-
1
-
-
0001906678
-
Zeroes, multiplicities and idempotents for zerodimensional systems
-
L. González and T. Recio, eds. (Birkhäuser, Basel)
-
M.E. Alonso, E. Becker, M.-F, Roy and T. Wörmann, Zeroes, multiplicities and idempotents for zerodimensional systems, in: L. González and T. Recio, eds., Algorithms in Algebraic Geometry and Applications, Progress in Mathematics, Vol. 142 (Birkhäuser, Basel, 1996) 1-15.
-
(1996)
Algorithms in Algebraic Geometry and Applications, Progress in Mathematics
, vol.142
, pp. 1-15
-
-
Alonso, M.E.1
Becker, E.2
Roy, M.-F.3
Wörmann, T.4
-
2
-
-
0000197849
-
Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levine formula
-
L. González and T. Recio, Eds. (Birkhäuser, Basel)
-
E. Becker, J.P. Cardinal, M.-F. Roy and Z. Szafraniec, Multivariate Bezoutians, Kronecker symhol and Eisenbud-Levine formula, in: L. González and T. Recio, Eds., Algorithms in Algebraic Geometry and Applications, Progress in Mathematics, Vol. 142 (Birkhäuser, Basel, 1996) 79-104.
-
(1996)
Algorithms in Algebraic Geometry and Applications, Progress in Mathematics
, vol.142
, pp. 79-104
-
-
Becker, E.1
Cardinal, J.P.2
Roy, M.-F.3
Szafraniec, Z.4
-
6
-
-
0021388907
-
On computing the determinant in small parallel time using a small number of processors
-
S.J. Berkowitz, On computing the determinant in small parallel time using a small number of processors, Inf. Proc. Lett. 18 (1984) 147-150.
-
(1984)
Inf. Proc. Lett.
, vol.18
, pp. 147-150
-
-
Berkowitz, S.J.1
-
8
-
-
0011044244
-
Un analogue arithmétique du théorème de Bézout
-
J.-B. Bost, H. Gillet and C. Soulé, Un analogue arithmétique du théorème de Bézout, C.R. Acad. Sci. Paris, Série I, Math. 312 (1991) 845-848.
-
(1991)
C.R. Acad. Sci. Paris, Série I, Math.
, vol.312
, pp. 845-848
-
-
Bost, J.-B.1
Gillet, H.2
Soulé, C.3
-
10
-
-
0001259424
-
Bounds for the degree in the Nullstellensatz
-
D.W. Brownawell, Bounds for the degree in the Nullstellensatz, Ann. Math. 126 (1987) 577-591.
-
(1987)
Ann. Math.
, vol.126
, pp. 577-591
-
-
Brownawell, D.W.1
-
12
-
-
0001250424
-
Borne simplement exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque
-
L. Caniglia, A. Galligo and J. Heintz, Borne simplement exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque, C.R. Acad. Sci. Paris, Série I, Math. 307 (1988) 255-258.
-
(1988)
C.R. Acad. Sci. Paris, Série I, Math.
, vol.307
, pp. 255-258
-
-
Caniglia, L.1
Galligo, A.2
Heintz, J.3
-
13
-
-
85027644628
-
Some new effectivity bounds in computational geometry
-
T. Mora, Ed.
-
L. Caniglia, A. Galligo and J. Heintz, Some new effectivity bounds in computational geometry, in: T. Mora, Ed., Proc. AAECC-6, Lecture Notes in Computer Science, Vol. 357 (1989) 131-152.
-
(1989)
Proc. AAECC-6, Lecture Notes in Computer Science
, vol.357
, pp. 131-152
-
-
Caniglia, L.1
Galligo, A.2
Heintz, J.3
-
16
-
-
0000538288
-
Fast parallel matrix inversion algorithms
-
L. Csanky, Fast parallel matrix inversion algorithms, SIAM J. Comp. 5 (1976) 618-623.
-
(1976)
SIAM J. Comp.
, vol.5
, pp. 618-623
-
-
Csanky, L.1
-
18
-
-
0001049080
-
-
preprint, Univ. Paul Sabatier, Toulouse
-
J.-P. Dedieu, Approximate solutions of numerical problems, condition number analysis and condition number theorems, preprint, Univ. Paul Sabatier, Toulouse, 1995.
-
(1995)
Approximate Solutions of Numerical Problems, Condition Number Analysis and Condition Number Theorems
-
-
Dedieu, J.-P.1
-
19
-
-
0000608946
-
Bornes pour le degré et les hauteurs dans le problème de division
-
M. Elkadi, Bornes pour le degré et les hauteurs dans le problème de division, Michigan Math. J. 40 (1993) 609-618.
-
(1993)
Michigan Math. J.
