The Virtual Computer Algebra Library

Articles about Groebner Bases

• Abhyankar S., Li W.:
  "On the Jacobian conjecture: A new approach via Grobner bases"
  J. Pure Appl. Algebra 61, 1989
  p. 211 - 222

• Adams W.W., Boyle A.K.:
  "Some results on Grobner bases over commutative rings"
  J. Symbolic Computation 13/5, 1992
  p. 473 - 484

• Alwash M.A.M.:
  "Periodic solutions of a quartic differential equation and Groebner bases"
  J. Comput. Appl. Math. 75, no. 1, 1996
  p. 67 - 76

• Apel J., Stückrad J., Tworzewski P., Winiarski T.
  "Reduction of everywhere convergent power series with respect to Gröbner bases"
  J. Pure Appl. Algebra 110, no. 2, 1996
  p. 113 - 129

• Armbruster D., Kredel H.:
  "Constructing universal unfoldings using Grobner bases"
  J. Symbolic Computation 2/4, 1986
  p. 383 - 388

• Attardi G., Traverso C.:
  "A strategy-Accurate Parallel Buchberger Algorithm"
  Proceedings of PASCO' 94
  World Scientific, 1994
• Bachmair L., Buchberger B.:
  "A simplified proof of the characterization theorem for Grobner bases"
  ACM SIGSAM Bulletin 14/4
  p. 29 - 34

• Becker T.:
  "Homogeneity, pseudo-homogeneity, and Grobner basis computations"
  In: Applied Algebra, Algebraic Algorithms, and Error-correcting Codes" (AAECC 9)
  Mattson H.F., Mora T., Rao T.R.N. (Editors)
  Springer LNCS 539, 1991 p. 65 - 73

• Becker T., Weispfenning:
  "The Chinese remainder problem, multivariate interpolation, and Grobner bases"
  In: Proc. International Symposium on Symbolic Computation (ISSAC'91)
  Watt S.M. (Editors)
  ACM Press, New York, 1991
  p. 64 - 69

• Boege W., Gebauer R., Kredel H.:
  "Some examples for solving systems of algebraic equations by calculating Groebner bases"
  J. of Symbolic Computation 2, no. 1, 1986
  p. 83 - 98

• Boge W., Gebauer R., Kredel H.:
  "Some examples for solving systems of algebraic equations by calculating Grobner bases"
  J. Symbolic Computation 2/1, 1986
  p. 83 - 98

• Bokut L.A., Klein A.A.
  "Serre relations and Gröbner-Shirshov" bases for simple Lie algebra I, II"
  Int. J. Algebra Comput. 6, no. 4, 1996
  p. 389 - 400, 401 - 412

• Bradford R.:
  "A parallelization of the Buchberger algorithm"
  In: Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC'90)
  Watanabe S., Nagata M. (Editors)
  ACM Press, New York, 1990
  p. 296

• Buchberger B.:
  "A Theoretical basis for the reduction of polynomials to canonical form"
  ACM SIGSAM Bulletin Vol. 10, No. 3, 1976
  p. 19 - 29

• Buchberger B.:
  "Critical-pair-completion algorithm for finitely generated ideals in rings"
  Logic and Machines: Decision problems and complexit
  E. Borger, G. Hasenjaeger, D. Rodding Editors
  Lecture Notes in Computer Science 171, Springer Verlag, 1984
  p. 137 - 161

• Buchberger B.:
  "Basic features and development of the critical-pair-completion procedure"
  Rewriting Techniques and Applications, J.P. Jouannaud Editor
  Lecture Notes in Computer Science 202, Springer Verlag, 1985
  p. 1 - 45

• Buchberger B.:
  "The parallelization of critical-pair-completion procedures on the L-Machines"
  Proceedings of the Japanese Symposium on Functional Programming, 1987
  p. 54 - 61

• Buchberger B.:
  "Some properties of Grobner bases for polynomial ideals"
  ACM SIGSAM Bulletin 10/4, 1976
  p. 19 - 24

• Buchberger B.:
  "A criterion for detecting unnecessary reductions in the construction of Grobner bases"
  In: "EUROSAM'79, An international Symposium on Symbolic and Algebraic Manipulation"
  Ng, E.W. (Editor)
  Springer LNCS 72, 1979
  p. 3 - 21

• Buchberger B.:
  "A note on the complexity of constructing Grobner bases"
  In: EUROCAL'83, European Computer Algebra Conference
  van Hulzen J.A. (Editor)
  Springer LNCS 162, 1983
  p. 137 - 145

• Buchberger B.:
  "Grobner bases: A method in symbolic mathematics"
  In: "Conference on systems and techniques of analytical computing and their applications in theoretical physics", Dubna
  1983

