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ApaTools: a software toolbox for approximate polynomial algebra

Published: 06 February 2009 Publication History
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References

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D.J. BATES, C. PETERSON AND A.J. SOMMESE, A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set, IEEE Trans. Signal Processing, 52 (2003), pp. 3394--3402.
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D.J. BATES, J.D. HAUENSTEIN, A.J. SOMMESE AND C.W. WAMPLER II, Software for numerical algebraic geometry: A paradigm and progress towards its implementation, in Software for Algebraic Geometry, IMA Volume 148, M. Stillman, N. Takayama, and J. Verschelde, eds., Springer, 2008, pp. 1--14.
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R. M. CORLESS, S. M. WATT, AND L. ZHI, QR factoring to compute the GCD of univariate approximate polynomials, IEEE Trans. Signal Processing, 52 (2003), pp. 3394--3402.
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B. DAYTON AND Z. ZENG, Computing the multiplicity structure in solving polynomial systems. Proceedings of ISSAC '05, ACM Press, pp 116--123, 2005.
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S. GAO, E. KALTOFEN, J. MAY, Z. YANG, AND L. ZHI, Approximate factorization of multivariate polynomials via differential equations. Proc. ISSAC '04, ACM Press, pp 167--174, 2004.
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C.-P. JEANNEROD AND G. LABAHN, The SNAP package for arithemetic with numeric polynomials. In International Congress of Mathematical Software, World Scientific, pages 61--71, 2002.
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A.J. SOMMESE AND C.W. WAMPLER II, The Numerical Solution of Systems of Polynomials, World Scientific Pub., Hackensack, NJ. 2005.
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H. J. STETTER, Numerical Polynomial Algebra, SIAM, 2004.
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J. VERSCHELDE, Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation, ACM Trans. on Math. Software, 25(1999), pp. 251--276.
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Z. ZENG, A polynomial elimination method for symbolic and numerical computation. to appear, 2008.
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Z. ZENG, Computing multiple roots of inexact polynomials, Math. Comp., 74 (2005), pp. 869--903.
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Z. ZENG, ApaTools: A Maple and Matlab toolbox for approximate polynomial algebra, in Software for Algebraic Geometry, IMA Volume 148, M. Stillman, N. Takayama, and J. Verschelde, eds., Springer, 2008, pp. 149--167.
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cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 42, Issue 3
September 2008
80 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/1504347
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 February 2009
Published in SIGSAM-CCA Volume 42, Issue 3

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  • (2022)Singularity Computation for Rational Parametric Surfaces Using Moving PlanesACM Transactions on Graphics10.1145/355138742:1(1-14)Online publication date: 3-Oct-2022

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