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Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations

  • Algorithms 2 — Polynomial Ideal Bases
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Computer Algebra (EUROCAL 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 162))

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References

  1. D.A. Bayer. The division algorithm and the Hilbert scheme, Ph D, Harward Univ., 1982.

    Google Scholar 

  2. B. Buchberger. Ein algorithmishes Kriterium fur die Lösbarkeit eines algebraischen Gleischungsystem. Aequationes Matematicea 4 (1970), p. 374–383.

    Google Scholar 

  3. B. Buchberger. A criterion for detecting unnecessary reductions in the construction of Gröbner bases, EUROSAM'79, Lect. Notes in Comp. Sc. no 72 (1979), p. 3–21.

    Google Scholar 

  4. B. Buchberger. A note on the complexity of constructing Gröbner bases. These proceedings.

    Google Scholar 

  5. I. Kaplansky. Commutative rings. Allyn and Bacon (Boston, 1970).

    Google Scholar 

  6. D. Lazard. Algèbre linéaire sur K[X1,...,Xn] et élimination. Bull. Soc. Math. France 105 (1977), p. 165–190.

    Google Scholar 

  7. D. Lazard. Systems of algebraic equations. EUROSAM 79, p. 88–94.

    Google Scholar 

  8. D. Lazard. Résolution des systèmes d'équations algébriques. Theor. Comp. Sciences 15 (1981), p. 77–110.

    Google Scholar 

  9. D. Lazard. Commutative Algebra and Computer Algebra, EUROCAM'82, Lect. Notes in Comp. Sc. no 144 (1982), p. 40–48.

    Google Scholar 

  10. F. Mora. An algorithm to compute the equations of tangent cones, EUROCAM'82, p. 158–165.

    Google Scholar 

  11. M. Pohst, D.Y.Y. Yun. On solving systems of algebraic equations via ideal bases and elimination theory SYMSAC 1981, p. 206–211.

    Google Scholar 

  12. W. Trinks, Ueber B. Buchberger Verfahren, Systeme algebraischer Gleischungen zu lösen, J. of Number Theory 10 (1978), p. 475–488.

    Google Scholar 

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J. A. van Hulzen

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© 1983 Springer-Verlag

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Lazard, D. (1983). Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations. In: van Hulzen, J.A. (eds) Computer Algebra. EUROCAL 1983. Lecture Notes in Computer Science, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12868-9_99

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  • DOI: https://doi.org/10.1007/3-540-12868-9_99

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12868-7

  • Online ISBN: 978-3-540-38756-5

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