• Buchberger B.:
  "A survey on the method of Grobner bases for solving problems in connection with systems of multivariate polynomials"
  In: The Second International Symposium on Symbolic and Algebraic Computation by Computers, RIKEN, Wako-Shi, Saitama, Japan
  1985
  7-1 - 7-15

• Buchberger B.
  "Grobner bases: An algorithmic method in polynomial ideal theory"
  In: Multidimensional Systems Theory, Bose N.K. Editor
  Reidel, Dordrecht, 1985
  p. 184 - 232

• Buchberger B.
  "Applications of Grobner bases in non-linear computational geometry"
  In: Trends in Computer Algebra, Janen R. Editor
  Lecture Notes in Computer Science 296
  Springer, 1987
  p. 52 - 80

• Carra Ferro G.
  "Some upper-bounds for the multiplicity of an autoreduced subset of ?? and their applications"
  In: Algebraic Algorithms and Error-Correcting Codes, Calmet J. Editor (AAECC 3)
  Lecture Notes in Computer Science 229
  Springer, 1985
  p. 306 - 315

• Carra Ferro G.
  "Grobner Bases and Hilbert schemes
  International Journal of Symbolic Computation 6/2,3, 1988
  p. 219 - 230

• Castro-Jiménez F.J., Núñez-Valdés J.:
  "Gröbner basis in the classification of characteristically nilpotent filiform Lie algebras of dimension 10"
  Proc. of Algorithms in algebraic geometry and Applications (Santander, 1994)
  Progress in Mathematics 143, Birkhäuser, 1996
  p. 115 - 133

• Chazarain J., Riscos A., Alonso J.A., Briales E.
  "Multivalued Logic and Grobner Bases with Applications to Modal Logic"
  Journal of Symbolic Computation 11, 1991
  p. 181 - 194

• Chou S.C.
  "Automated reasoning in geometries using the characteristic set method and Grobner basis method"
  In: Proc. Int. Symposium on Symbolic and Algebraic Computation (ISSAC '90), Watanabe S, Nagata M. Eds.
  ACM Press, New York, 1990
  p. 255 - 260

• Clegg M., Edmonds J., Impagliazzo R.
  "Using the Groebner basis algorithm to find proofs of unsatisfiability"
  In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996)
  ACM, New York, 1996
  p. 174 - 183

• Conti P., Traverso C.
  "Buchberger's algorithm and integer programming"
  AAECC-9
  Lecture Notes in Computer Science, Springer Verlag, 1991

• Czapor S.R., Geddes K.O.
  "On implementing Buchberger's algorithm for Grobner bases"
  In: 1986 ACM Symposium on Symbolic and Algebraic Computation, Char B.W. Ed.
  University of Waterloo, Ontario, 1986
  p. 233 - 238

• Czapor S.R.
  "Solving algebraic equations via Buchberger's algorithm"
  In: EUROCAL '87, European Conference on Computer Algebra, Davenport J.H. Ed.
  Lecture Notes in Computer Science 378
  Springer, 1987
  p. 260 - 269

• Czapor S.R.
  "Solving algebraic equations: Combining Buchberger's algorithm with multivariate factorization"
  Journal of Symbolic Computation 7/1, 1989
  p. 49 - 53

• de Loera, J.A., Sturmfels B., Rekha R.:
  "Gröbner bases and triangulations of the second hypersimplex"
  Combinatorica 15, no. 3, 1995
  p. 409 - 424

• Dubé T.W.
  "The structure of polynomial ideals and Grobner bases"
  SIAM J. Comput. 19/4, 1990
  p. 750 - 773

• Ebert G.L.
  "Some comments on the modular approach to Grobner bases"
  ACM SIGSAM Bulletin 17/2, 1983
  p. 28 - 32

• Faugere J.C.
  "Parallelization of Groebner basis"
  Proceedings of PASCO' 94
  World Scientific, 1994

• Faugere J.C., Gianni P., Lazard D., Mora T.
  "Efficient computation of zero-dimensional Grobner bases by change of ordering"
  J. of Symbolic Computation, 1994

• Fenf G.C., Wu W.D., Huang K.:
  "The construction of eigenvalue problem equivalent to multivariate polynomial system and the Groebner basis"
  Adv. in Math. (China) 22, no. 3., 1993
  p. 282 - 284

• Ferro A. Gallo G.
  "Grobner bases, Ritt's algorithm, and decision procedures for algebraic theories"
  In: Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes" (AAECC 5), Huguet L., Poli A. Eds
  Lecture Notes in Computer Science 356
  Springer, 1987
  p. 230 - 237

• Gianni P., Trager B., Zacharias G.
  "Grobner Bases and Primary Decomposition of Polynomial Ideals"
  J. of Symbolic Computation 6 (2 - 3), 1988
  (Special Issue on Computational Aspects of Commutative Algebra)
  p. 149 - 168