, vol.40
, pp. 609-618
-
-
Elkadi, M.1
-
21
-
-
0000252436
-
Diophantine approximation on abelian varieties
-
G. Fallings, Diophantine approximation on abelian varieties, Ann. Math. 133 (1991) 549-576.
-
(1991)
Ann. Math.
, vol.133
, pp. 549-576
-
-
Fallings, G.1
-
22
-
-
0000415960
-
Sur la complexité du théorème des zéros
-
M. Florenzano et al., Eds. (Peter Lang Verlag, Frankfurt
-
N. Fitchas, M. Giusti and F. Smietanski, Sur la complexité du théorème des zéros, in: M. Florenzano et al., Eds., Approximation and Optimization in the Caribbean II. Proc. 2nd Internat. Conf. on Approximation and Optimization, La Habana, 1993, Approximation and Optimization (Peter Lang Verlag, Frankfurt, 1995) 274-329.
-
(1995)
Approximation and Optimization in the Caribbean II. Proc. 2nd Internat. Conf. on Approximation and Optimization, La Habana, 1993, Approximation and Optimization
, pp. 274-329
-
-
Fitchas, N.1
Giusti, M.2
Smietanski, F.3
-
23
-
-
85034753633
-
Algebraic solution of systems of polynomial equations using Gröbner bases
-
Springer, Berlin
-
P. Gianni and T. Mora, Algebraic solution of systems of polynomial equations using Gröbner bases, in: Proc. AAECC-5, LNCS, Vol. 356 (Springer, Berlin, 1989) 247-257.
-
(1989)
Proc. AAECC-5, LNCS
, vol.356
, pp. 247-257
-
-
Gianni, P.1
Mora, T.2
-
24
-
-
0000936391
-
La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial
-
D. Eisenbud and L. Robbiano, Eds. Computational Algebraic Geometry and Commutative Algebra, Istituto Nazionale di Alta Matematica (Cambridge Univ. Press, Cambridge)
-
M. Giusti and J. Heintz, La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial, in: D. Eisenbud and L. Robbiano, Eds., Computational Algebraic Geometry and Commutative Algebra, Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica, vol. XXXIV, Istituto Nazionale di Alta Matematica (Cambridge Univ. Press, Cambridge, 1993).
-
(1993)
Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica
, vol.34
-
-
Giusti, M.1
Heintz, J.2
-
25
-
-
0040645028
-
Straight-line programs in geometric elimination theory
-
to appear
-
M. Giusti, J. Heintz, J.E. Morais, J. Morgenstern and L.M. Pardo, Straight-line programs in geometric elimination theory, J. Pure Appl. Algebra, to appear.
-
J. Pure Appl. Algebra
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Morgenstern, J.4
Pardo, L.M.5
-
26
-
-
84955611783
-
When polynomial equation systems can be "solved" fast?
-
G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris 1995. (Springer, Berlin)
-
M. Giusti, J. Heintz, J.E. Morais and L.M. Pardo, When polynomial equation systems can be "solved" fast? in: G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris 1995, Lecture Notes in Computer Science, Vol. 948 (Springer, Berlin, 1995) 205-231.
-
(1995)
Lecture Notes in Computer Science
, vol.948
, pp. 205-231
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Pardo, L.M.4
-
27
-
-
0001905196
-
On the efficiency of effective Nullstellensätze
-
M. Giusti, J. Heintz and J. Sabia, On the efficiency of effective Nullstellensätze, Comput. Complexity 3 (1993) 56-95.
-
(1993)
Comput. Complexity
, vol.3
, pp. 56-95
-
-
Giusti, M.1
Heintz, J.2
Sabia, J.3
-
28
-
-
0000627865
-
Fast quantifier elimination over algebraically closed fields
-
J. Heintz, Fast quantifier elimination over algebraically closed fields, Theoret. Comput. Sci. 24 (1983) 239-277.
-
(1983)
Theoret. Comput. Sci.
, vol.24
, pp. 239-277
-
-
Heintz, J.1
-
29
-
-
0010993169
-
-
(Leningrad branch of the Mathematical Institute Steklov), Nauka, Leningrad
-
J. Heintz, T. Krick, A. Slissenko and P. Solernó, Searching for a shortest path surrounding semi- algebraic obstacles in the plane (in russian): Teorija sloznosti vyčislenij, 5, Zapiski naučnyh seminarov LOMI (Leningrad branch of the Mathematical Institute Steklov), Nauka, Leningrad, Vol. 192 (1991) 163-173.
