-
1
-
-
0036901031
-
Real solving for positive dimensional systems
-
P. Aubry, F. Rouillier, and M. Safey El Din. Real solving for positive dimensional systems. Journal of Symbolic Computation, 34(6):543-560, 2002.
-
(2002)
Journal of Symbolic Computation
, vol.34
, Issue.6
, pp. 543-560
-
-
Aubry, P.1
Rouillier, F.2
Safey El Din, M.3
-
2
-
-
0031097237
-
Polar varieties and efficient real equation solving: The hypersurface case
-
B. Bank, M. Giusti, J. Heintz, and G.-M. Mbakop. Polar varieties and efficient real equation solving: The hypersurface case. Journal of Complexity, 13(1):5-27, 1997.
-
(1997)
Journal of Complexity
, vol.13
, Issue.1
, pp. 5-27
-
-
Bank, B.1
Giusti, M.2
Heintz, J.3
Mbakop, G.-M.4
-
3
-
-
12144249591
-
Generalized polar varieties and efficient real elimination procedure
-
B. Bank, M. Giusti, J. Heintz, and L.-M. Pardo. Generalized polar varieties and efficient real elimination procedure. Kybernetika, 40(5):519-550, 2004.
-
(2004)
Kybernetika
, vol.40
, Issue.5
, pp. 519-550
-
-
Bank, B.1
Giusti, M.2
Heintz, J.3
Pardo, L.-M.4
-
5
-
-
0030291482
-
On the combinatorial and algebraic complexity of quantifier elimination
-
S. Basu, R. Pollack, and M.-F. Roy. On the combinatorial and algebraic complexity of quantifier elimination. Journal of ACM, 43(6):1002-1045, 1996.
-
(1996)
Journal of ACM
, vol.43
, Issue.6
, pp. 1002-1045
-
-
Basu, S.1
Pollack, R.2
Roy, M.-F.3
-
8
-
-
49449101716
-
-
E. Becker and R. Neuhaus. Computation of real radicals for polynomial ideals. Computational Algebraic Geometry, 109 of Progress in Mathematics, pp. 1-20, Birkhäuser, 1993.
-
E. Becker and R. Neuhaus. Computation of real radicals for polynomial ideals. Computational Algebraic Geometry, vol. 109 of Progress in Mathematics, pp. 1-20, Birkhäuser, 1993.
-
-
-
-
10
-
-
84968513706
-
Heights of projective varieties and positive Green forms
-
J.-B. Bost, H. Gillet, and C. Soulet. Heights of projective varieties and positive Green forms, J. Amer. Math. Soc., 7(4):903-1027, 1994.
-
(1994)
J. Amer. Math. Soc
, vol.7
, Issue.4
, pp. 903-1027
-
-
Bost, J.-B.1
Gillet, H.2
Soulet, C.3
-
11
-
-
85029837057
-
Quantifier elimination for real closed fields by cylindrical algebraic decomposition
-
G. E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Lecture notes in computer science, 33:515-532, 1975.
-
(1975)
Lecture notes in computer science
, vol.33
, pp. 515-532
-
-
Collins, G.E.1
-
12
-
-
7444253514
-
-
S. Corvez and F. Rouillier. Using computer algebra tools to classify serial manipulators, Proceedings of Automated Deduction in Geometry, F. Winkler (eds), Lecture Notes in Artificial Intelligence, 2930:31-43, 2003.
-
S. Corvez and F. Rouillier. Using computer algebra tools to classify serial manipulators, Proceedings of Automated Deduction in Geometry, F. Winkler (eds), Lecture Notes in Artificial Intelligence, 2930:31-43, 2003.
-
-
-
-
15
-
-
57449105861
-
-
Available at
-
J.-C. Faugère. Gb/FGb. Available at http://fgbrs.lip6.fr.
-
Gb/FGb
-
-
Faugère, J.-C.1
-
16
-
-
0033143274
-
A new efficient algorithm for computing Gröbner bases (F4)
-
J.-C. Faugère. A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure and Applied Algebra, 139(1-3):61-88, 1999.
-
(1999)
Journal of Pure and Applied Algebra
, vol.139
, Issue.1-3
, pp. 61-88
-
-
Faugère, J.-C.1
-
17
-
-
0036045901
-
A new efficient algorithm for computing Gröbner without reduction to zero (F5)
-
ACM Press
-
J.-C. Faugère. A new efficient algorithm for computing Gröbner without reduction to zero (F5). In: Proceedings of ISSAC 2002, pp. 75-83. ACM Press, 2002.
