-
1
-
-
3142641823
-
Zeroes, multiplicites and idempotents for zerodimensional systems
-
to appear
-
[1] M.E. Alonso, E. Becker, M.-F. Roy and T. Wörmann, Zeroes, multiplicites and idempotents for zerodimensional systems, Proc. MEGA'94, Birkhäuser Progress in Mathematics, to appear.
-
Proc. MEGA'94, Birkhäuser Progress in Mathematics
-
-
Alonso, M.E.1
Becker, E.2
Roy, M.-F.3
Wörmann, T.4
-
2
-
-
0005478995
-
The complexity of partial derivatives
-
[2] W. Baur and V. Strassen, The complexity of partial derivatives, Theoret. Comput. Sci. 22 (1982) 317-330.
-
(1982)
Theoret. Comput. Sci.
, vol.22
, pp. 317-330
-
-
Baur, W.1
Strassen, V.2
-
5
-
-
0021388907
-
On computing the determinant in small parallel time using a small number of processors
-
[5] 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
-
6
-
-
0001369361
-
Sur le degré des relations entre polynômes
-
[6] J. Briançon, Sur le degré des relations entre polynômes, C.R. Acad. Sci. Paris Sér. I Math. 297 (1982) 553-556.
-
(1982)
C.r. Acad. Sci. Paris Sér. I Math.
, vol.297
, pp. 553-556
-
-
Briançon, J.1
-
7
-
-
0001259424
-
Bounds for the degree in the Nullstellensatz
-
[7] 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
-
8
-
-
0001250424
-
Borne simplement exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque
-
[8] 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. Sér. I Math. 307 (1988) 255-258.
-
(1988)
C.r. Acad. Sci. Paris. Sér. I Math.
, vol.307
, pp. 255-258
-
-
Caniglia, L.1
Galligo, A.2
Heintz, J.3
-
9
-
-
85027644628
-
Some new effectivity bounds in computational geometry
-
T. Mora, Ed., Springer, Berlin
-
[9] 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 (Springer, Berlin, 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
-
13
-
-
0000232715
-
-
manuscript University Bonn
-
[13] F. Cucker, M. Karpinski, P. Koiran, T. Lickteig and K. Werther, On real Turing machines that toss coins, manuscript University Bonn, 1995.
-
(1995)
On Real Turing Machines That Toss Coins
-
-
Cucker, F.1
Karpinski, M.2
Koiran, P.3
Lickteig, T.4
Werther, K.5
-
14
-
-
38249007719
-
m, Y)
-
m, Y), J. Number Theory 42(2) (1992) 141-157.
-
(1992)
J. Number Theory
, vol.42
, Issue.2
, pp. 141-157
-
-
Dèbes, P.1
-
15
-
-
0000006297
-
A probabilistic remark on algebraic program testing
-
[15] R.A. De Millo and R.J. Lipton, A probabilistic remark on algebraic program testing, Inform. Process. Lett. Vol. 7 (4) (1978) 193-195.
-
(1978)
Inform. Process. Lett.
, vol.7
, Issue.4
, pp. 193-195
-
-
De Millo, R.A.1
Lipton, R.J.2
-
16
-
-
0003208975
-
The membership problem of unmixed ideals is solvable in single exponential time
-
[16] A. Dickenstein, N. Fitchas, M. Giusti and C. Sessa, The membership problem of unmixed ideals is solvable in single exponential time, Discrete Appl. Math. 33 (1991) 73-94.
-
(1991)
Discrete Appl. Math.
, vol.33
, pp. 73-94
-
-
Dickenstein, A.1
Fitchas, N.2
Giusti, M.3
Sessa, C.4
-
17
-
-
38249006094
-
A combinatorial proof of effective Nullstellensatz
-
[17] T.W. Dubé, A combinatorial proof of effective Nullstellensatz, J. Symbol. Comput. 15 (1993) 277-296.
-
(1993)
J. Symbol. Comput.
, vol.15
, pp. 277-296
-
-
Dubé, T.W.1
-
18
-
-
0000198793
-
Évaluation dynamique et clôture algébrique en axiom
-
[18] D. Duval, Évaluation dynamique et clôture algébrique en axiom, J. Pure Appl. Algebra 99 (1995) 267-295.
