-
2
-
-
0001906678
-
Multiplicities and idempotents for zero dimensional systems
-
Birkhäuser
-
Alonso M.E., Becker E., Roy M.-F., Wörmann T. Zeroes, multiplicities and idempotents for zero dimensional systems, in Prog. Math. 143 (1996), pp. 1-16, Birkhäuser.
-
(1996)
Prog. Math
, vol.143
, pp. 1-16
-
-
Alonso, M.E.1
Becker, E.2
Roy, M.-F.3
Zeroes, W.T.4
-
6
-
-
0000631665
-
Triangular set for solving polynomial systems: A comparative implementation of four methods
-
Aubry P., Moreno Maza M., Triangular set for solving polynomial systems: a comparative implementation of four methods, J. Symb. Comp. 28 (1999), 125-154.
-
(1999)
J. Symb. Comp
, vol.28
, pp. 125-154
-
-
Aubry, P.1
Moreno Maza, M.2
-
7
-
-
0346109328
-
Using galois ideals for computing relative resolvents
-
Aubry P., Valibouze A., Using Galois ideals for computing relative resolvents, J. Symb. Comp. 30 (2000), 635-651.
-
(2000)
J. Symb. Comp
, vol.30
, pp. 635-651
-
-
Aubry, P.1
Valibouze, A.2
-
8
-
-
0001308767
-
On the theories of triangular sets
-
Aubry P., Lazard D., Moreno Maza M., On the theories of triangular sets, J. Symb. Comp. 28 (1999), 105-124.
-
(1999)
J. Symb. Comp
, vol.28
, pp. 105-124
-
-
Aubry, P.1
Lazard, D.2
Moreno Maza, M.3
-
9
-
-
0002783070
-
An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations
-
Birkhäuser
-
Auzinger W., Stetter H.J., An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, in I.S.N.M. 86 (1988), pp. 11-30, Birkhäuser.
-
(1988)
I.S.N.M
, vol.86
, pp. 11-30
-
-
Auzinger, W.1
Stetter, H.J.2
-
10
-
-
0000197849
-
Multivariate bezoutians, kronecker symbol and eisenbud-levin formula
-
Birkhäuser
-
Becker E., Cardinal J.-P., Roy M.-F., Szafraniec Z., Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levin formula, in Prog. Math. 143 (1996), pp. 79-104, Birkhäuser.
-
(1996)
Prog. Math
, vol.143
, pp. 79-104
-
-
Becker, E.1
Cardinal, J.-P.2
Roy, M.-F.3
Szafraniec, Z.4
-
11
-
-
0002884078
-
Recherches sur le degré des équations résultantes de l’évanouissement des inconnues, et sur les moyens qu’il convient d’employer pour trouver ses équations
-
Bézout E., Recherches sur le degré des équations résultantes de l’évanouissement des inconnues, et sur les moyens qu’il convient d’employer pour trouver ses équations, Mém. Acad. Roy. Sci. Paris (1764), 288-233.
-
(1764)
Mém. Acad. Roy. Sci. Paris
, pp. 233-288
-
-
Bézout, E.1
-
14
-
-
0346885832
-
Fast algorithm for zero-dimensional polynomial systems using duality
-
Bostajn A., Salvy B., Schost E., Fast algorithm for zero-dimensional polynomial systems using duality, J. AAECC 14 (2003), 239-272.
-
(2003)
J. AAECC
, vol.14
, pp. 239-272
-
-
Bostajn, A.1
Salvy, B.2
Schost, E.3
-
17
-
-
85032875512
-
Generalized characteristic polynomials
-
Springer
-
Canny J., Generalized characteristic polynomials, in L. N. Comp. Sci. 358 (1988), pp. 293-299, Springer.
-
(1988)
L. N. Comp. Sci
, vol.358
, pp. 293-299
-
-
Canny, J.1
-
18
-
-
85010519644
-
An effective algorithm for the sparse mixed resultant
-
Springer
-
Canny J., An effective algorithm for the sparse mixed resultant, in L. N. Comp. Sci. 673 (1993), pp. 89-104, Springer.
-
(1993)
L. N. Comp. Sci
, vol.673
, pp. 89-104
-
-
Canny, J.1
-
20
-
-
0001675230
-
Algebraic approach of residues and applications
-
American Mathematical Society Press
-
Cardinal J.P., Mourrain B., Algebraic approach of residues and applications, in L. N. Appl. Math. 32 (1999), American Mathematical Society Press.
-
(1999)
L. N. Appl. Math
, vol.32
-
-
Cardinal, J.P.1
Mourrain, B.2
-
21
-
-
84952713592
-
Usage des fonctions interpolaires dans ls determination des fonctions sym-metriques des racines d’une équation algébrique donnée
-
Cauchy A., Usage des fonctions interpolaires dans ls determination des fonctions sym-metriques des racines d’une équation algébrique donnée, C.R. Acad. Sci. Paris 11 (1840), 933.
-
(1840)
C.R. Acad. Sci. Paris
, vol.11
, pp. 933
-
-
Cauchy, A.1
-
22
-
-
84952662328
-
-
T. V, Gauthier-Villars, Paris
-
Cauchy A., Oeuvres T. V, Gauthier-Villars, Paris, (1882).
