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Computing the irreducible real factors and components of an algebraic curve

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Abstract

We present algorithms that decompose an algebraic curve with rational coefficients in its defining bivariate equation into its irreducible real factors and its non-empty irreducible real components. We show that our algorithms are of polynomial bit complexity in the degree of the equation and the size of its coefficients. Our construction is based on computing the irreducible complex factors and then investigating high precision complex floating point coefficients of these factors and the complex norms.

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Authors and Affiliations

  1. Department of Computer Science, Rensselaer Polytechnic Institute, 12180-3590, Troy, NY, USA

    Erich Kaltofen

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  1. Erich Kaltofen
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Additional information

This material is based on work supported by the National Science Foundation under Grant No. CCR-87-05363 and under Grant No. CDA-8805910. A preliminary version of this paper appears in the Proceedings of the 5th Annual Symposium on Computational Geometry, ACM Press, pp. 79–87 (1989)

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Kaltofen, E. Computing the irreducible real factors and components of an algebraic curve. AAECC 1, 135–148 (1990). https://doi.org/10.1007/BF01810297

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  • DOI: https://doi.org/10.1007/BF01810297

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