# Symbolic Computation [Lecture notes] by Clemens Heuberger PDF

By Clemens Heuberger

version sixteen may possibly 2011

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Clemens Heuberger's Symbolic Computation [Lecture notes] PDF

version sixteen may possibly 2011

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Seien p0 (n), . . , pd (n) Polynome in n, L = i=0 pi (n)N i und h = i=1 hn eine (i) hypergeometrische geschlossene Form mit paarweise nicht ähnlichen hn . Dann gilt Lh = 0 genau (i) dann, wenn Lhn = 0 für 1 ≤ i ≤ r gilt. Man kann also alle hypergeometrischen geschlossenen Formen h, die Lh = 0 lösen, dadurch (i) (i) finden, dass man alle Linearkombinationen von hypergeometrischen Termen hn bildet, die Lhn = 0 lösen. 35 Kapitel 3 Faktorisierung von Polynomen Sei in diesem Kapitel K immer ein Körper der Charakteristik 0 oder ein endlicher Körper der Charakteristik p für eine Primzahl p.

15. Dann gilt H(g) ≤ LC(g) n 2 f . LC(f ) 39 f . 3 Hensel-Lifting r Gegeben: p, F , G0 = j=0 gj X j , H0 = Gesucht: Gt , Ht ∈ Z[X] mit F ≡ Gt · Ht n = deg F Setze  g0 g1 g2 . .  0 g0 g1 g2  0 0 g0 g1   .. .. . .  0 0 . . 0 M = h0 h1 h2 . .   0 h0 h1 h2  0 0 h0 h1  . .. . . . 0 0 ... 10, t ≥ 0, p LC(F ) (mod pt+1 ) gr−1 ... g2 .. gr gr−1 ... . g0 hs−1 ... h2 .. g1 hs hs−1 ... . h0 h1 0 gr 0 0 gr .. ... ... . g2 0 hs hs−1 ... 0 0 hs .. gr−1 ... ... . h2 ... hs−1 gr−1  0 0  0  ..

41 Literaturverzeichnis [1] W. Adams, Ph. Loustaunau: An introduction to Gröbner bases, Graduate Studies in Mathematics, vol. 3, American Mathematical Society, 1994 [2] Th. Becker, V. Weispfenning: Gröbner bases. A computational approach to commutative algebra, Graduate Texts in Mathematics, vol. 141, Springer, 1993 [3] B. Buchberger: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems, Aequationes Math. 4, 373-383, 1970 [4] B. Buchberger: Introduction to Gröbner bases, in Buchberger, Winkler [5], pp.