The Virtual Computer Algebra Library

Articles about Real Solutions of Polynomial Systems

• Alonso M.E., Becker E., Roy M.-F., Wormann T.
  "Zeroes, Multiplicities and Idempotents for Zerodimensional Systems
  Proceedings of the Conference "Effective Methods in Algebraic Geometry" (MEGA' 94)

• Auzinger W., Stetter H.J.
  "An Elimination Algorithm for the Computation of all Zeros of a System of Multivariate Polynomial Equations"
  Int. Series in Numerical Mathematics 86, Birkhauser, 1988
  p. 11 - 30

• Bareiss E.H.
  "Sylvester's identity and multistep integer-preserving gaussian elimination"
  Math. Comp. 22, 1968
  p. 565 - 578

• Basu S., Pollack R., Roy M.-F.
  "A new algorithm to find a point in every cell defined by a family of polynomials"
  Quantifier Elimination and Cylindrical Algebraic Decomposition
  Texts and monographs in Symbolic Computation, Caviness B., Johnson J. Eds
  Springer Verlag, Wien, New York, 1994

• Becker E., Cardinal J.P., Roy M.-F., Szafraniec Z.
  "Multivariate Bezoutians, Kronecker Symbol and Eisenbud-Levine formula"
  Proceedings of the Conference "Effective Methods in Algebraic Geometry" (MEGA' 94)

• Becker E., Marinari M.G., Mora T., Traverso C.
  "The shape of the Shape lemma"
  Proceedings of the Conference "International Symposium on Symbolic and Algebraic Computation" (ISSAC' 94)
  ACM Press, 1994
  p. 129 - 133

• Becker E., Wormann T.
  "On the Trace Formula for Quadratic Forms"
  Proc. RAGSQUAD (1992)
  Contemp. Math, 1993

• Becker E., Wormann T.
  "Radical Computations of Zero-dimensional Ideals and Real Root Counting"
  Mathematics and Computers in Simulation

• Ben-Or M., Kozen D., Reif J.
  "The complexity of elementary algebra and geometry"
  J. of Computation and Systems Sciences 32, 1986
  p. 251 - 264

• Brown W.S.
  "The Subresultant PRS Algorithm"
  ACM Transactions on Mathematical Software 4, 1978
  p. 237 - 249

• Brown W.S., Traub J.F.
  "On Euclid's Algorithm and the Theory of Subresultants"
  Journal of Associate for Computing Machinery 18, 1971
  p. 505 - 514

• Canny J.F.
  "Some algebraic and geometric computations in PSPACE"
  Proc. of the 20th ACM Symposium on Theory of Computing, 1988
  p. 460 - 467

• Ceballos L., Gonzalez-Vega L.
  Manipulation of real roots of polynomials: Isolating Intervals or Thom's Codes
  MapleTech, Volume 2, Number 2, Birkhauser, 1995
  p. 42 - 47

• Collins G.E., Loos R.
  "Real zeroes of polynomials"
  In: Computer Algebra, Symbolic and Algebraic Computation, Buchberger B., Collins G.E., Loos R. Eds
  Springer Verlag, New York, 1982
  p. 83 - 94

• Collins G.E.
  "Polynomial Remainder Sequences and Determinants"
  American Mathematical Society 73, 1966
  p. 708 - 712

• Collins G.E.
  "Subresultants and Reduced Polynomial Remainder Sequences"
  Journal of Association for Computing Machinery 14, 1967
  p. 128 - 142

• Collins G.E.
  "The Calculation of Multivariate Polynomial Resultants"
  Journal of Association for Computing Machinery 19, 1971
  p. 515 - 532

• Collins G.E., Horowitz E.
  "The Minimum Root Separation of a Polynomial"
  Mathematics of Computation, 28 (126), April 1974
  p. 589 - 597
• Coste M., Roy M.-F.
  "Thom's lemma, the coding of real algebraic numbers and the topology of semi-algebraic sets"
  J. of Symbolic Computation 5, 1988
  p. 121 - 129

• Cucker F., Laneau H., Mishra B., Pedersen P., Roy M.-F.
  "NC Algorithms for Real algebraic numbers"
  Applicable Algebra in Engineering, Communication and Computing 3, 1992
  p. 79 - 98

• Faugére J.C., Gianni P., Lazard D., Mora T.
  "Efficient Computation of Zero-dimensional Grobner basis by change of ordering"
  J. of Symbolic Computation, 1994

• Faugére J.C., Lazard D.
  "The combinatorial classes of parallel manipulators"
  Mechanism and Machine Theory, Febrary 1994

• Frobenius
  "Uber das Traegheitsgesetz des quadratishen Formen"
  S-B Pruss. Akad. Wiss., May 1884
  p. 241 - 256 and p. 403 - 431

• Giusti M., Heintz J.
  "La détermination des points isolés et de la dimension d'une variét´ algébrique peut se faire en temps polynomial"
  Proc. of the Int. Meeting on Computational Commutative Algebra, 1991

• Giusti M., Heintz J.
  "Algorithmes - disons rapides - pour la d&ecautecomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles"
  Proc. of the Conference "Effective Methods in Algebraic Geometry (MEGA' 90), Mora T., Traverso C. Eds
  Progress in Mathematics 94, Birkhauser, 1991
  p. 169 - 193

• Giusti M., Heintz J., Morais, Pardo
  "When Polynomial Equation Systems can be "solved" fast ?"
  Proc. of the Conference AAECC - 11
  Lecture Notes in Computer Science 948
  Springer Verlag, 1995

