Grobner bases, Ritt's algorithm and decision procedures for algebraic theories

  • Alfredo Ferro
  • Giovanni Gallo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 356)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bayer D.A. The division algorithm and the Hilbert scheme. Ph.d. Thesis Harvard 1982.Google Scholar
  2. [2]
    Ben-Or M.,Kozen D.,Reif J. The complexity of Elementary Algebra and Geometry. J.of Computation and System Science 32 p.109–138 (1986).Google Scholar
  3. [3]
    Blum L. Differentially closed fields: a model theoretic tour. in Contribution to Algebra p.37–60 Academic Press 1977.Google Scholar
  4. [4]
    Buchberger B. A critical pair completion algorithm for finitely generated ideals in rings. Proc. logic and Machines: Decision problems and Complexity, Springer LNCS 171 p.137–161 (1983).Google Scholar
  5. [5]
    Buchberger B.,Loos J. Algebraic Simplification in Computer Algebra p.11–43 Springer 1982.Google Scholar
  6. [6]
    Carra' G. Some upper bounds for the multiplicity of an autoreduced subset of Nn and their applications. Proc.AAECC 3 Springer LNCS 299 p.306–315.Google Scholar
  7. [7]
    Carra' G., Gallo G. A procedure to prove geometrical statements. submitted to AAECC 5.Google Scholar
  8. [8]
    Enderton H.B. A Mathematical Introduction to Logic Academic Press (1973).Google Scholar
  9. [9]
    Giusti M. A note on complexity of constructing standard bases Proc.EUROCAL 85,II Springer LNCS p.411–412 1985.Google Scholar
  10. [10]
    Hermann G. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math.Ann. 95 (1926), p.736–788.CrossRefGoogle Scholar
  11. [11]
    Heintz J. Definability and fast quantifier elimination in algebraically closed fields. Theoretical Computer Science 24(1983) p.239–277.CrossRefGoogle Scholar
  12. [12]
    Heintz J. and Wutrich R. An efficient quantifier elimination algorithm for algebraically closed field of any characteristic. SIGSAM Bull. 9(4) (1975) 11.Google Scholar
  13. [13]
    Kolchin E. Differential Algebra and algebraic groups. Academic Press 1973.Google Scholar
  14. [14]
    Kapur D.K. Using Gröbner bases to reason about geometry problems. J.of Sym.Computation 2,p.399–408, 1986.MathSciNetGoogle Scholar
  15. [15]
    Knuth D.E. and Bendix P.B. Simple words problems in universal algebras. Proc.Conf.Comp.problems in abstract algebra,1967 p.263–297 Pergamon Press 1970.Google Scholar
  16. [16]
    Kutzler B. and Stifter S. On the application of Buchberger's algorithm to automated geometry theorem proving J. of Sym. Computation 2, p. 389–397, 1986.MathSciNetGoogle Scholar
  17. [17]
    Möller H.M., Mora F. Upper and lower bounds for the degree of Gröbner bases. Proc EUROSAM 84 Springer LNCS 174 p.172–183Google Scholar
  18. [18]
    Ritt J.F. Differential Algebra AMS 1950.Google Scholar
  19. [19]
    Seidenberg A. Constructions in Algebra Trans. AMS 197, p.273–313 (1974).Google Scholar
  20. [20]
    Wu W. Basic Principles of mechanical theorem proving in elementary geometries. J.Sys.Sci. & Math.Scis. 4(3) 1984, p.207–235.Google Scholar
  21. [21]
    Wu W. Mechanical Theorem Proving in Elementary Geometry and differential geometry. Proc. 1980 Beijing Simp. on Diff.Geom.& Diff.Eqs vol.2 (1982) Science Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Alfredo Ferro
    • 1
    • 2
  • Giovanni Gallo
    • 1
    • 2
  1. 1.Dipartimento di MatematicaCataniaItaly
  2. 2.Courant InstituteNew YorkU.S.A.

Personalised recommendations