-
(2002)
Proceedings of ISSAC
, pp. 75-83
-
-
Faugère, J.-C.1
-
19
-
-
0031142051
-
Lower bounds for Diophantine approximation
-
M. Giusti, K. Hägele, J. Heintz, J.-E Morais, J.-L. Montaña, and L.-M. Pardo. Lower bounds for Diophantine approximation. In: Proceedings of MEGA'96, number 117, 118 in Journal of Pure and Applied Algebra, pages 277-317, 1997.
-
(1997)
Proceedings of MEGA'96, number 117, 118 in Journal of Pure and Applied Algebra
, 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
-
-
0031992346
-
Straight-line programs in geometric elimination theory
-
M. Giusti, J. Heintz, J.-E. Morais, J. Morgenstern, and L.-M. Pardo. Straight-line programs in geometric elimination theory. Journal of Pure and Applied Algebra, 124:101-146, 1998.
-
(1998)
Journal of Pure and Applied Algebra
, vol.124
, pp. 101-146
-
-
Giusti, M.1
Heintz, J.2
Morais, J.-E.3
Morgenstern, J.4
Pardo, L.-M.5
-
21
-
-
84955611783
-
When polynomial equation systems can be solved fast?
-
Proceedings of AAECC, 948 of, Springer
-
M. Giusti, J. Heintz, J.-E. Morais, and L.-M. Pardo. When polynomial equation systems can be solved fast? In: Proceedings of AAECC-11, volume 948 of LNCS, pages 205-231. Springer, 1995.
-
(1995)
LNCS
, vol.11
, pp. 205-231
-
-
Giusti, M.1
Heintz, J.2
Morais, J.-E.3
Pardo, L.-M.4
-
22
-
-
0035294718
-
A Gröbner free alternative for polynomial system solving
-
M. Giusti, G. Lecerf, and B. Salvy. A Gröbner free alternative for polynomial system solving. Journal of Complexity, 17(1):154-211, 2001.
-
(2001)
Journal of Complexity
, vol.17
, Issue.1
, pp. 154-211
-
-
Giusti, M.1
Lecerf, G.2
Salvy, B.3
-
23
-
-
85025493187
-
Solving systems of polynomials inequalities in subexponential time
-
D. Grigoriev and N. Vorobjov. Solving systems of polynomials inequalities in subexponential time. Journal of Symbolic Computation, 5:37-64, 1988.
-
(1988)
Journal of Symbolic Computation
, vol.5
, pp. 37-64
-
-
Grigoriev, D.1
Vorobjov, N.2
-
24
-
-
0003007076
-
On the complexity of semi-algebraic sets
-
89 San Francisco, North-Holland
-
J. Heintz, M.-F. Roy, and P. Solernò. On the complexity of semi-algebraic sets. In Proceedings IFIP'89 San Francisco, North-Holland, 1989.
-
(1989)
Proceedings IFIP
-
-
Heintz, J.1
Roy, M.-F.2
Solernò, P.3
-
25
-
-
0001366292
-
On the theoretical and practical complexity of the existential theory of the reals
-
J. Heintz, M.-F. Roy, and P. Solernò. On the theoretical and practical complexity of the existential theory of the reals. The Computer Journal, 36(5):427-431, 1993.
-
(1993)
The Computer Journal
, vol.36
, Issue.5
, pp. 427-431
-
-
Heintz, J.1
Roy, M.-F.2
Solernò, P.3
-
26
-
-
0033460961
-
Testing sets for properness of polynomial mappings
-
Z. Jelonek. Testing sets for properness of polynomial mappings. Mathematische Annalen, 315(1):1-35, 1999.
-
(1999)
Mathematische Annalen
, vol.315
, Issue.1
, pp. 1-35
-
-
Jelonek, Z.1
-
27
-
-
16844386045
-
Topological characterization of finite mappings
-
Z. Jelonek. Topological characterization of finite mappings. Bull. Polish Acad. Sci. Math., 49(3):279-283, 2001.
-
(2001)
Bull. Polish Acad. Sci. Math
, vol.49
, Issue.3
, pp. 279-283
-
-
Jelonek, Z.1
-
29
-
-
0000176380
-
Quantifier elimination: Optimal solution for two classical examples
-
D. Lazard. Quantifier elimination: optimal solution for two classical examples. Journal of Symbolic Computation, 5(1-2):261-266, 1988.
-
(1988)
Journal of Symbolic Computation
, vol.5
, Issue.1-2
, pp. 261-266
-
-
Lazard, D.1
-
32
-
-
49449105739
-
-
Y. N. Lakshman. A single exponential bound of the complexity of computing Gröbner bases of zero-dimensional ideals. In: C. Traverso, T. Mora, editor, Proc. Effective Methods in Algebraic Geometry, MEGA, 94 of Progress in Mathematics, pp. 227-234. Birkhäuser, 1991.
