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CoCoA: A user-friendly system for commutative algebra

  • Symbolic And Algebraic Computation — Systems Design
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 429))

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Bibliography

  1. D. A. Bayer, The Division Algorithm and the Hilbert Scheme, Ph. D. Thesis, Harvard Univ., Cambridge, Mass., 1982.

    Google Scholar 

  2. B. Buchberger, Ein Algorithmus zum Auffiden des Restklassenringes nach einem nulldimensionalen Polynomideale, Ph.D. Thesis, Univ. Innsbrück, Austria, 1965.

    Google Scholar 

  3. B. Buchberger, Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems, Aequationes Math. 4 (1970), 364–383.

    Google Scholar 

  4. B. Buchberger, A criterion for detecting unnecessary reductions in the construction of Gröbner bases, in “Proc. EUROSAM '79”, 3–21, Lect. Notes in Comp. Sci., vol. 72, 1979.

    Google Scholar 

  5. B. Buchberger, Gröbner bases: An algorithmic method in polynomial ideal theory, in “Recent Trends in Multidimensional System Theory” (N. K. Bose, Ed.), Reidel, Dordrecht, 1985.

    Google Scholar 

  6. G. Carra' Ferro, Some upper bounds for multiplicity of an autoreduced subset of INm and their applications, in “Proc. AAECC-3”, 306–315, Lect. Notes in Comp. Sci., vol. 229, 1986.

    Google Scholar 

  7. J. H. Davenport, Y. Siret, E. Tournier, “Computer Algebra”, Academic Press, London, 1988.

    Google Scholar 

  8. R. Gebauer — M. Möller, On an Installation of Buchberger's Algorithm, J. of Symb. Comp. 6 (1988), 275–286.

    Google Scholar 

  9. A. Giovini — G. Niesi, CoCoA User's Manual (v.0.99b–May 1989), University of Genova

    Google Scholar 

  10. P. Gianni — B. Trager — G. Zacharias, Gröbner and Primary Decomposition of Polynomial Ideals, J. of Symb. Comp. 6 (1988), 149–167.

    Google Scholar 

  11. H. Kredel — V. Weispfenning, computing Dimension and Independent Set for Polynomial Ideals, J. of Symb. Comp. 6 (1988), 231–247.

    Google Scholar 

  12. D. Lazard, Gröbner bases, Gaussian elimination, and resolution of systems of algebraic equations, in “Proc. EUROCAL '83”, 146–156, Lect. Notes in Comp. Sci., vol. 162, 1983.

    Google Scholar 

  13. D. Lazard, Ideal bases and primary decomposition: case of two variables, J. of Symb. Comp. 1 (1985), 261–270.

    Google Scholar 

  14. H.M. Möller — F. Mora, Upper and lower bounds for the degree of Gröbner bases, in “Proc. EUROSAM '84”, 172–183, Lect. Notes in Comp. Sci., vol.162, 1983.

    Google Scholar 

  15. H.M. Möller — F. Mora, The computation of the Hilbert function, in “Proc. EUROCAL '83”, 157–167, Lect. Notes in Comp. Sci., vol.174, 1984.

    Google Scholar 

  16. H.M. Möller — F. Mora, New Constructive Methods in Classical Ideal Theory, J. Alg. 100 (1986), 138–178.

    Google Scholar 

  17. F. Mora, An algorithm to compute the equations of tangent cones, in “Proc. EUROCAM '82”, 158–165, Lect. Notes in Comp. Sci., vol.144, 1982.

    Google Scholar 

  18. L. Robbiano, Term Orderings on the Polynomial Ring, in “Proc. EUROCAL '85”, 513–517, Lect. Notes in Comp. Sci., vol.204, 1985.

    Google Scholar 

  19. L. Robbiano, On the theory of graded structures, J.of Symb. Comp. 2 (1986), 139–170.

    Google Scholar 

  20. L. Robbiano, Introduction to the theory of Gröbner Bases, in “Queen's Papers in Pure and Applied Mathematics”, n. 80 (1988).

    Google Scholar 

  21. L. Robbiano, Computer and Commutative Algebra, in “Proc. AAECC 6”, 157–167, Lect. Notes in Comp. Sci., vol.357, 1988.

    Google Scholar 

  22. L. Robbiano, Gröbner Bases: a Foundation for Commutative Algebra, notes of a tutorial given at MIT in June 1989.

    Google Scholar 

  23. L. Robbiano — G. Valla, On set theoretic complete intersections in the projective space, Rend. Sem. Mat. Fis. Milano 53 (1983), 333–346.

    Google Scholar 

  24. M. Stillman — M. Stillman — D. Bayer, Macaulay User Manual, May 25, 1989

    Google Scholar 

  25. C. Traverso, Experimenting the Gröbner basis algorithm with the AIPI system, in “Proc. of ISSAC '89”, ACM Press, 192–198

    Google Scholar 

  26. W. Trinks, Über B. Buchberger's Verfahren, Systeme algebraischerm Gleichungen zu Losen, J. of Number Theory 10 (1978), 475–488.

    Google Scholar 

  27. S. Wolfram, “Mathematica, A System for Doing Mathematics by Computer”, Addison Wesley, Reading, Mass, 1988

    Google Scholar 

  28. G. Zacharias, Generalized Gröbner basis in commutative polynomial Rings, Bachelor Thesis, MIT, 1978.

    Google Scholar 

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Alfonso Miola

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© 1990 Springer-Verlag Berlin Heidelberg

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Giovini, A., Niesi, G. (1990). CoCoA: A user-friendly system for commutative algebra. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1990. Lecture Notes in Computer Science, vol 429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52531-9_120

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  • DOI: https://doi.org/10.1007/3-540-52531-9_120

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52531-8

  • Online ISBN: 978-3-540-47014-4

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