-
(1882)
Oeuvres
-
-
Cauchy, A.1
-
23
-
-
0001713268
-
On the theory of elimination
-
Cayley A., On the theory of elimination, Camb. Dublin Math. J. 3 (1848), 116-120.
-
(1848)
Camb. Dublin Math. J
, vol.3
, pp. 116-120
-
-
Cayley, A.1
-
24
-
-
0011401763
-
Note sur la méthode d’élimination de bezout
-
Cayley A., Note sur la méthode d’élimination de Bezout, J. Reine Ang. Math. 53 (1857), 366-367
-
(1857)
J. Reine Ang. Math
, vol.53
, pp. 366-367
-
-
Cayley, A.1
-
25
-
-
77951154009
-
A fourth memoir upon quantics
-
Cayley, A., A fourth memoir upon quantics, Phil. Trans. Royal Soc. London 168 (1858), 415-427.
-
(1858)
Phil. Trans. Royal Soc. London
, vol.168
, pp. 415-427
-
-
Cayley, A.1
-
26
-
-
84952671363
-
Un algorithm pour les calcul des resultants
-
Birkhäuser
-
Charden M., Un algorithm pour les calcul des resultants, in Prog. Math. 94 (1990), pp. 47-62, Birkhäuser.
-
(1990)
Prog. Math
, vol.94
, pp. 47-62
-
-
Charden, M.1
-
27
-
-
0002912359
-
The resultant via a koszul complex
-
Birkhäuser
-
Charden M., The resultant via a Koszul complex, Prog. Math. 109 (1993), pp. 29-40, Birkhäuser.
-
(1993)
Prog. Math
, vol.109
, pp. 29-40
-
-
Charden, M.1
-
28
-
-
38149093283
-
Comprehensive triangular decomposition
-
Chen C., Golubitsky O., Lemaire F., Moreno Maza M., Comprehensive triangular decomposition, in Proc. CASC2007 (2007), pp. 73-101.
-
(2007)
Proc. CASC
, vol.2007
, pp. 73-101
-
-
Chen, C.1
Golubitsky, O.2
Lemaire, F.3
Moreno Maza, M.4
-
30
-
-
27644512413
-
Sharp estimates for triangular sets
-
Association for Computing Machinery
-
Dahan X., Schost E., Sharp estimates for triangular sets, in Proc. ISSAC’04 (2004), pp. 103-110, Association for Computing Machinery.
-
(2004)
Proc. ISSAC’04
, pp. 103-110
-
-
Dahan, X.1
Schost, E.2
-
31
-
-
33748961047
-
Lifting techniques for triangular decomposition, in
-
Dahan X., Moreno Maza M., Schost E., Wu W., Xie Y., Lifting techniques for triangular decomposition, in Proc. ISSAC’05 (2005), pp. 108-115.
-
(2005)
Proc. ISSAC’05
, pp. 108-115
-
-
Dahan, X.1
Moreno Maza, M.2
Schost, E.3
Wu, W.4
Xie, Y.5
-
32
-
-
84952713593
-
Sur les systèmes algébriques et leurs relations avec certains systèmes d’equations aux dérivées partielles
-
Delassus E., Sur les systèmes algébriques et leurs relations avec certains systèmes d’equations aux dérivées partielles. Ann. Éc. Norm. 3e série 14 (1897), 21-44.
-
(1897)
e série
, vol.14
, pp. 21-44
-
-
Delassus, E.1
-
33
-
-
84960585591
-
On a form of the eliminant of two quantics
-
Dixon, A.L., On a form of the eliminant of two quantics, Proc. London Math. Soc. 6 (1908a), 468-478.
-
(1908)
Proc. London Math. Soc
, vol.6
, pp. 468-478
-
-
Dixon, A.L.1
-
34
-
-
84960589566
-
The eliminant of three quantics in two independent variables
-
Dixon, A.L., The eliminant of three quantics in two independent variables, Proc. London Math. Soc. 7 (1908b), 49-69.
-
(1908)
Proc. London Math. Soc
, vol.7
, pp. 49-69
-
-
Dixon, A.L.1
-
35
-
-
84952713594
-
Some results in the theory of elimination
-
Dixon, A.L., Some results in the theory of elimination, Proc. Roy. Soc. London 82 (1909), 468-478.
-
(1909)
Proc. Roy. Soc. London
, vol.82
, pp. 468-478
-
-
Dixon, A.L.1
-
37
-
-
33645987866
-
The lex game and some applications
-
Felszeghy B., Rath B., Ronyai L., The lex game and some applications, J. Symb. Comp. 41 (2006), 663-681.
-
(2006)
J. Symb. Comp
, vol.41
, pp. 663-681
-
-
Felszeghy, B.1
Rath, B.2
Ronyai, L.3
-
38
-
-
0010070016
-
Effective algorithms and bounds for wu-ritt characteristic sets
-
Birkhäuser
-
Gallo G., Mishra B., Effective algorithms and bounds for Wu-Ritt characteristic sets, in Prog. Math. 94 (1990), pp. 119-142, Birkhäuser.