-
(1995)
J. Pure Appl. Algebra
, vol.99
, pp. 267-295
-
-
Duval, D.1
-
19
-
-
0000415960
-
Sur la complexité du théorème des zéros
-
M. Florenzano et al., Eds., Approximation and Optimization Peter Lang Verlag, Frankfurt
-
[19] 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
, pp. 274-329
-
-
Fitchas, N.1
Giusti, M.2
Smietanski, F.3
-
20
-
-
51249178457
-
On the Sprindžuk-Weissauer approach to universal Hilbert subsets
-
[20] M. Fried, On the Sprindžuk-Weissauer approach to universal Hilbert subsets, Israel J. Math. 51 (4) (1985) 347-363.
-
(1985)
Israel J. Math.
, vol.51
, Issue.4
, pp. 347-363
-
-
Fried, M.1
-
21
-
-
0004233493
-
-
Ergebnisse der Mathematik, 3 Folge, Band 2 Springer, Berlin
-
[21] W. Fulton, Intersection Theory, Ergebnisse der Mathematik, 3 Folge, Band 2 (Springer, Berlin, 1984).
-
(1984)
Intersection Theory
-
-
Fulton, W.1
-
22
-
-
0003767860
-
-
Prentice-Hall, Englewood Cliffs, NJ
-
[22] C.B. García and W.I. Zangwill, Pathways to Solutions, Fixed Points and Equilibria (Prentice-Hall, Englewood Cliffs, NJ, 1981).
-
(1981)
Pathways to Solutions, Fixed Points and Equilibria
-
-
García, C.B.1
Zangwill, W.I.2
-
23
-
-
84957621752
-
Parallel arithmetic computations: A survey
-
Springer, Berlin
-
[23] J. von zur Gathen, Parallel arithmetic computations: a survey, Proc. 13th Conf. MFCS, Lecture Notes in Computer Science, Vol. 233 (Springer, Berlin, 1986) 93-112.
-
(1986)
Proc. 13th Conf. MFCS, Lecture Notes in Computer Science
, vol.233
, pp. 93-112
-
-
Von Zur Gathen, J.1
-
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., Istituto Nazionale di Alta Matematica Cambridge Univ. Press, Cambridge
-
[24] 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)
Computational Algebraic Geometry and Commutative Algebra, Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica
, vol.34
-
-
Giusti, M.1
Heintz, J.2
-
25
-
-
84955611783
-
When polynomial equation systems can be "solved" fast?
-
G. Cohen, M. Giusti and T. Mora, Eds., Springer, Berlin
-
[25] 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)
Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-correcting Codes, AAECC-11, Paris 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
-
26
-
-
0001905196
-
On the efficiency of effective Nullstellensätze
-
[26] 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
-
27
-
-
84955599076
-
Using symmetric functions to describe the solution of a zero-dimensional ideal
-
G. Cohen, M. Giusti and T. Mora, Eds., Springer, Berlin
-
[27] L. González Vega and G. Trujilo, Using symmetric functions to describe the solution of a zero-dimensional ideal, 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) 232-247.
-
(1995)
Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-correcting Codes, AAECC-11, Paris 1995, Lecture Notes in Computer Science
, vol.948
, pp. 232-247
-
-
Vega, L.G.1
Trujilo, G.2
-
29
-
-
0000627865
-
Fast quantifier elimination over algebraically closed fields
-
[29] 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
-
30
-
-
0001365155
-
On the computational complexity of polynomials and bilinear mappings
-
L. Huguet and A. Poli, Eds., Springer, Berlin
-
[30] J. Heintz, On the computational complexity of polynomials and bilinear mappings, in: L. Huguet and A. Poli, Eds., Proc., 5th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes AAECC-5, Menorca 1987, Lecture Notes in Computer Science, Vol. 356 (Springer, Berlin, 1989) 269-300.
-
Proc., 5th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes AAECC-5, Menorca 1987, Lecture Notes in Computer Science
, vol.356
, Issue.1989
, pp. 269-300
-
-
Heintz, J.1
-
31
-
-
0001197574
-
On the intrinsic complexity of elimination theory
-
[31] 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
-
[32] 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
-
-
85119641402
-
Logic and algorithmic
-
held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève
-
[32] 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)
An Internat. Symp.
, pp. 237-254
-
-
-
34
-
-
0002694831
-
Absolute primality of polynomials is decidable in random polynomial time in the number of the variables
-
Springer, Berlin
-
[33] J. Heintz and M. Sieveking, Absolute primality of polynomials is decidable in random polynomial time in the number of the variables, Proc. 8th Internat. Colloq. on Automata, Languages and Programming ICALP 81, Lecture Notes in Computer Science, Vol. 115 (Springer, Berlin, 1981) 16-28.