• Gianni P., Mora T.
  "Algebraic solution of polynomial equations using Grobner bases" Proc. of the Conference AAECC - 5
  Lecture Notes in Computer Science 359
  Springer Verlag, 1989
  p. 247 - 257

• Gonzalez-Vega L.
  Some examples of problem solving by using the symbolic viewpoint when dealing with polynomial systems of equations
  Computer Algebra in Science and Engineering (editors J. Fleischer, J. Grabmeier, F. W. Hehl and W. Küchlin), World Scientific Publishing, 1995
  p. 102 - 116

• Gonzalez L., Lombardi H., Recio T., Roy M.-F.
  "Sturm-Habicht Sequence"
  Proc. of the Conference "International Symposium in Algebraic Computation" (ISSAC' 89)
  ACM Press, 1989
  p. 136 - 146

• Gonzalez L., Lombardi H., Recio T., Roy M.-F.
  "Spécialisation de la suite de Sturm et sous-résultants I"
  Informatique théorique et applications 28, 1994
  p. 1 - 24

• Gonzalez L., Lombardi H., Recio T., Roy M.-F.
  "Sturm-Habicht sequence, determinants and real roots of univariate polynomials"
  Quantifier elimination and Cylindrical Algebraic Decomposition
  Texts and Monographs in Symbolic Computation, Caviness B., Johnson J. Eds
  Springer Verlag, Wien, New York, 1994

• Gonzalez-Vega L., Trujillo G.
  "Using symmetric functions to describe the solution set of a zero-dimensional ideal"
  Proc. of the Conference AAECC - 11.
  Lecture Notes in Computer Science 948
  Springer Verlag, 1995
  p. 232 - 247

• Habicht W.
  "Eine Verallgemeinerung des Sturmschen Wurzelzahl verfahrens"
  Comm. Math. Helvetici 21, 1948
  p. 99 - 116

• Heintz J., Recio T., Roy M.-F.
  "Algorithms in Real Algebraic Geometry and Applications to Computational Geometry"
  Discrete and Computational Geometry, Papers from the DIMACS Special Year, Vol. 6
  Edited by Goodman J.E., Pollack R. and Steiger W.
  AMS and ACM, 1991
  p. 137 - 164

• Hermite C.
  "Remarques sur le théoreme de Sturm"
  C.R. Acad. Sci. Paris 36, 1853
  p. 52 - 54

• Junker F.
  "Uber symmetrische Funktionen von mehreren Reihen von Veranderlichen"
  Mathematische Annalen 43, 1893
  p. 232-247

• Kakié
  "The Resultant of Several Homogeneous Polynomials in Two Indeterminates"
  Proceedings of American Math. Society 54, 1976
  p. 1 - 7

• Lakshman Y.N., Lazard D.
  "On the complexity of Zero-dimensional Algebraic Systems"
  Effective Methods in Algebraic geometry
  Progress in Mathematics 94, Birkhauser, 1991
  p. 217 - 225

• Lazard D.
  "Solving Zero-dimensional algebraic systems"
  J. Symbolic Computation 13, 1992
  p. 117 - 132

• Lazard D.
  "Résolution des systèmes d'équations algébriques"
  Theoretical Computer Science 15, 1981
  p. 77 - 110

• Lazard D.
  "Grobner Bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations"
  In: Proceedings for EUROCAL' 83
  Lecture Notes in Computer Science 162, 1983
  p. 146 - 156

• Ligatsikas Z., Roy M.-F.
  "Séries de Puiseux sur un corps réel clos"
  C.R. Acad. Sci. Paris 311, 1990
  p. 625 - 628

• Loos R.
  "Generalize polynomial remainder sequences"
  In: Computer Algebra, Symbolic and Algebraic Computation
  Springer Verlag, Berlin, 1982

• Mishra B, Pedersen P.
  "Computation with Sign Representations of Real Algebraic Numbers"
  In: Proceedings of ISSAC' 90, 1990
  p. 120 - 126

• Pedersen P.,Roy M.-F., Szpirglas A.
  "Counting real zeroes in the multivariate case"
  Computational algebraic geometry, Eyssette, Galligo Eds
  Progress in Mathematics 109, 1993
  p. 203 - 224

• Pollack R., Roy M.-F.
  "On the number of cells defined by a set of polynomials"
  C.R. Acad. Sci. Paris 316, 1993
  p. 573 - 577

• Renegar J.
  "On the computational complexity and geometry of the first-order theory of the reals, parts I, II and III"
  J. of Symbolic Computation 13(3), 1992
  p. 255 - 352

• Rouillier F.
  "Formules de Bareiss et ré de formes quadratiques"
  C.R. Acad. Sci. Paris 320, 1995
  p. 1273 - 1278

• Roy M.-F., Szpirglas A.
  "Complexity of computations with real algebraic numbers"
  J. of Symbolic Computation 10, 1990
  p. 39 - 51

• Rump S.M.
  "Polynomial Minimum Root Separation"
  Mathematics of Computation 33 (145), 1979
  p. 327 - 336

• Sturm C.
  "Mémoire sur la résolution des équations num´riques"
  Inst. France Sc. Math. Phys. 6, 1835

• Sylvester J.J.
  "On a theory of syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's function"
  Trans. Roy. Soc. London, 1853

• Yokoyama K., Noro M., Takeshima T.
  "Solutions of Systems of Algebraic Equations and Linear Maps on Residue Class Rings"
  J. of Symbolic Computation 14, 1992
  p. 399 - 417

Go to:
Literature about Real Solutions
Bibliographies
Real Solutions Menu
The Computer Algebra Library
CAIN Home page