-
(1991)
Searching for a Shortest Path Surrounding Semi-algebraic Obstacles in the Plane (in Russian): Teorija Sloznosti Vyčislenij, 5, Zapiski Naučnyh Seminarov LOMI
, vol.192
, pp. 163-173
-
-
Heintz, J.1
Krick, T.2
Slissenko, A.3
Solernó, P.4
-
31
-
-
0001197574
-
On the intrinsic complexity of elimination theory
-
J. Heintz and J. Morgenstern, On the intrinsic complexity of elimination theory, J. Complexity 9 (1993) 471-498.
-
(1993)
J. Complexity
, vol.9
, pp. 471-498
-
-
Heintz, J.1
Morgenstern, J.2
-
32
-
-
84944060784
-
Testing polynomials which are easy to compute
-
J. Heintz and C.P. Schnorr, Testing polynomials which are easy to compute, Proc. 12th Ann. ACM Symp. on Computing (1980) 262-268; also in Logic and Algorithmic. An Internat. Symp. held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève (1982) 237-254.
-
(1980)
Proc. 12th Ann. ACM Symp. on Computing
, pp. 262-268
-
-
Heintz, J.1
Schnorr, C.P.2
-
33
-
-
85119635775
-
-
An Internat. Symp. held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève
-
J. Heintz and C.P. Schnorr, Testing polynomials which are easy to compute, Proc. 12th Ann. ACM Symp. on Computing (1980) 262-268; also in Logic and Algorithmic. An Internat. Symp. held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève (1982) 237-254.
-
(1982)
Logic and Algorithmic
, pp. 237-254
-
-
-
34
-
-
84968474102
-
Sharp Effective Nullstellensatz
-
J. Kollár, Sharp Effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988) 963-975.
-
(1988)
J. Amer. Math. Soc.
, vol.1
, pp. 963-975
-
-
Kollár, J.1
-
35
-
-
0000697864
-
A computational method for diophantine approximation
-
L. González and T. Recio, eds. (Birkhäuser, Basel)
-
T. Krick and L.M. Pardo, A computational method for diophantine approximation, in: L. González and T. Recio, eds., Algorithms in Algebraic Geometry and Applications, Progress in Mathematics, Vol. 142 (Birkhäuser, Basel, 1996) 193-254.
-
(1996)
Algorithms in Algebraic Geometry and Applications, Progress in Mathematics
, vol.142
, pp. 193-254
-
-
Krick, T.1
Pardo, L.M.2
-
36
-
-
0001379976
-
Une approche informatique pour l'approximation diophantienne
-
Série I
-
T. Krick and L.M. Pardo, Une approche informatique pour l'approximation diophantienne, C.R. Acad. Sci. Paris, t. 318, Série I (5) (1994) 407-412.
-
(1994)
C.R. Acad. Sci. Paris
, vol.318
, Issue.5
, pp. 407-412
-
-
Krick, T.1
Pardo, L.M.2
-
39
-
-
0003242570
-
Generic Local Structure of the Morphisms in Commutative Algebra
-
Springer, Berlin
-
B. Iversen, Generic Local Structure of the Morphisms in Commutative Algebra, Lecture Notes in Computer Science, Vol. 310 (Springer, Berlin, 1973).
-
(1973)
Lecture Notes in Computer Science
, vol.310
-
-
Iversen, B.1
-
43
-
-
84936242145
-
Estimates for the order of zero o functions of a certain class and applications in the theory of transcendental numbers
-
Yu.V. Nesterenko, Estimates for the order of zero o functions of a certain class and applications in the theory of transcendental numbers. Math. USSR Izvestija 11 (2) (1977) 239-270.
-
(1977)
Math. USSR Izvestija
, vol.11
, Issue.2
, pp. 239-270
-
-
Nesterenko, Yu.V.1
-
44
-
-
0000789663
-
On a measure of the algebraic independence of the values of certain functions
-
Yu.V. Nesterenko, On a measure of the algebraic independence of the values of certain functions. Math. USSR Sbornik 56 (1987) 545-567.
-
(1987)
Math. USSR Sbornik
, vol.56
, pp. 545-567
-
-
Nesterenko, Yu.V.1
-
45
-
-
84955604612
-
How lower and upper complexity bounds meet in elimination theory
-
G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error- Correcting Codes, AAECC-11, Paris 1995. (Springer, Berlin)
-
L.M. Pardo, How lower and upper complexity bounds meet in elimination theory, in: G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error- Correcting Codes, AAECC-11, Paris 1995, Lecture Notes in Computer Science, Vol. 948 (Springer, Berlin, 1995) 33-69.