-
(1990)
Prog. Math
, vol.94
, pp. 119-142
-
-
Gallo, G.1
Mishra, B.2
-
39
-
-
0011417325
-
A solution to kronecker’s problem
-
Gallo G., Mishra, B., A solution to Kronecker’s problem, J. AAECC 5 (1994), 343-370.
-
(1994)
J. AAECC
, vol.5
, pp. 343-370
-
-
Gallo, G.1
Mishra, B.2
-
40
-
-
84955591390
-
Some constructions in rings of differential polynomials
-
Springer
-
Gallo G., Mishra, B., Olivier F., Some constructions in rings of differential polynomials, in L. N. Comp. Sci. 539 (1991), pp. 171-182, Springer.
-
(1991)
L. N. Comp. Sci
, vol.539
, pp. 171-182
-
-
Gallo, G.1
Mishra, B.2
Olivier, F.3
-
41
-
-
85033721578
-
Properties of gröbner bases under specialization
-
Springer
-
Gianni P., Properties of Gröbner bases under specialization, in L. N. Comp. Sci. 378 (1987), pp. 293-297, Springer.
-
(1987)
L. N. Comp. Sci
, vol.378
, pp. 293-297
-
-
Gianni, P.1
-
42
-
-
0000750175
-
Algorithmes-disons rapides-pour la décomposition d’une variété algébrique en composantes irréductibles
-
Birkhäuser
-
Giusti M., Heintz J., Algorithmes-disons rapides-pour la décomposition d’une variété algébrique en composantes irréductibles, in Prog. Math. 94 (1990), pp. 169-194, Birkhäuser.
-
(1990)
Prog. Math
, vol.94
, pp. 169-194
-
-
Giusti, M.1
Heintz, J.2
-
43
-
-
0000936391
-
La detérmination des point isolés et de la dimension d’une variété algébrique peut se faire en temps polynomial
-
Cambridge University Press
-
Giusti M., Heintz J., La detérmination des point isolés et de la dimension d’une variété algébrique peut se faire en temps polynomial, in Symp. Math. 34 (1993), pp. 216-256, Cambridge University Press.
-
(1993)
Symp. Math
, vol.34
, pp. 216-256
-
-
Giusti, M.1
Heintz, J.2
-
44
-
-
85139861192
-
Solving some overdetermined polynomial systems
-
Association for Computing Machinery
-
Giusti M., Schost E., Solving some overdetermined polynomial systems, in Proc. ISSAC’99 (1999), pp. 1-8, Association for Computing Machinery.
-
(1999)
Proc. ISSAC’99
, pp. 1-8
-
-
Giusti, M.1
Schost, E.2
-
45
-
-
84955611783
-
When polynomial equation systems can be “solved” fast?
-
Springer
-
Giusti M., Heintz J., Morais J.E., Pardo L.M., When polynomial equation systems can be “solved” fast?, in L. N. Comp. Sci. 948 (1995), pp. 205-231, Springer.
-
(1995)
L. N. Comp. Sci
, vol.948
, pp. 205-231
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Pardo, L.M.4
-
46
-
-
0031142051
-
Lower bounds for diophantine approximation
-
Giusti M., Heintz J., Hagele K., Moráis J.E., Pardo L.M., Montaña J.M., Lower bounds for diophantine approximation, J. Pure Appl. Algebra 117-118 (1997a), 277-311.
-
(1997)
J. Pure Appl. Algebra
, vol.117-118
, pp. 277-311
-
-
Giusti, M.1
Heintz, J.2
Hagele, K.3
Moráis, J.E.4
Pardo, L.M.5
Montaña, J.M.6
-
47
-
-
0031539424
-
Le rôle des structures de données dans les problèmes d’élimination
-
Giusti M., Heintz J., Morais J.E., Pardo L.M., Le rôle des structures de données dans les problèmes d’élimination, C.R. Acad. Sci. Paris 325 (1997b), 1223-1228.
-
(1997)
C.R. Acad. Sci. Paris
, vol.325
, pp. 1223-1228
-
-
Giusti, M.1
Heintz, J.2
Morais, J.E.3
Pardo, L.M.4
-
48
-
-
0031992346
-
Straight-line programs in geometric elimination theory
-
Giusti M., Heintz J., Morais J.E., Morgensten J., Pardo L.M., 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
Morgensten, J.4
Pardo, L.M.5
-
49
-
-
0034259150
-
The projective noether maple package: Computing the dimension of a projective variety
-
Giusti M., Hagele K., Lecerf G., Marchand J., Salvy B., The projective Noether maple package: computing the dimension of a projective variety, J. Symb. Comp. 30 (2000), 291-307.
-
(2000)
J. Symb. Comp
, vol.30
, pp. 291-307
-
-
Giusti, M.1
Hagele, K.2
Lecerf, G.3
Marchand, J.4
Salvy, B.5
-
50
-
-
0035294718
-
A grobner free alternative for polynomial system solving
-
Giusti M., Lecerf G., Salvy B., A Grobner 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
-
51
-
-
0002377042
-
Symbolic recipes for polynomial system solving
-
A. Cohen, Springer
-
Gonzalez-Vega L., Rouiller F., Roy M.-F., Symbolic recipes for polynomial system solving, in Some Tapas of Computer Algebra, ed. A. Cohen, (1997), Springer.
