Computing the irreducible real factors and components of an algebraicf curve

Authors:
E. Kaltofen
Affiliations:
Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York
Venue:
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Year:
1989

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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.