koiran, Approximating the volume of definable sets, in: 36th Annual IEEE Symposium FOCS, 1995, pp. 134-141.
-
(1995)
, pp. 134-141
-
-
Koiran, P.1
-
32
-
-
0000697864
-
A computational method for diophantine approximation
-
Birkhäuser, Basel
-
T. Krick, L.M. Pardo, A computational method for diophantine approximation, in: Algorithms in Algebraic Geometry and Applications, Proceedings MEGA'94, Progress in Mathematics, Vol. 143, Birkhäuser, Basel, 1996, pp. 193-254.
-
(1996)
Algorithms in Algebraic Geometry and Applications, Proceedings MEGA'94, Progress in Mathematics
, vol.143
, pp. 193-254
-
-
Krick, T.1
Pardo, L.M.2
-
33
-
-
0001555828
-
Sombra, Sharp estimates for the arithmetic nullstellensatz
-
T. Krick, Luis M. Pardo, M. Sombra, Sharp estimates for the arithmetic nullstellensatz, Duke Math. J. 109 (2001) 521-598.
-
(2001)
Duke Math. J.
, vol.109
, pp. 521-598
-
-
Krick, T.1
Luis, M.2
Pardo, M.3
-
34
-
-
0004281096
-
Une Alternative aux Méthodes de Réécriture pour la Résolution des Systèmes Algébriques
-
Ph.D. Thesis, École Polytechnique, France
-
G. Lecerf, Une Alternative aux Méthodes de Réécriture pour la Résolution des Systèmes Algébriques, Ph.D. Thesis, École Polytechnique, France, 2001.
-
(2001)
-
-
Lecerf, G.1
-
35
-
-
0000605515
-
Sylvester-Habicht sequences and fast cauchy index computation
-
T. Lickteig, M.F. Roy, Sylvester-Habicht sequences and fast cauchy index computation, J. Symb. Comput. 31 (2001) 315-341.
-
(2001)
J. Symb. Comput.
, vol.31
, pp. 315-341
-
-
Lickteig, T.1
Roy, M.F.2
-
36
-
-
0004167555
-
-
Lecture Notes, Institut des Hautes Etudes Scientiques, Presses Universitaires de France
-
S. Lojasiewicz, Ensembles Semi-Analytiques, Lecture Notes, Institut des Hautes Etudes Scientiques, Presses Universitaires de France, 1966.
-
(1966)
Ensembles Semi-Analytiques
-
-
Lojasiewicz, S.1
-
37
-
-
0003062680
-
Generalised polynomial remainder sequences
-
B. Buchberger, G.E. Collins, R. Loos, R. Albrecht (Eds.), Springer, Berlin
-
R. Loos, Generalised polynomial remainder sequences, in: B. Buchberger, G.E. Collins, R. Loos, R. Albrecht (Eds.), Computer Algebra, Symbolic and Algebraic Computation, Springer, Berlin, 1982.
-
(1982)
Computer Algebra, Symbolic and Algebraic Computation
-
-
Loos, R.1
-
38
-
-
84966260816
-
On the Betti numbers of real varieties
-
J. Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964) 275-280.
-
(1964)
Proc. Amer. Math. Soc.
, vol.15
, pp. 275-280
-
-
Milnor, J.1
-
40
-
-
0344237865
-
On some arithmetical results in the geometry of numbers
-
L.J. Mordell, On some arithmetical results in the geometry of numbers, Compositio Math. 1 (1934) 248-253.
-
(1934)
Compositio Math.
, vol.1
, pp. 248-253
-
-
Mordell, L.J.1
-
41
-
-
0001632852
-
Estimates of the Betti numbers of real algebraic hypersurfaces
-
O.A. Oleinik, Estimates of the Betti numbers of real algebraic hypersurfaces, Mat. Sbornik 70 (1951) 635-640.
-
(1951)
Mat. Sbornik
, vol.70
, pp. 635-640
-
-
Oleinik, O.A.1
-
42
-
-
0345100090
-
On the topology of real algebraic surfaces
-
(Trans. of the Amer. Math. Soc.)
-
O.A. Oleinik, I.B. Petrovsky, On the topology of real algebraic surfaces, Izv. Akad. Nauk SSSR (in Trans. of the Amer. Math. Soc.) 1 (1962) 399-417.
-
(1962)
Izv. Akad. Nauk SSSR
, vol.1
, pp. 399-417
-
-
Oleinik, O.A.1
Petrovsky, I.B.2
-
43
-
-
84955604612
-
How lower and upper complexity bounds meet in elimination theory
-
G.Cohen, M. Giusti, T. Mora (Eds.), Proceedings of the 11th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes AAECC-11, Paris Springer, Berlin
-
L.M. Pardo, How lower and upper complexity bounds meet in elimination theory, in: G. Cohen, M. Giusti, T. Mora (Eds.), Proceedings of the 11th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris, Lecture Notes in Computer Science, Vol. 948, Springer, Berlin, 1995, pp. 33-69.