-
(1997)
Some Tapas of Computer Algebra
-
-
Gonzalez-Vega, L.1
Rouiller, F.2
Roy, M.-F.3
-
53
-
-
84952642114
-
Sur les caractéristiques des systèmes d’équations aux dérivées partialles
-
Gunther N., Sur les caractéristiques des systèmes d’équations aux dérivées partialles, C.R. Acad. Sci. Paris 156 (1913), 1147-1150.
-
(1913)
C.R. Acad. Sci. Paris
, vol.156
, pp. 1147-1150
-
-
Gunther, N.1
-
54
-
-
84918831557
-
Sur la forme canonique des equations algébriques
-
Gunther N., Sur la forme canonique des equations algébriques, C.R. Acad. Sci. Paris 157 (1913), 577-80.
-
(1913)
C.R. Acad. Sci. Paris
, vol.157
, pp. 577-580
-
-
Gunther, N.1
-
55
-
-
0034695774
-
On the intrinsic complexity of the arithmetic nullstellensatz
-
Hagele K., Morais J.E., Pardo L.M., Sombra M., On the intrinsic complexity of the arithmetic Nullstellensatz, J. Pure Appl. Algebra 146 (2000), 103-183.
-
(2000)
J. Pure Appl. Algebra
, vol.146
, pp. 103-183
-
-
Hagele, K.1
Morais, J.E.2
Pardo, L.M.3
Sombra, M.4
-
56
-
-
77957277141
-
Structure et complexité des bases de grobner
-
Hashemi A., Structure et Complexité des bases de Grobner, J. Symb. Comp. 45 (2010), 1330-1340.
-
(2010)
J. Symb. Comp
, vol.45
, pp. 1330-1340
-
-
Hashemi, A.1
-
57
-
-
80051767567
-
Sharper complexity bounds for zero-dimensional grobner bases and polynomial system solving
-
Hashemi A., Lazard D., Sharper complexity bounds for zero-dimensional Grobner bases and polynomial system solving, Int. J. Algebra Comp. 21 (2011), 705-713.
-
(2011)
Int. J. Algebra Comp
, vol.21
, pp. 705-713
-
-
Hashemi, A.1
Lazard, D.2
-
58
-
-
0013416339
-
De eliminatione variabilis e duabus aequationibus algebraicas
-
Jacobi C.G.I., De eliminatione variabilis e duabus aequationibus algebraicas, J. Reine Ang. Math. 15 (1836) 101-124.
-
(1836)
J. Reine Ang. Math
, vol.15
, pp. 101-124
-
-
Jacobi, C.1
-
59
-
-
38149144730
-
Le formalisme du résultant
-
Jouanoulou J.-P., Le formalisme du résultant, Adv. Math. 90 117-263.
-
Adv. Math
, vol.90
, pp. 117-263
-
-
Jouanoulou, J.-P.1
-
60
-
-
85033676092
-
Solving systems of algebraic equations by using grobner bases
-
Springer
-
Kalkbrener M., Solving systems of algebraic equations by using Grobner bases, in L. N. Comp. Sci. 378 (1987), pp. 282-292, Springer.
-
(1987)
N. Comp. Sci
, vol.378
, pp. 282-292
-
-
Kalkbrener, M.1
-
62
-
-
38249006658
-
A generic euclidean algorithm for computing triangular representations of algebraic varieties
-
Kalkbrener M., A generic euclidean algorithm for computing triangular representations of algebraic varieties, J. Symb. Comp. 15 (1993), 153-167.
-
(1993)
J. Symb. Comp
, vol.15
, pp. 153-167
-
-
Kalkbrener, M.1
-
63
-
-
0031185293
-
On the stability of grobner bases under specialization
-
Kalkbrener M., On the stability of Grobner bases under specialization, J. Symb. Comp. 24 (1997), 51-58.
-
(1997)
J. Symb. Comp
, vol.24
, pp. 51-58
-
-
Kalkbrener, M.1
-
64
-
-
72149099072
-
An algorithm for computing a grobner basis of a polynomial ideal over a ring with zero divisors
-
Kapur D., Cai Y., An algorithm for computing a Grobner basis of a polynomial ideal over a ring with zero divisors, Math. Comput. Sci. 2 (2009), 601-634.
-
(2009)
Math. Comput. Sci
, vol.2
, pp. 601-634
-
-
Kapur, D.1
Cai, Y.2
-
65
-
-
0033645331
-
Conditions for exact resultants using the dixon resultant formulation
-
Association for Computing Machinery
-
Kapur D., Chtcherba A.D., Conditions for exact resultants using the Dixon resultant formulation, in Proc. ISSAC 2000 (2000), pp. 62-70, Association for Computing Machinery.
-
(2000)
Proc. ISSAC
, vol.2000
, pp. 62-70
-
-
Kapur, D.1
Chtcherba, A.D.2
-
66
-
-
0036042386
-
On the efficiency and optimality of dixon-based resultant method
-
Association for Computing Machinery
-
Kapur D., Chtcherba A.D., On the efficiency and optimality of Dixon-based resultant method, in Proc. ISSAC 2002 (2002), pp. 29-36, Association for Computing Machinery.