-
(1981)
Proc. 8th Internat. Colloq. on Automata, Languages and Programming ICALP 81, Lecture Notes in Computer Science
, vol.115
, pp. 16-28
-
-
Heintz, J.1
Sieveking, M.2
-
35
-
-
84976819141
-
Probabilistic algorithms for deciding equivalence of straight-line programs
-
[34] O. Ibarra and H. Moran, Probabilistic algorithms for deciding equivalence of straight-line programs, J. ACM 30(1) (1983) 217-228.
-
(1983)
J. ACM
, vol.30
, Issue.1
, pp. 217-228
-
-
Ibarra, O.1
Moran, H.2
-
36
-
-
0003242570
-
Generic Local Structures of the Morphisms in Commutative Algebra
-
Springer, Berlin
-
[35] B. Iversen, Generic Local Structures of the Morphisms in Commutative Algebra, Lecture Notes in Math., Vol. 310 (Springer, Berlin, 1973).
-
(1973)
Lecture Notes in Math.
, vol.310
-
-
Iversen, B.1
-
38
-
-
0023826531
-
Greatest common divisors of polynomials given by straight line programs
-
[37] E. Kaltofen, Greatest common divisors of polynomials given by straight line programs, J. ACM 35 (1) (1988) 234-264.
-
(1988)
J. ACM
, vol.35
, Issue.1
, pp. 234-264
-
-
Kaltofen, E.1
-
39
-
-
0010017974
-
Factorization of polynomials given by striaght-line programs
-
S. Micali, Ed., JAI Press Inc., Greenwich, CT
-
[38] E. Kaltofen, Factorization of polynomials given by striaght-line programs, in: S. Micali, Ed., Randomness in Computation, Advances in Computing Research 5 (JAI Press Inc., Greenwich, CT, 1989) 375-412.
-
(1989)
Randomness in Computation, Advances in Computing Research
, vol.5
, pp. 375-412
-
-
Kaltofen, E.1
-
40
-
-
84968474102
-
Sharp effective Nullstellensatz
-
[39] J. Kollár, Sharp effective Nullstellensatz, J. AMS 1 (1988) 963-975.
-
(1988)
J. AMS
, vol.1
, pp. 963-975
-
-
Kollár, J.1
-
41
-
-
0001379976
-
Une approche informatique pour l'approximation diophantienne
-
[40] T. Krick and L.M. Pardo, Une approche informatique pour l'approximation diophantienne, C.R. Acad. Sci. Paris, Sér. 318 (1994) 407-412.
-
(1994)
C.R. Acad. Sci. Paris, Sér.
, vol.318
, pp. 407-412
-
-
Krick, T.1
Pardo, L.M.2
-
44
-
-
0003367986
-
On the complexity of zero-dimensional algebraic systems
-
C. Traverso, Ed., Birkhäuser, Boston
-
[43] Y.N. Lakshman and D. Lazard, On the complexity of zero-dimensional algebraic systems, in: C. Traverso, Ed., Proc. MEGA'90, Progress in Mathematics, Vol. 94 (Birkhäuser, Boston, 1991) 217-225.
-
(1991)
Proc. MEGA'90, Progress in Mathematics
, vol.94
, pp. 217-225
-
-
Lakshman, Y.N.1
Lazard, D.2
-
45
-
-
0002548511
-
Résolution des systèmes d'équations algébriques
-
[44] D. Lazard, Résolution des systèmes d'équations algébriques, Theoret. Comput. Sci. 15 (1981) 77-110.
-
(1981)
Theoret. Comput. Sci.
, vol.15
, pp. 77-110
-
-
Lazard, D.1
-
46
-
-
34250244723
-
Factoring polynomials with rational coefficients
-
[45] A.K. Lenstra, H.W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982) 515-534.
-
(1982)
Math. Ann.
, vol.261
, pp. 515-534
-
-
Lenstra, A.K.1
Lenstra, H.W.2
Lovász, L.3
-
48
-
-
85027646416
-
Systems of algebraic equations solved by means of endomorphisms
-
G. Cohen, T. Mora and O. Moreno, Eds., Springer, Berlin
-
[47] M. Moeller, Systems of algebraic equations solved by means of endomorphisms, in: G. Cohen, T. Mora and O. Moreno, Eds., Proc. 10th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes AAECC-10, Puerto Rico 1993, Lecture Notes in Computer Science (Springer, Berlin, 1993).