• Gianni P., Mora T.:
  "Algebraic solution of systems of polynomial equations using Groebner bases"
  In: Proceedings of Applied algebra, algebraic algorithms and error-correcting codes (Menorca, 1987)
  Lecture Notes in Computer Sci., Springer Verlag, 1989
  p. 247 - 257

• Giovini A., Mora T., Niesi G., Robbiano L., Traverso C.
  "One sugar cube, please. Selection strategies in the Buchberger algorithm"
  Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation (ISSAC). S.M. Watt Editor
  ACM Press, 1991

• Grabe H., Lassner W.
  "A parallel Groebner factorizer"
  Proceedings of PASCO' 94
  World Scientific 1994

• Hartley D., Tuckey P.
  "Gröbner bases in Clifford and Grassmann algebras"
  J. of Symbolic Comput. 20, no. 2, 1995
  p. 197 - 205

• Heegard C., Little J., Saints K.:
  "Systematic encoding via Gröbner bases for a class of algebraic geometric Goppa codes"
  IEEE Trans. Inform. Theory 41, no. 6, part 1 (Special issue on algebraic geometry codes), 1995
  p. 1752 - 1761

• Hreinsdòttir F.:
  "A case where choosing a product order makes the calculations of a Groebner basis much faster"
  J. of Symbolic Computation 18, no. 4, 1994
  p. 373 - 378

• Huynh D.T.
  "A Superexponential Lower Bound for Grobner Bases and Church-Rosser Commutative Thue Systems"
  Information and Control 86, 1986
  p. 196 - 206

• Kalkbrener M.:
  "Implicitization by Gröbner basis conversion"
  Euromath Bull. 2, no. 1, 1996
  p. 197 - 204

• Kamoi Y., Vogel W.:
  "On Gröbner bases and Buchsbaum algebras"
  Arch. Math. 67, no. 6, 1996
  p. 457 - 464

• Kandri-rody A., Kapur D.
  "Algorithms for Computing the Grobner Bases of Polynomial Ideals over Various Euclidean Rings"
  In: Proceedings of EUROSAM' 84
  Lecture Notes in Computer Science 174
  Edited by Fitch J.
  Springer Verlag, Berlin, 1984
  p. 195 - 206

• Kapur D.
  "Geometry Theorem Proving Using Grobner Bases"
  Journal of Symbolic Computation 2, 1986
  p. 399 - 412

• Kutzler B., Stifter S.
  "Automated Geometry Theorem Proving Using Buchberger's Algorithm"
  In: Proceedings of the 1986 Symposium on Symbolic and Algebraic Computation, 1986
  p. 209 - 214

• Lakshman Y.N.
  "On the Complexity of Computing Grobner Bases for the Radical of a Zero-Dimensional Ideal"
  In: Proceedings of the 22th Symposium on Theory of Computing
  ACM Press, 1990
  p. 555 - 563

• Lakshman Y.N.
  "A Single Exponential Bound on the Complexity of Computing Grobner Bases of Zero-Dimensional Ideals"
  Progress in Mathematics, Effective Methods in Algebraic Geometry, Volume 94
  Edited by Mora F., Traverso C.
  Birkhauser, Boston, 1991
  p. 227 - 234

• Lakshman Y.N., Lazard D.
  "On the Complexity of Zero Dimensional Algebraic Systems"
  Progress in Mathematics, Effective Methods in Algebraic Geometry, Volume 94
  Edited by Mora F., Traverso C.
  Birkhauser, Boston, 1991
  p. 217 - 225

• Lankford D.
  "Generalized Grobner Bases: Theory and Applications"
  In: Rewriting Techniques and Applications
  Lecture Notes in Computer Science 355
  Edited by Dershowitz N.
  Springer Verlag, New York, 1989
  p. 203 - 221

• 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

• Lazard D.
  "Solving Zero-Dimensional Algebraic Systems"
  Journal of Symbolic Computation 13 (2), 1992
  p. 117 - 131

• Melenk H.:
  "Solving polynomial equation systems by Groebner type methods"
  CWI Quarterly 3, no. 2, 1990
  p. 121 - 136

• Mikhalev A.A.:
  "Shirshov composition techniques in Lie superalgebras (noncommutative Gröbner bases"
  J. Math. Sci. 80, no. 5, 1996
  p. 2153 - 2160

• Miller J.L.:
  "Analogs of Gröbner bases in polynomial rings over a ring"
  J. Symbolic Comput. 21, no. 2, 1996
  p. 139 - 153

• Mishra B., Yap C.
  "Notes on Grobner Bases"
  Information Sciences 48, 1989
  p. 219 - 252