-
(1995)
Lecture Notes in Computer Science
, vol.948
, pp. 33-69
-
-
Pardo, L.M.1
-
44
-
-
0344669297
-
Universal elimination requires exponential running time
-
(Extended Abstract), A. Montes (Ed.), Barcelona
-
L.M. Pardo, Universal elimination requires exponential running time (Extended Abstract), in: A. Montes (Ed.), Proceedings EACA' 2000, Barcelona, 2000, pp. 25-51.
-
(2000)
Proceedings EACA' 2000
, pp. 25-51
-
-
Pardo, L.M.1
-
45
-
-
0002172421
-
Basic algorithms in real algebraic geometry and their complexity: From Sturm's theorem to the existential theory of reals
-
F. Broglia (Ed.), Walter de Gruyter and Co
-
M.F. Roy, Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals, in: F. Broglia (Ed.), Lecture on Real Algebraic Geometry in Memoriam of Mario Raimondo, de Gruyter Expositions in Mathematics, Vol. 23, Walter de Gruyter and Co. 1996, pp. 1-67.
-
(1996)
Lecture on Real Algebraic Geometry in Memoriam of Mario Raimondo, De Gruyter Expositions in Mathematics
, vol.23
, pp. 1-67
-
-
Roy, M.F.1
-
46
-
-
0001096069
-
A new decision method for elementary algebra
-
A. Seidenberg, A new decision method for elementary algebra, Ann. Math. 60 (2) (1954) 365-374.
-
(1954)
Ann. Math.
, vol.60
, Issue.2
, pp. 365-374
-
-
Seidenberg, A.1
-
47
-
-
0001861435
-
Some remark's on Bézout's theorem and complexity theory
-
M. Hirsch, J. Marsden, M. Shub (Eds.), Springer
-
M. Shub, Some remark's on Bézout's theorem and complexity theory, in: M. Hirsch, J. Marsden, M. Shub (Eds.), From Topology to Computation: Proceedings of the Smalefest, Springer, 1993, pp. 443-455.
-
(1993)
From Topology to Computation: Proceedings of the Smalefest
, pp. 443-455
-
-
Shub, M.1
-
48
-
-
0000537756
-
Complexity of Bézout's theorem II: Volumes and probabilities
-
Birkhäuser, Basel
-
M. Shub, S. Smale, Complexity of Bézout's theorem II: volumes and probabilities, in: Proceedings MEGA' 92, Progress in Mathematics, Vol. 109, Birkhäuser, Basel, 1993, pp. 267-285.
-
(1993)
Proceedings MEGA' 92, Progress in Mathematics
, vol.109
, pp. 267-285
-
-
Shub, M.1
Smale, S.2
-
49
-
-
84968505377
-
Complexity of Bézout's theorem I: Geometric aspects
-
M. Shub, S. Smale, Complexity of Bézout's theorem I: geometric aspects, J. Amer. Math. Soc. 6 (1993) 459-501.
-
(1993)
J. Amer. Math. Soc.
, vol.6
, pp. 459-501
-
-
Shub, M.1
Smale, S.2
-
50
-
-
0000675799
-
Complexity of Bezout's theorem. IV: Probability of success; extensions
-
M. Shub, S. Smale, Complexity of Bezout's theorem. IV: probability of success; extensions, SIAM J. Numer. Anal. 33 (1996) 128-148.
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, pp. 128-148
-
-
Shub, M.1
Smale, S.2
-
52
-
-
0002586126
-
Sur l'Homologie des Variétés Algébriques Réelles
-
Princeton University Press, Princeton
-
R. Thom, Sur l'Homologie des Variétés Algébriques Réelles, in: Differential and Combinatorial Topology, A Symposium in Honor of Marston Morse, Princeton University Press, Princeton, 1965, pp. 255-265.
-
(1965)
Differential and Combinatorial Topology, A Symposium in Honor of Marston Morse
, pp. 255-265
-
-
Thom, R.1
-
53
-
-
84968464817
-
Some extremal functions in Fourier analysis
-
J.D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (NS) 12 (1985) 183-216.
-
(1985)
Bull. Amer. Math. Soc. (NS)
, vol.12
, pp. 183-216
-
-
Vaaler, J.D.1
-
54
-
-
84968495010
-
Lower bounds for approximation by non linear manifolds
-
H.E. Warren, Lower bounds for approximation by non linear manifolds, Trans. AMS 133 (1968) 167-178.
-
(1968)
Trans. AMS
, vol.133
, pp. 167-178
-
-
Warren, H.E.1
-
55
-
-
0037960194
-
Über die Gleichverteilung von Zahlen Modulo 1
-
H. Weyl, Über die Gleichverteilung von Zahlen Modulo 1, Math. Ann. 77 (1916) 313-352.
-
(1916)
Math. Ann.
, vol.77
, pp. 313-352
-
-
Weyl, H.1
|