Skip to main content

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

  • Conference paper
  • First Online:
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 356))

  • 189 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bayer D.A. The division algorithm and the Hilbert scheme. Ph.d. Thesis Harvard 1982.

    Google Scholar 

  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. Blum L. Differentially closed fields: a model theoretic tour. in Contribution to Algebra p.37–60 Academic Press 1977.

    Google Scholar 

  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. Buchberger B.,Loos J. Algebraic Simplification in Computer Algebra p.11–43 Springer 1982.

    Google Scholar 

  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. Carra' G., Gallo G. A procedure to prove geometrical statements. submitted to AAECC 5.

    Google Scholar 

  8. Enderton H.B. A Mathematical Introduction to Logic Academic Press (1973).

    Google Scholar 

  9. Giusti M. A note on complexity of constructing standard bases Proc.EUROCAL 85,II Springer LNCS p.411–412 1985.

    Google Scholar 

  10. Hermann G. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math.Ann. 95 (1926), p.736–788.

    Article  Google Scholar 

  11. Heintz J. Definability and fast quantifier elimination in algebraically closed fields. Theoretical Computer Science 24(1983) p.239–277.

    Article  Google Scholar 

  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. Kolchin E. Differential Algebra and algebraic groups. Academic Press 1973.

    Google Scholar 

  14. Kapur D.K. Using Gröbner bases to reason about geometry problems. J.of Sym.Computation 2,p.399–408, 1986.

    MathSciNet  Google Scholar 

  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. 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.

    MathSciNet  Google Scholar 

  17. Möller H.M., Mora F. Upper and lower bounds for the degree of Gröbner bases. Proc EUROSAM 84 Springer LNCS 174 p.172–183

    Google Scholar 

  18. Ritt J.F. Differential Algebra AMS 1950.

    Google Scholar 

  19. Seidenberg A. Constructions in Algebra Trans. AMS 197, p.273–313 (1974).

    Google Scholar 

  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. 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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Llorenç Huguet Alain Poli

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ferro, A., Gallo, G. (1989). Grobner bases, Ritt's algorithm and decision procedures for algebraic theories. In: Huguet, L., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1987. Lecture Notes in Computer Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51082-6_81

Download citation

  • DOI: https://doi.org/10.1007/3-540-51082-6_81

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51082-6

  • Online ISBN: 978-3-540-46150-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics