Abstract
We show that a constructive version of the fundamental theorem of algebra [3], combined with the basis reduction algorithm from [1], yields a polynomial-time algorithm for factoring polynomials in one variable with rational coefficients.
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References
A.K. Lenstra, H.W. Lenstra, Jr., L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1972), 515–534.
M. Mignotte, An inequality about factors of polynomials, Math. Comp. 28 (1974), 1153–1157.
A. Schönhage, The fundamental theorem of algebra in terms of computational complexity, manuscript, 1982.
A. Schönhage, Factorization of univariate integer polynomials by diophantine approximation and by an improved basis reduction algorithm, manuscript, 1983.
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© 1984 Springer-Verlag Berlin Heidelberg
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Lenstra, A.K. (1984). Polynomial factorization by root approximation. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032849
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DOI: https://doi.org/10.1007/BFb0032849
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