• Möller H.M., Mora F.
  "Upper and Lower Bounds for the Degree of Gröbner Bases"
  Lecture Notes in Computer Science 174
  Springer Verlag, 1984
  p. 172 - 183

• Möller H.M.:
  "On the construction of cubature formulae with few nodes using Groebner bases"
  Math. Phys. Sci. 203, Reidel, 1987
  p. 177 - 192

• Mora T.
  "Groebner Bases for Non Commutative Polynomial Rings"
  In: Proceedings for the AAECC
  Lecture Notes in Computer Science 229, 1986
  p. 353 - 362

• Mora T.:
  "Groebner bases in noncommutative algebras"
  In: Proceedings of Symbolic and Algebraic Computation (Rome, 1988)
  Lecture Notes in Computer Sci. 358, Springer Verlag, 1989
  p. 150 - 161

• Mora T.:
  "Gröbner duality and multiple points in linearly general position"
  Proc. Amer. Math. Soc.

• Oaku T.:
  "Gröbner bases for D-modules on a non-singular affine algebraic variety"
  Tôhoku Math. J. (2) 48, no. 4, 1996
  p. 575 - 600

• Pauer F., Zampieri S.
  "Gröbner bases with respect to generalized term orders and their application to the modelling problem"
  J. Symbolic Comput. 21, no. 2, 1996
  p. 155 - 168

• Robbiano L.
  "Introduction to the Theory of Gröbner Bases"
  Queen's Papers in Pure and Applied Mathematics, Volume V, Number 80, 1988

• Saints K., Heegard C.:
  "Algebraic geometric codes and multidemsional cyclic codes: a unified theory and algorithms for decoding using Gröbner bases"
  IEEE Trans. Inform. Theory 41, no. 6, part 1, (Special issue on algebraic geometry codes), 1995
• Sakata S.
  "Synthesis of two-dimensional linear feedback shift registers and Groebner bases"
  In: Proceedings of Applied algebra, algebraic algorithms and error-correcting codes (Menorca, 1987)
  Lecture Notes in Computer Sci., Springer, 1989
  p. 394 - 407

• Sato Y.
  "Gröbner bases for set constraints"
  Theory of rewriting systems and its applications (Japanese), No. 918, Kyoto, 1995
  p. 277 - 291

• Senechaud P.
  "Implementation of a parallel algorithm to compute a Groebner basis on boolean polynomials"
  Computer Algebra and Parallelism
  Academic Press, 1989
  p. 159 - 166

• Shirayanagi K.:
  "An algorithm to compute floating point Groebner bases"
  In: Proceedings of Mathematical Computation with Maple V: ideas and applications (Ann Arbor, MI, 1993)
  Birkhäuser, Boston, MA, 1993
  p. 95 - 106

• Siegl K.
  "A parallel factorization tree Groebner basis algorithm"
  Proceedings of PASCO' 94
  World Scientific, 1994

• Sturmfels B., Weismantel R., Ziegler G.:
  "Gröbner bases of lattices, corner polyhedra, and integer programming"
  Beiträge Algebra Geom. 36, no. 2, 1995
  p. 281 - 298

• Sweedler M.:
  "Using Groebner bases to determine the algebraic and transcendental nature of field extensions: return of the killer tag variables"
  In: Proceedings of Applied algebra, algebraic algorithms and error correcting codes (San Juan, PR, 1993)
  Lecture Notes in Computer Science 673, Springer Verlag, 1993
  p. 66 - 75

• Sweedler M.:
  "Groebner bases"
  In: Transactions of the Sixth Army Conference on Applied Mathematics and Computing (Boulder, CO, 1988)
  ARO Rep. 89-1, U.S. Army Res. Office, Research Triangle Park, NC, 1989
  p. 699 - 711

• Vidal J.
  "The computation of Groebner bases on a shared memory multiprocessor
  Design and Implementation of Symbolic Computation Systems
  Lecture Notes in Computer Science 429, Springer Verlag, 1990

• Wang M.S., Dai Q.P.:
  "An application of Gröbner bases"
  Kexue Tongbao (Chinese) 41, no. 7, 1996
  p. 586 - 588

• Winiarski T.:
  "Estimation of growth of dominating mappings via Gröbner bases"
  Bull. Polish Acad. Sci. Math. 44, no. 2, 1996
  p. 237 - 244

• Wu, W.J.:
  "On the construction of Groebner basis of a polynomial ideal based on Riquier-Janet theory"
  Systems Sci. Math. Sci. 4, no. 3, 1991
  p. 193 - 207

• Yap C.K.
  "A Double-Exponential Lower Bound for Degree-Compatible Gröbner Bases"
  Journal of Symbolic Computation 12, 1991
  p. 1 - 27

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