-
Y. N. Lakshman. A single exponential bound of the complexity of computing Gröbner bases of zero-dimensional ideals. In: C. Traverso, T. Mora, editor, Proc. Effective Methods in Algebraic Geometry, MEGA, vol. 94 of Progress in Mathematics, pp. 227-234. Birkhäuser, 1991.
-
-
-
-
33
-
-
0039183572
-
On sums of squares
-
A. Lax and P. Lax, On sums of squares, Linear Algebra App., 20:71-75, 1978.
-
(1978)
Linear Algebra App
, vol.20
, pp. 71-75
-
-
Lax, A.1
Lax, P.2
-
34
-
-
0042156945
-
Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers
-
G. Lecerf. Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers. Journal of Complexity, 19(4):564-596, 2003.
-
(2003)
Journal of Complexity
, vol.19
, Issue.4
, pp. 564-596
-
-
Lecerf, G.1
-
35
-
-
0013172386
-
Semi-algebraic Sard's theorem for generalized critical values
-
K. Kurdyka, P. Orro, and S. Simon, Semi-algebraic Sard's theorem for generalized critical values. Journal of Differentiable Geometry, 56:67-92, 2000.
-
(2000)
Journal of Differentiable Geometry
, vol.56
, pp. 67-92
-
-
Kurdyka, K.1
Orro, P.2
Simon, S.3
-
36
-
-
85025505234
-
On the computational complexity and geometry of the first-order theory of the reals
-
J. Renegar. On the computational complexity and geometry of the first-order theory of the reals. Journal of Symbolic Computation, 13(3):255-352, 1992.
-
(1992)
Journal of Symbolic Computation
, vol.13
, Issue.3
, pp. 255-352
-
-
Renegar, J.1
-
37
-
-
49449089235
-
-
F. Rouillier. RS, RealSolving. available at http://fgbrs.lip6.fr.
-
F. Rouillier. RS, RealSolving. available at http://fgbrs.lip6.fr.
-
-
-
-
38
-
-
0033131339
-
Solving zero-dimensional systems through the Rational Univariate Representation
-
F. Rouillier. Solving zero-dimensional systems through the Rational Univariate Representation. AAECC Journal, 9(5):433-461, 1999.
-
(1999)
AAECC Journal
, vol.9
, Issue.5
, pp. 433-461
-
-
Rouillier, F.1
-
39
-
-
0000076609
-
Finding at least one point in each connected component of a real algebraic set defined by a single equation
-
F. Rouillier, M.-F. Roy, and M. Safey El Din. Finding at least one point in each connected component of a real algebraic set defined by a single equation. Journal of Complexity, 16:716-750, 2000.
-
(2000)
Journal of Complexity
, vol.16
, pp. 716-750
-
-
Rouillier, F.1
Roy, M.-F.2
Safey El Din, M.3
-
40
-
-
49449107022
-
-
F. Rouillier, M. Safey El Din, and E. Schost. Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study, Lecture Notes in Computer Science, Automated deduction in geometry, ADG'2000, Zurich, Switzerland, September 25-27, revised papers, Editors: J. Richter-Gebert, D. Wang, Springer-Verlag, Heidelberg, 2000.
-
F. Rouillier, M. Safey El Din, and E. Schost. Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study, Lecture Notes in Computer Science, Automated deduction in geometry, ADG'2000, Zurich, Switzerland, September 25-27, revised papers, Editors: J. Richter-Gebert, D. Wang, Springer-Verlag, Heidelberg, 2000.
-
-
-
-
44
-
-
4744362177
-
Properness defects of projections and computation of one point in each connected component of a real algebraic set
-
M. Safey El Din and É. Schost. Properness defects of projections and computation of one point in each connected component of a real algebraic set. Journal of Discrete and Computational Geometry, 32(3):417-430, 2004.
-
(2004)
Journal of Discrete and Computational Geometry
, vol.32
, Issue.3
, pp. 417-430
-
-
Safey El Din, M.1
Schost, E.2
-
45
-
-
84948709979
-
Finding sampling points on real hypersurfaces is easier in singular situations
-
M. Safey El Din. Finding sampling points on real hypersurfaces is easier in singular situations. Electronic proceedings of MEGA, 2005.
-
(2005)
Electronic proceedings of MEGA
-
-
Safey El Din, M.1
-
48
-
-
34547940429
-
Global optimization of polynomials using gradient tentacles and sums of squares
-
M. Schweighofer. Global optimization of polynomials using gradient tentacles and sums of squares, SIAM Journal on Optimization, 17(3):920-942, 2006.
-
(2006)
SIAM Journal on Optimization
, vol.17
, Issue.3
, pp. 920-942
-
-
Schweighofer, M.1
|