-
(1995)
Lecture Notes in Computer Science
, vol.948
, pp. 33-69
-
-
Pardo, L.M.1
-
46
-
-
51249177761
-
Critères pour l'independence algébrique
-
P. Philippon, Critères pour l'independence algébrique, Pub. Math. de l'IHFS 64 (1987) 5-52.
-
(1987)
Pub. Math. de l'IHFS
, vol.64
, pp. 5-52
-
-
Philippon, P.1
-
47
-
-
0000572440
-
Sur des hauteurs alternatives, I
-
P. Philippon, Sur des hauteurs alternatives, I, Math. Ann. 289 (1991) 255-283.
-
(1991)
Math. Ann.
, vol.289
, pp. 255-283
-
-
Philippon, P.1
-
48
-
-
0000924409
-
Sur des hauteurs alternatives, II
-
P. Philippon, Sur des hauteurs alternatives, II, Ann. Inst. Fourier, Grenoble, 44 (2) (1994) 1043-1065.
-
(1994)
Ann. Inst. Fourier, Grenoble
, vol.44
, Issue.2
, pp. 1043-1065
-
-
Philippon, P.1
-
49
-
-
0000801815
-
Sur des hauteurs alternatives, III
-
P. Philippon, Sur des hauteurs alternatives, III, J. Math. Pures Appl. 74 (1995) 345-365.
-
(1995)
J. Math. Pures Appl.
, vol.74
, pp. 345-365
-
-
Philippon, P.1
-
50
-
-
0000874914
-
Bounds for traces in complete intersections and degrees in the Nullstellensatz
-
J. Sabia and P, Solernó, Bounds for traces in complete intersections and degrees in the Nullstellensatz, Appl. Algebra in Eng. Commun. Comput. (AAECC J.) 6 (1996) 353-376.
-
(1996)
Appl. Algebra in Eng. Commun. Comput. (AAECC J.)
, vol.6
, pp. 353-376
-
-
Sabia, J.1
Solernó, P.2
-
52
-
-
84968505377
-
Complexity of Bezout's theorem I: Geometric aspects
-
M. Shub and S. Smale, Complexity of Bezout'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
-
53
-
-
0000537756
-
Complexity of Bezout's theorem II: Volumes and probabilities
-
F. Eyssette and A. Galligo, eds. (Birkhäuser, Basel)
-
M. Shub and S. Smale, Complexity of Bezout's theorem II: Volumes and probabilities, in: F. Eyssette and A. Galligo, eds., Computational Algebraic Geometry, Progress in Mathematics, Vol. 109 (Birkhäuser, Basel, 1993) 267-285.
-
(1993)
Computational Algebraic Geometry, Progress in Mathematics
, vol.109
, pp. 267-285
-
-
Shub, M.1
Smale, S.2
-
54
-
-
0002102930
-
Complexity of Bezout's theorem III: Condition number and packing
-
M. Shub and S. Smale, Complexity of Bezout's theorem III: condition number and packing, J. Complexity 9 (1993) 4-14.
-
(1993)
J. Complexity
, vol.9
, pp. 4-14
-
-
Shub, M.1
Smale, S.2
-
55
-
-
0028516294
-
Complexity of Bezout's theorem V: Polynomial time
-
M. Shub and S. Smale, Complexity of Bezout's theorem V: polynomial time, Theoret. Comput. Sci. 133 (1994).
-
Theoret. Comput. Sci.
, vol.133
, Issue.1994
-
-
Shub, M.1
Smale, S.2
-
56
-
-
0011037169
-
On the intractability of Hubert's Nullstellensatz and an algebraic version of NP ≠ P?
-
Yorktown Heights
-
M. Shub and S. Smale, On the intractability of Hubert's Nullstellensatz and an algebraic version of NP ≠ P?, IBM Research Report, Yorktown Heights (1994).
-
(1994)
IBM Research Report
-
-
Shub, M.1
Smale, S.2
-
57
-
-
0000675799
-
Complexity of Bezout's theorem IV: Probability of success, extensions
-
to appear
-
M. Shub and S. Smale, Complexity of Bezout's theorem IV: probability of success, extensions, SIAM J. Numer. Anal., to appear.
-
SIAM J. Numer. Anal.
-
-
Shub, M.1
Smale, S.2
-
58
-
-
0010951612
-
-
Personal communication
-
C. Soulé, Personal communication.
-
-
-
Soulé, C.1
|