-
(1993)
Proc. 10th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes AAECC-10, Puerto Rico 1993, Lecture Notes in Computer Science
-
-
Moeller, M.1
-
49
-
-
0002392671
-
Lower bounds for arithmetic networks
-
[48] J.L. Montaña and L.M. Pardo, Lower bounds for arithmetic networks, AAECC 4 (1993) 1-24.
-
(1993)
AAECC
, vol.4
, pp. 1-24
-
-
Montaña, J.L.1
Pardo, L.M.2
-
51
-
-
84955604612
-
How lower and upper complexity bounds meet in elimination theory
-
Springer, Berlin
-
[50] L.M. Pardo, How lower and upper complexity bounds meet in elimination theory, 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)
Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris 1995, Lecture Notes in Computer Science
, vol.948
, pp. 33-69
-
-
Pardo, L.M.1
-
52
-
-
0002224113
-
Dénominateurs dans le théorème des zéros de Hilbert
-
[51] P. Philippon, Dénominateurs dans le théorème des zéros de Hilbert, Acta Arith. 58 (1991) 1-25.
-
(1991)
Acta Arith.
, vol.58
, pp. 1-25
-
-
Philippon, P.1
-
53
-
-
0000874914
-
Bounds for traces in complete intersections and degrees in the Nullstellensatz
-
[52] J. Sabia and P. Solernó, Bounds for traces in complete intersections and degrees in the Nullstellensatz, AAECC 6 (1995) 353-376.
-
(1995)
AAECC
, vol.6
, pp. 353-376
-
-
Sabia, J.1
Solernó, P.2
-
55
-
-
85036616973
-
On the power of random acces machines
-
[54] A. Schönhage, On the power of random acces machines, Proc. 6th Internat. Conf. on Automata, Languages and Programming, ICALP, Graz (1979) 520-529.
-
(1979)
Proc. 6th Internat. Conf. on Automata, Languages and Programming, ICALP, Graz
, pp. 520-529
-
-
Schönhage, A.1
-
56
-
-
84976779342
-
Fast probabilistic algorithms for verification of polynomial identities
-
[55] J.T. Schwartz, Fast probabilistic algorithms for verification of polynomial identities, J. ACM 27 (1980) 701-717.
-
(1980)
J. ACM
, vol.27
, pp. 701-717
-
-
Schwartz, J.T.1
-
57
-
-
0028516294
-
Complexity of bezout's theorem V: Polynomial time
-
[56] M. Shub and S. Smale, Complexity of Bezout's theorem V: polynomial time, Theoret. Comput. Sci. 133 (1994) 141-164.
-
(1994)
Theoret. Comput. Sci.
, vol.133
, pp. 141-164
-
-
Shub, M.1
Smale, S.2
-
59
-
-
0009983886
-
Diophantine equations involving unknown primes
-
[58] V.G. Sprindžuk, Diophantine equations involving unknown primes, Trudy MIANSSR 158 (1981) 180-196.
-
(1981)
Trudy MIANSSR
, vol.158
, pp. 180-196
-
-
Sprindžuk, V.G.1
-
60
-
-
84961475121
-
Vermeidung von divisionen
-
[59] V. Strassen, Vermeidung von Divisionen, Crelle J. Reine Angew. Math. 264 (1973) 184-202.
-
(1973)
Crelle J. Reine Angew. Math.
, vol.264
, pp. 184-202
-
-
Strassen, V.1
-
61
-
-
0001063303
-
Die Berechungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoffizienten
-
[60] V. Strassen, Die Berechungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoffizienten, Numer. Math. 20 (1973) 238-251.
-
(1973)
Numer. Math.
, vol.20
, pp. 238-251
-
-
Strassen, V.1
-
62
-
-
0001052336
-
Algebraic complexity theory
-
Elsevier, Amsterdam
-
[61] V. Strassen. Algebraic complexity theory, in: Handbook of Theoretical Computer Science, Vol. 11 (Elsevier, Amsterdam, 1990) 634-671.
-
(1990)
Handbook of Theoretical Computer Science
, vol.11
, pp. 634-671
-
-
Strassen, V.1
-
65
-
-
84925463455
-
Probabilistic algorithms for sparse polynomials
-
Springer, Berlin
-
[64] R.E. Zippel, Probabilistic algorithms for sparse polynomials, Lecture Notes in Computer Science, Vol. 72 (Springer, Berlin, 1979) 216-226.
-
(1979)
Lecture Notes in Computer Science
, vol.72
, pp. 216-226
-
-
Zippel, R.E.1
|