Hilbert functions and the Buchberger algorithm

Journal of Symbolic Computation

Volumn 22, Issue 4, 1996, Pages 355-376

  Traverso, Carlo ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030268743     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0056     Document Type: Article

References (62)

1. AlPi 1988-96: C. Traverso, AlPi: a system for experimenting with Buchberger algorithm; ftp://posso.dm.unipi.it
2. Audoly, S., Bellu G., Buttu, A., D'Angiò, L. (1991). Procedure to investigate injectivity of polynomial maps and to compute the inverse, AAECC J., 2, 91-103.
3. Backelin, J., Fröberg, R. (1991). How we proved that there are exactly 926 cyclic n-roots, ISSAC'91, ACM, 103-111.
4. Bayer, D. (1982). The division algorithm and the Hilbert scheme. Thesis, Harvard.
5. Bayer, D., Stillman, M. (1992). Computation of Hilbert functions, J. Symbolic Computation 14, 31-50.
6. Becker, T., Weispfenning, V. (1993). Gröbner Bases, Graduate Texts in Mathematics 141, Springer-Verlag.
7. Bigatti, A.M. (1966). Computations of Hilbert-Poincaré Series, J. Pure and Applied Algebra.
8. Bigatti, A.M., Caboara, M., Robbiano, L. (1991). On the computation of Hilbert-Poincaré series, AAECC J., 2, 21-33.
9. Bigatti, A.M., Conti, P., Robbiano, L., Traverso, C. (1992). A "Divide and conquer" algorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals, Proc. AAECC-10 LNCS 673, Springer
10. n, whose Fourier transforms have constant modulus, and "cyclic n-roots", J.S. Byrnes and J.F. Byrnes, (eds), Recent Advances in Fourier Analysis and its Applications, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., Kluwer 315, 131-140.
11. Björk, G., Fröberg, R. (1991). A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots, J. Symbolic Computation 12, 329-336.
12. Björk, G., Fröberg, R. (1994). Methods to divide out certain solutions from systems of algebraic equations, applied to find all cyclic 8-roots, Lect. Notes in Pure and Appl. Math. vol. 156, Gyllenberg, M. and Persson, L.E. (eds), Marcel Dekker, 57-70.
13. Boege, W., Gebauer, R., Kredel, H. (1986). Some examples for solving systems of algebraic equations by calculating Gröbner bases, J. Symbolic Computation 2, 83-89.
14. Buchberger, B. (1979). A criterion for detecting unnecessary reduction in the construction of Gröbner bases, EUROSAM '79, Springer LNCS 72, 3-21.
15. Caboara, M., De Dominicis, G., Robbiano, L. (1996). Multigraded Hilbert functions and Buchberger Algorithm, ISSAC'96, ACM, 72-78.
16. Caboara, M., Traverso, C. (1966). The powerful Buchberger algorithm for modules, (preprint).
17. Capani, A., De Dominicis, G., Niesi, G., Robbiano, L. (1996). Computing Minimal Free Resolutions, preprint; MEGA-96, Eindhoven.
18. CoCoA3 1995: Capani, A., Niesi, G., Robbiano, L. (1995). CoCoA 3, a system for doing Computations in Commutative Algebra. ftp://lancelot.dima.unige.it
19. Cohn, H. (1982). An explicit modular equation in two variables and Hilbert's Twelfth Problem, Math. of Comp. 38 227-236.
20. Collart, S., Kalkbrener, M., Mall, D. (1996). Converting bases with the Gröbner walk, J. Symbolic Computation (to appear).
21. 3 Theorem, Proc. AAECC-11, LNCS 948, 183-193.
22. Corless, R., Gianni, P., Trager, B., Watt, S. (1995). The singular value decomposition for polynomial systems, 195-207, Proc. ISSAC'95, ACM Press.
23. Eisenbud, D. (1995). Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics 150, Springer-Verlag.
24. Faugère, J.C. (1994). Résolution des Systèmes d'équations algébriques, Thesis.
25. Faugère, J.C., Gianni, P., Lazard, D., Mora, T. (1993). Efficient computation of zero-dimensional Gröbner bases by change of ordering, J. Symbolic Computation 16(4), 329-344.
26. Gao, X.-S., Chou, S.-C. (1992). Solving parametric algebraic systems, Proc. ISSAC'92, ACM Press, 335-341.
27. GB system 1990-96, Faugère, J.C., GB: system for Gröbner basis computations, ftp://posso.ibp.fr
28. Gebauer, R., Moeller, H.M. (1988). On an installation of Buchberger's algorithm, J. Symbolic Computation 6, 275-286.
29. Gianni, P., Mora, T. (1989). Algebraic solutions of systems of polynomial equations using Gröbner bases, AAECC-5, LNCS 356.
30. Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C. (1991). "One sugar cube, please" OR Selection strategies in Buchberger algorithm, ISSAC'91, ACM Press, 49-54.
