Abstract
We present an improved algorithm to compute the normal chain from a given regular chain such that their saturation ideals are the same. Our algorithm is based on solving a system of linear equations and the original method computes the resultants of multivariate polynomials. From the experiments, for the random polynomials, our algorithm is much more efficient than the original one.
Partially supported by NKBRPC (2004CB318000) and NSFC (10771206).
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References
Aubry, P., Lazard, D., Maza, M.M.: On the Theories of Triangular Sets. J. Symbolic Computation 28, 105–124 (1999)
Bouziane, D., Kandri Rody, A.K., Maarouf, H.: Unmixed-dimensional Decomposition of a Finitely Generated Perfect Differential Ideal. J. Symbolic Computation. 31, 631–649 (2001)
Gao, X.S., Chou, S.C.: Solving parametric algebraic systems. In: Proceedings ISSAC 1992, Berkeley, July 27-29, pp. 335–341. Association for Computing Machinery, New York (1992)
Kalbrener, M.: A Generalized Euclidean Algorithm for Computing Triangular Representations of Algebraic Varieties. J. Symbolic Computation 15, 143–167 (1993)
Lazard, D.: A new method for solving algebraic systems of positive demension. Discrete Appl. Math. 33, 147–160 (1991)
Moreno, M.M.: On triangular decompositions of algebraic varieties. In: MEGA 2000, Bath, England (presented, 2000)
Pan, V.Y.: Sturctured Matrices and Polynomials. Birkhäuser, Boston (2001)
Wang, D.K., Zhang, Y.: An algorithm for decomposing a polynomial system into normal ascending sets. Science in China, Series A: Mathematics 50(10), 1441–1450 (2007)
Wang, D.M.: Some Notes on Algebraic Method for Geometric Theorem Proving
Wang, D.M.: Elimination Method. Springer, New York (2001)
Wu, W.T.: Basic principles of mechanical theorem proving in elementray geometries. J. Syst. Sci. Math. Sci. 4, 20–235 (1984)
Yang, L., Zhang, J.Z.: Search dependency between algebraic equations: An algorithm applied to automated reasoning. Technical Report ICTP/91/6, International Center For Theoretical Physics, Trieste (1991)
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Li, B., Wang, D. (2008). An Algorithm for Transforming Regular Chain into Normal Chain . In: Kapur, D. (eds) Computer Mathematics. ASCM 2007. Lecture Notes in Computer Science(), vol 5081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87827-8_20
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DOI: https://doi.org/10.1007/978-3-540-87827-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87826-1
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