-
(2002)
Proc. ISSAC
, vol.2002
, pp. 29-36
-
-
Kapur, D.1
Chtcherba, A.D.2
-
67
-
-
85020527472
-
Algebraic and geometric reasoning using dixon resultants
-
Association for Computing Machinery
-
Kapur D., Saxena T., Yang, L., Algebraic and geometric reasoning using Dixon resultants, in Proc. ISSAC 94 (1994), pp. 99-136, Association for Computing Machinery.
-
(1994)
Proc. ISSAC
, vol.94
, pp. 99-136
-
-
Kapur, D.1
Saxena, T.2
Yang, L.3
-
68
-
-
0030659943
-
Extraneous factors in the dixon resultant formulation
-
Association for Computing Machinery
-
Kapur D., Saxena T., Extraneous factors in the Dixon resultant formulation, in Proc. ISSAC 97 (1997), pp. 141-148, Association for Computing Machinery.
-
(1997)
Proc. ISSAC
, vol.97
, pp. 141-214
-
-
Kapur, D.1
Saxena, T.2
-
69
-
-
0010051183
-
On radical zero-dimensional ideals
-
Kobayashi H., Moritsugu S., Hogan R.W., On radical zero-dimensional ideals, J. Symb. Comp. 8 (1989), 545-552.
-
(1989)
J. Symb. Comp
, vol.8
, pp. 545-552
-
-
Kobayashi, H.1
Moritsugu, S.2
Hogan, R.W.3
-
71
-
-
0001379976
-
Une approache informatique pour l’approximation diophantienne
-
Krick T., Pardo L.M., Une approache informatique pour l’approximation diophantienne, C.R. Acad. Sci. Paris 318 (1994), 407-412.
-
(1994)
C.R. Acad. Sci. Paris
, vol.318
, pp. 407-412
-
-
Krick, T.1
Pardo, L.M.2
-
72
-
-
0000697864
-
A computational method for diphantine approximation
-
Birkhäuser
-
Krick T., Pardo L.M., A computational method for Diphantine approximation, in Prog. Math. 143 (1996), pp. 193-254, Birkhäuser.
-
(1996)
Prog. Math
, vol.143
, pp. 193-254
-
-
Krick, T.1
Pardo, L.M.2
-
73
-
-
0003367986
-
On the complexity of zero-dimensional algebraic systems
-
Birkhäuser
-
Lakshman Y.N., Lazard D., On the complexity of zero-dimensional algebraic systems, in Prog. Math. 94 (1990), pp. 217-226, Birkhäuser.
-
(1990)
Prog. Math
, vol.94
, pp. 217-226
-
-
Lakshman, Y.N.1
Lazard, D.2
-
74
-
-
0000713722
-
Algèbre linéaire sur k[ap…, xn] et élimination
-
Lazard D., Algèbre linéaire sur K[Ap…, Xn] et élimination, Bull. Soc. Math. France 105 (1977), 165-190.
-
(1977)
Bull. Soc. Math. France
, vol.105
, pp. 165-190
-
-
Lazard, D.1
-
75
-
-
85034863243
-
Systems of algebraic equations
-
Springer
-
Lazard D., Systems of algebraic equations, in L. N. Comp. Sci. 72 (1979), pp. 88-94, Springer.
-
(1979)
L. N. Comp. Sci
, vol.72
, pp. 88-94
-
-
Lazard, D.1
-
76
-
-
0002548511
-
Resolution des systemes d’equations algebriques
-
Lazard, D., Resolution des systemes d’equations algebriques, Theoret. Comput. Sci. 15 (1981), 77-110.
-
(1981)
Theoret. Comput. Sci
, vol.15
, pp. 77-110
-
-
Lazard, D.1
-
77
-
-
0000069912
-
A new method for solving algebraic systems of positive dimension
-
Lazard, D., A new method for solving algebraic systems of positive dimension, Disc. Appl. Math. 33 (1991), 147-160.
-
(1991)
Disc. Appl. Math
, vol.33
, pp. 147-160
-
-
Lazard, D.1
-
78
-
-
0000167385
-
Solving zero-dimensional algebraic systems
-
Lazard D., Solving zero-dimensional algebraic systems, J. Symb. Comp. 15 (1992), 117-132.
-
(1992)
J. Symb. Comp
, vol.15
, pp. 117-132
-
-
Lazard, D.1
-
79
-
-
33645954818
-
Systems of algebraic equations (Algorithms and complexity)
-
Cambridge University Press
-
Lazard D., Systems of algebraic equations (algorithms and complexity), Symp. Math. 34 (1993), 84-106, Cambridge University Press.
-
(1993)
Symp. Math
, vol.34
, pp. 84-106
-
-
Lazard, D.1
-
80
-
-
84865533115
-
Resolution of polynomial systems
-
World Scientific
-
Lazard D., Resolution of polynomial systems, in Proc. ASCM 2000 (2000), pp. 1-8, World Scientific.
-
(2000)
Proc. ASCM
, vol.2000
, pp. 1-8
-
-
Lazard, D.1
-
81
-
-
84952671742
-
On the specification for solvers of polynomial systems
-
World Scientific
-
Lazard D., On the specification for solvers of polynomial systems, in Proc. ASCM 2001 (2001), pp. 1-10, World Scientific.
