Shift equivalence of P-finite sequences.
Kauers, Manuel (2006)
The Electronic Journal of Combinatorics [electronic only]
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Kauers, Manuel (2006)
The Electronic Journal of Combinatorics [electronic only]
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Beslin, Scott J. (1992)
International Journal of Mathematics and Mathematical Sciences
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Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis (2013)
Serdica Journal of Computing
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In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences...
Barbero, Stefano, Cerruti, Umberto, Murru, Nadir (2010)
Journal of Integer Sequences [electronic only]
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Devitt, J.S., Mollin, R.A. (1986)
International Journal of Mathematics and Mathematical Sciences
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Woods, Kevin (2005)
The Electronic Journal of Combinatorics [electronic only]
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Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis (2014)
Serdica Journal of Computing
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ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2. In 1971 using pseudo-divisions - that is, by working in Z[x] - Brown and Traub computed Euclid’s polynomial remainder sequences (prs’s) and (proper) subresultant prs’s using sylvester1, the most widely known form of Sylvester’s matrix, whose determinant defines the resultant of two polynomials. In this paper we use, for the first time in the literature, the Pell-Gordon Theorem of 1917, and sylvester2, a little...
Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis (2015)
Serdica Journal of Computing
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In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell...
Manfred Peter (2002)
Acta Arithmetica
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Petkovšek, Marko, Wilf, Herbert S. (1996)
The Electronic Journal of Combinatorics [electronic only]
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Xavier Vidaux (2011)
Acta Arithmetica
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Barat, Guy, Frougny, Christiane, Pethő, Attila (2005)
Integers
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Andrica, Dorin, Piticari, Mihai (2002)
Acta Universitatis Apulensis. Mathematics - Informatics
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K. Martín, Juan Manuel Olazábal (1991)
Extracta Mathematicae
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