Abstract
We present new functionalities that we have added to the RegularChains library in Maple to efficiently compute irredundant triangular decompositions. We report on the implementation of different strategies. Our experiments show that, for difficult input systems, the computing time for removing redundant components can be reduced to a small portion of the total time needed for solving these systems.
Chapter PDF
Similar content being viewed by others
References
Aubry, P., Lazard, D., Moreno Maza, M.: On the theories of triangular sets. J. Symb. Comp. 28(1-2), 105–124 (1999)
Aubry, P., Moreno Maza, M.: Triangular sets for solving polynomial systems: A comparative implementation of four methods. J. S. Com. 28(1-2), 125–154 (1999)
Dahan, X., Schost, É.: Sharp estimates for triangular sets. In: ISSAC 04, pp. 103–110. ACM Press, New York (2004)
Lazard, D.: A new method for solving algebraic systems of positive dimension. Discr. App. Math. 33, 147–160 (1991)
Lemaire, F., Moreno Maza, M., Xie, Y.: The RegularChains library. In: Kotsireas, I.S. (ed.) Maple Conference 2005, pp. 355–368 (2005)
Moreno Maza, M.: On triangular decompositions of algebraic varieties. Technical Report TR 4/99, NAG Ltd., Oxford, UK (1999), http://www.csd.uwo.ca/~moreno
Sommese, A.J., Verschelde, J., Wampler, C.W.: Numerical decomposition of the solution sets of polynomial systems into irreducible components. SIAM J. Numer. Anal. 38(6), 2022–2046 (2001)
The SymbolicData Project (2000–2006), http://www.SymbolicData.org
Wang, D.: Elimination Methods. Springer, Heidelberg (2001)
Lecerf, G.: Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers. J. Complexity 19(4), 564–596 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Chen, C., Lemaire, F., Maza, M.M., Pan, W., Xie, Y. (2007). Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72586-2_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-72586-2_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72585-5
Online ISBN: 978-3-540-72586-2
eBook Packages: Computer ScienceComputer Science (R0)