-
(2001)
Proc. ASCM
, vol.2001
, pp. 1-10
-
-
Lazard, D.1
-
82
-
-
60549092093
-
Thirty years of polynomial system solving, and now?
-
Lazard D., Thirty years of polynomial system solving, and now?, J. Symb. Comp. 44 (2009), 222-239.
-
(2009)
J. Symb. Comp
, vol.44
, pp. 222-239
-
-
Lazard, D.1
-
83
-
-
34247632237
-
Solving parametric polynomial systems
-
Lazard D., Rouillier F., Solving parametric polynomial systems, J. Symb. Comp. 42 (2007), 636-667.
-
(2007)
J. Symb. Comp
, vol.42
, pp. 636-667
-
-
Lazard, D.1
Rouillier, F.2
-
85
-
-
58849106380
-
Complexity of comparing monomials and two improvements of the bm-algorithm
-
Springer
-
Lundqvist S., Complexity of comparing monomials and two improvements of the BM-algorithm, in L. N. Comp. Sci. 5393 (2008), pp. 105-125, Springer.
-
(2008)
L. N. Comp. Sci
, vol.5393
, pp. 105-125
-
-
Lundqvist, S.1
-
86
-
-
70350604334
-
Vector space bases associated to vanishing ideals of points
-
Lundqvist S., Vector space bases associated to vanishing ideals of points, J. Pure Appl. Algebra 214 (2010), 309-321.
-
(2010)
J. Pure Appl. Algebra
, vol.214
, pp. 309-321
-
-
Lundqvist, S.1
-
87
-
-
84960556527
-
Some formulae in elimination
-
Macaulay F. S., Some formulae in elimination, Proc. London Math. Soc. (1) 35 (1903), 3-27.
-
(1903)
Proc. London Math. Soc
, vol.35
, Issue.1
, pp. 3-27
-
-
Macaulay, F.S.1
-
90
-
-
0002345405
-
Multipolynomial resultant algorithms
-
Manocha D., Cannon J.F., Multipolynomial resultant algorithms, J. Symb. Comp. 15 (1993), 99-122.
-
(1993)
J. Symb. Comp
, vol.15
, pp. 99-122
-
-
Manocha, D.1
Cannon, J.F.2
-
91
-
-
85027646416
-
Systems of algebraic equations solved by means of endomorphisms
-
Springer
-
Möller H.M., Systems of algebraic equations solved by means of endomorphisms, in L. N. Comp. Sci. 673 (1993a), pp. 43-56, Springer.
-
(1993)
L. N. Comp. Sci
, vol.673
, pp. 43-56
-
-
Möller, H.M.1
-
92
-
-
0001332043
-
On decomposing systems of polynomial equations with finitely many solutions
-
Möller H.M., On decomposing systems of polynomial equations with finitely many solutions, J. AAECC 4 (1993b), 217-230.
-
(1993)
J. AAECC
, vol.4
, pp. 217-230
-
-
Möller, H.M.1
-
93
-
-
21844490170
-
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
-
Möller M., Stetter H., Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Num. Math. 70 (1995), 311-325.
-
(1995)
Num. Math
, vol.70
, pp. 311-325
-
-
Möller, M.1
Stetter, H.2
-
94
-
-
0036851562
-
Computing the primary decomposition of zero-dimensional ideals
-
Monico C., Computing the primary decomposition of zero-dimensional ideals, J. Symb. Comp. 34 (2002), 451-459.
-
(2002)
J. Symb. Comp
, vol.34
, pp. 451-459
-
-
Monico, C.1
-
96
-
-
84955583152
-
Polynomial gcd computation over tower of algebraic extension
-
Springer
-
Moreno Maza M., Rioboo R., Polynomial gcd computation over tower of algebraic extension, in L. N. Comp. Sci. 948 (1995), pp. 365-382, Springer.
-
(1995)
L. N. Comp. Sci
, vol.948
, pp. 365-382
-
-
Moreno Maza, M.1
Rioboo, R.2
-
97
-
-
0013301023
-
On multiple zeros of systems of algebraic equations
-
Association for Computing Machinery
-
Moritzugu S., Kuriyama K., On multiple zeros of systems of algebraic equations, in Proc. ISSAC’99 (1999), pp. 23-30, Association for Computing Machinery.
-
(1999)
Proc. ISSAC
, vol.99
, pp. 23-30
-
-
Moritzugu, S.1
Kuriyama, K.2
-
98
-
-
0032349485
-
Computing the isolated roots by matrix methods
-
Mourrain B., Computing the isolated roots by matrix methods, J. Symb. Comp. 26 (1998), 715-738.
-
(1998)
J. Symb. Comp
, vol.26
, pp. 715-738
-
-
Mourrain, B.1
-
99
-
-
84957631580
-
A new criterion for normal form algorithms
-
Springer
-
Mourrain B., A new criterion for normal form algorithms, in L. N. Comp. Sci. 1719 (1999), pp. 430-443, Springer.
-
(1999)
L. N. Comp. Sci
, vol.1719
, pp. 430-443
-
-
Mourrain, B.1
-
100
-
-
14944367312
-
Bezoutian and quotient ring structure
-
Mourrain B., Bezoutian and quotient ring structure, J. Symb. Comp. 39 (2005), 397-415.