31. Grassmann H., Greuel, G.M., Martin, B., Neumann, W., Pfister, G., Pohl, W., Schönemann, H., Siebert, T. (1955). Standard Bases, Syzygies and their Implementation in Singular, preprint.
32. Greuel, G.M., Pfister, G. (1996). Advances and improvements in the theory of standard bases and syzygies, Arch. Math. 66, 163-176.
33. Hoffmann, C.M. (1989). Geometric & Solid Modeling: An Introduction, Morgan Kaufmann Publ. Inc.
34. Hollman, J. (1992). On the computation of the Hilbert series, Latin 92, Saõ Paulo, LNCS 583, Springer-Verlag
35. Katsura, S., Fukuda, W., Inawashiro, S., Fujiki, N.M., Gebauer, R. (1987). Distribution of effective field in the Ising spin glass of the ± J model at T = 0, Cell Biophysics Vol. 11, p. 309-319.
36. Kondrat'eva, M.V., Pankrat'ev, E.V. (1987). A recursive algorithm for the computation of Hilbert polynomial, EUROCAL 87, LNCS 387, Springer-Verlag.
37. La Scala, R. (1994). An algorithm for complexes, Proc. ISSAC'94, ACM Press, 264-268.
38. La Scala, R. (1996). A computational approach to minimal free resolutions, Ph.D thesis.
39. Licciardi, S., Mora, T. (1994). Implicitization of hypersurfaces and curves by the Primbasissatz and the FGLM algorithm, ISSAC'94, ACM Press, 191-196.
40. Liu, Z. (1987). An algorithm for finding all isolated zeroes of polynomial equations, MM Research Preprints, 4, Inst. Sys. Sci., Acad. Sinica.
41. Macaulay-2 (1966). Grayson, D., Stillman, M., a systems for computations in commutative algebra and algebraic geometry, beta version, see http://www.math.uiuc.edu/~dan/Macaulay2/index.html
42. Marinari, M., Möller, M., Mora, T. (1993). Gröbner bases of ideals defined by functionals with an application to ideals of protective points, AAECC 4, 103-145.
43. Matsumura, H. (1986). Commutative Ring Theory, Cambridge studies in advanced Mathematics 8, Cambridge University Press.
44. Möller, M., Mora, T. (1983). The computation of the Hilbert function, Proc. EUROCAL 83, LNCS 162, 157-167.
45. Möller, M., Mora, T. (1984). Upper and lower bounds for the degree of Gröbner bases, Proc. EUROSAM 84, LNCS 174, 172-183.
46. Möller, M., Mora, T. (1986). New constructive methods in classical ideal theory. J. Algebra 100, 138-178.
47. Möller, M., Mora, T. (1986). Computational aspects of reduction strategies to construct resolutions of monomial ideals, AAECC2, LNCS 228, 182-197.
48. Möller, M., Mora, T., Traverso, C. (1992). Gröbner basis computing using syzygies, Proc. ISSAC'92, 320-328.
49. L), Disc. Appl. Math., 33, 161-190.
50. Mora, T., Pfister, G., Traverso, C. (1991). An introduction to the tangent cone algorithm, in: Issues in non-linear geometry and robotics, Hoffman, C., (ed.), JAI Press.
51. Mora, T., Robbiano, L. (1988). The Gröbner fan of an ideal J. Symbolic Computaton 6, 183-208.
52. Niermann, M. (1992). Computing Gröbner bases of arbitrary ideals by change of term orders, Preprint.
53. Pavelle, R. (1985). MACSYMA: capabilities and applications to problems in engineering and the sciences, technical report, Symbolics.
54. PoSSo: Polynomial System Solving (1992-95). Basic Research ESPRIT contract 6846, posso@dm.unipi.it; http://posso.dm.unipi.it; PoSSo test suites: a series of examples of polynomial systems, ftp://posso.dm.unipi.it/pub/posso
55. Robbiano, L. (1990). On the theory of Hilbert functions, Queen's Papers in Pure and Appl. Math., Kingston Canada, 85 Vol VII.
56. Schreyer, F.O. (1980). Die Berechnung von Syzygien mit dem verallgemeinertem Weierstrass'schen Divisionsatz. Diplomarbeit, Hamburg.
57. Shannon, D., Sweedler, M. (1988). Using Groebner bases to determine algebra membership, split surjective algebra homomorphisms and determine birational equivalence, J. Symbolic Computation 6, 267-273.
58. Singular: Greuel, G.M., Pfister, G., Schönemann, H., (1995). Singular: a system for computation in algebraic geometry and singularity theory: system and user manual available by anonymous ftp from helios.mathematik.uni-kl.de
59. Spear, D. (1977). A constructive approach to commutative ring theory, Proc. Macsyma User's conference 369-376.
60. Traverso, C., Donati, L. (1989). Experimenting the Gröbner basis algorithm with the AlPi system, ISSAC'89 Proc. ACM, 192-198.
61. Traverso, C. (1988). Gröbner trace algorithms, ISSAC'88, LNCS 358, 125-138.
62. Traverso, C. (1993). Computing the Hilbert-Poincaré series of monomial ideals, applications to Gröbner bases, FPSAC Proc., 443-453.