Summary
Polynomial factorization is one of the main chapters of Computer Algebra. Recently, significant progress was made on absolute factorization (i.e., over the complex field) of a multivariate polynomial with rational coefficients, with two families of algorithms proposing two different strategies of computation. One is represented by Gao’s algorithm and is explained in Lecture 2. The other is represented by the Galligo-Rupprecht-Chèze algorithm, presented in Lectures 4 and 5. The latter relies on an original use of the monodromy map attached to a generic projection of a plane curve on a line. It also involves zero-sums relations (introduced by Sasaki and his collaborators) with efficient semi-numerical computations to produce a certified exact result.
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© 2005 Springer-Verlag Berlin Heidelberg
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Chèze, G., Galligo, A. (2005). Four lectures on polynomial absolute factorization. In: Bronstein, M., et al. Solving Polynomial Equations. Algorithms and Computation in Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27357-3_9
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DOI: https://doi.org/10.1007/3-540-27357-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24326-7
Online ISBN: 978-3-540-27357-8
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