-
(2005)
J. Symb. Comp
, vol.39
, pp. 397-415
-
-
Mourrain, B.1
-
101
-
-
0000692349
-
Multivariate polynomials, duality and structured matrices
-
Mourrain B., Pan Y.V., Multivariate polynomials, duality and structured matrices, J. Complexity 16 (2000), 110-180.
-
(2000)
J. Complexity
, vol.16
, pp. 110-180
-
-
Mourrain, B.1
Pan, Y.V.2
-
102
-
-
0036331164
-
Relation between roots and coefficients, interpolation and application to system solving
-
Mourrain B., Ruatta O., Relation between roots and coefficients, interpolation and application to system solving, J. Symb. Comp. 33 (2002), 679-699.
-
(2002)
J. Symb. Comp
, vol.33
, pp. 679-699
-
-
Mourrain, B.1
Ruatta, O.2
-
103
-
-
0033650331
-
Solving projective complete intersection faster
-
Association for Computing Machinery
-
Mourrain B., Trebuchet P., Solving projective complete intersection faster, in Proc. ISSAC’00 (2000), pp. 234-241, Association for Computing Machinery.
-
(2000)
Proc. ISSAC’00
, pp. 234-241
-
-
Mourrain, B.1
Trebuchet, P.2
-
106
-
-
84955604612
-
How lower and upper complexity bounds meet in elimination
-
Springer
-
Pardo L.M., How lower and upper complexity bounds meet in elimination, in L. N. Comp. Sci. 948 (1995), pp. 33-69, Springer.
-
(1995)
L. N. Comp. Sci
, vol.948
, pp. 33-69
-
-
Pardo, L.M.1
-
107
-
-
0003336859
-
Modules over commutaive regular rings
-
Pierce R.S., Modules over commutaive regular rings, Mem. A.M.S. 70 (1967).
-
(1967)
Mem. A.M.S
, pp. 70
-
-
Pierce, R.S.1
-
108
-
-
84915850913
-
On solving systems of algebraic equations via ideal bases and elimination
-
Association for Computing Machinery
-
Pohst M., Yun D., On solving systems of algebraic equations via ideal bases and elimination, in Proc. 1981 SymSAC (1981), pp. 206-211, Association for Computing Machinery.
-
(1981)
Proc. 1981 Symsac
, pp. 206-211
-
-
Pohst, M.1
Yun, D.2
-
109
-
-
84910798943
-
Mémoire sur l’élimination dans les équations algébriques
-
Poisson, S.D. Mémoire sur l’élimination dans les équations algébriques, J. École Polytechnique t. 4 (1802), 199-203.
-
(1802)
J. École Polytechnique T
, vol.4
, pp. 199-203
-
-
Poisson, S.D.1
-
110
-
-
0033236946
-
Calcule de résolventes avec les modules de cauchy
-
Rennert N., Valibouze A., Calcule de résolventes avec les modules de Cauchy, Exp. Math. 8 (1999), 351-366.
-
(1999)
Exp. Math
, vol.8
, pp. 351-366
-
-
Rennert, N.1
Valibouze, A.2
-
112
-
-
0002533613
-
Prime and composite polynomials
-
Ritt J.F., Prime and composite polynomials, Trans. A.M.S. 23 (1922), 51-66.
-
(1922)
Trans. A.M.S
, vol.23
, pp. 51-66
-
-
Ritt, J.F.1
-
114
-
-
84952713599
-
-
A.M.S. Colloquium Publications
-
Ritt J.F., Differential Algebra, A.M.S. Colloquium Publications 33 (1950).
-
(1950)
Differential Algebra
-
-
Ritt, J.F.1
-
117
-
-
0033131339
-
Solving zero-dimensional systems through the rational univariate representation
-
Rouillier F., Solving zero-dimensional systems through the Rational Univariate Representation, J. AAECC 9 (1999), 433-461.
-
(1999)
J. AAECC
, vol.9
, pp. 433-461
-
-
Rouillier, F.1
-
120
-
-
0002386546
-
Matrix eigenprobelms are at the heart of polynomial system solving
-
Stetter H., Matrix eigenprobelms are at the heart of polynomial system solving, SIGSAM Bull. 30 (1996), 22-25.
-
(1996)
SIGSAM Bull
, vol.30
, pp. 22-25
-
-
Stetter, H.1
-
123
-
-
0003207762
-
A method of determining by mere inspection the derivatives from two equations of any degree
-
Sylvester J.J., A method of determining by mere inspection the derivatives from two equations of any degree, Phil. Mag. 16 (1840), 132-135.
-
(1840)
Phil. Mag
, vol.16
, pp. 132-135
-
-
Sylvester, J.J.1
-
124
-
-
0038052673
-
Memoir on the dialytic method of elimination. Part i
-
Sylvester J.J., Memoir on the dialytic method of elimination. Part I. Phil. Mag. 26 (1842), 534-539.
-
(1842)
Phil. Mag
, vol.26
, pp. 534-539
-
-
Sylvester, J.J.1
-
125
-
-
0001453534
-
On a theory of the syzygietic relations of two rational integral functions, comprising an application to the theory of sturm’s functions, and that of the greatest algebraic common measure
-
Sylvester J.J., On a theory of the syzygietic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraic common measure, Phil. Trans. Royal Soc. London 163 (1853), 407-548.
