Invariants of singularities of polynomials in two complex variables and the Newton diagrams.
Masternak, Mateusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Masternak, Mateusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Janusz Gwoździewicz (1998)
Banach Center Publications
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Karim Belabas, Mark van Hoeij, Jürgen Klüners, Allan Steel (2009)
Journal de Théorie des Nombres de Bordeaux
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We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.
Jordi Guàrdia, Jesús Montes, Enric Nart (2011)
Journal de Théorie des Nombres de Bordeaux
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We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a -adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good.
Karaś, Marek (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Maria Frontczak, Przemysław Skibiński, Stanisław Spodzieja (1999)
Colloquium Mathematicae
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Yuri Bilu, Robert Tichy (2000)
Acta Arithmetica
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Panagiotis Tzekis, Nicholas Karampetakis, Haralambos Terzidis (2007)
International Journal of Applied Mathematics and Computer Science
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The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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