-
(1853)
Phil. Trans. Royal Soc. London
, vol.163
, pp. 407-548
-
-
Sylvester, J.J.1
-
126
-
-
0001277020
-
Systeme algebraischer gleichungen zu lösen
-
Trinks W., Über B., Buchberger Verfahren, Systeme algebraischer Gleichungen zu lösen, J. Numb. Theory 10 (1978), 475-488.
-
(1978)
J. Numb. Theory
, vol.10
, pp. 475-488
-
-
Trinks, W.1
Über Verfahren, B.B.2
-
127
-
-
84952713600
-
Resolutions et functions symmetriques
-
Association for Computing Machinery
-
Valibouze A., Resolutions et functions symmetriques, in Proc. ISSAC’89 (1989), pp. 390-399, Association for Computing Machinery.
-
(1989)
Proc. ISSAC’89
, pp. 390-399
-
-
Valibouze, A.1
-
128
-
-
84955619805
-
Computation of the galois groups of the resolvent factors for the direct and inverse galois problems
-
Springer
-
Valibouze A., Computation of the Galois groups of the resolvent factors for the direct and inverse Galois problems, in L. N. Comp. Sci. 948 (1995), pp. 456-468, Springer.
-
(1995)
L. N. Comp. Sci
, vol.948
, pp. 456-468
-
-
Valibouze, A.1
-
129
-
-
0009097352
-
Étude des relations algébriques entre les racines d’un polynôme d’une variable
-
Valibouze A., Étude des relations algébriques entre les racines d’un polynôme d’une variable, Bull. Belg. Math. Soc. Simon Stevin 6 (1999), 507-535.
-
(1999)
Bull. Belg. Math. Soc. Simon Stevin
, vol.6
, pp. 507-535
-
-
Valibouze, A.1
-
131
-
-
0003161187
-
An elimination method for polynomial systems
-
Wang D.-M., An elimination method for polynomial systems, J. Symb. Comp. 16 (1993), 83-114.
-
(1993)
J. Symb. Comp
, vol.16
, pp. 83-114
-
-
Wang, D.-M.1
-
132
-
-
0032016328
-
Decomposing polynomial systems into simple systems
-
Wang D.-M., Decomposing polynomial systems into simple systems, J. Symb. Comp. 25 (1998), 295-314.
-
(1998)
J. Symb. Comp
, vol.25
, pp. 295-314
-
-
Wang, D.-M.1
-
133
-
-
0011405387
-
On the history of the bezoutian and the resultant matrix
-
Wimmer H.K., On the history of the Bezoutian and the resultant matrix, Linear Algebra Appl. 128 (1990), 27-34.
-
(1990)
Linear Algebra Appl
, vol.128
, pp. 27-34
-
-
Wimmer, H.K.1
-
134
-
-
0003343439
-
On the decision problem and the mechanization of the theorem-proving in elementary geometry
-
Wu W.-T., On the decision problem and the mechanization of the theorem-proving in elementary geometry, Scinetia Sinica 21 (1978), 159-172.
-
(1978)
Scinetia Sinica
, vol.21
, pp. 159-172
-
-
Wu, W.-T.1
-
135
-
-
0000060015
-
Basic principles of mechanical theorem proving in elementary geometry
-
Wu W.-T., Basic principles of mechanical theorem proving in elementary geometry, J. Sys. Sci. & Math. Sci. 4 (1984), 207-235.
-
(1984)
J. Sys. Sci. & Math. Sci
, vol.4
, pp. 207-235
-
-
Wu, W.-T.1
-
136
-
-
0038256188
-
On the decision problem and the mechanization of the theorem-proving in elementary geometry
-
American Mathematical Society
-
Wu W.-T., On the decision problem and the mechanization of the theorem-proving in elementary geometry, in Contemp. Math. 29 (1984), pp. 213-234, American Mathematical Society.
-
(1984)
Contemp. Math
, vol.29
, pp. 213-234
-
-
Wu, W.-T.1
-
137
-
-
0037580578
-
Some recent advances in mechanical theorem-proving of geometry
-
American Mathematical Society
-
Wu W.-T., Some recent advances in mechanical theorem-proving of geometry, (reprinted) in Contemp. Math. 29 (1984), pp. 235-241, American Mathematical Society.
-
(1984)
Contemp. Math
, vol.29
, pp. 235-241
-
-
Wu, W.-T.1
-
138
-
-
0002971341
-
A zero structure theorem for polynomial equations solving
-
Wu W.-T., A zero structure theorem for polynomial equations solving, M.M. Research Preprints 1 (1987), 2-12.
-
(1987)
M.M. Research Preprints
, vol.1
, pp. 2-12
-
-
Wu, W.-T.1
-
140
-
-
38249010304
-
Solutions of systems of algebraic equations and linear maps on residue class rings
-
Yokoyama K., Noro M., Takeshima T., Solutions of systems of algebraic equations and linear maps on residue class rings, J. Symb. Comp. 14 (1992), 399-417.
-
(1992)
J. Symb. Comp
, vol.14
, pp. 399-417
-
-
Yokoyama, K.1
Noro, M.2
Takeshima, T.3
|