### D.4.1 absfact_lib

Library:
  absfact.lib
Purpose:
  Absolute factorization for characteristic 0
Authors:
  Wolfram Decker, decker at math.uni-sb.de
  Gregoire Lecerf, lecerf at math.uvsq.fr
  Gerhard Pfister, pfister at mathematik.uni-kl.de Martin Lee, mlee at mathematik.uni-kl.de

Overview:
  A library for computing the absolute factorization of multivariate polynomials f with coefficients in a field K of characteristic zero. Using Trager's idea, the implemented algorithm computes an absolutely irreducible factor by factorizing over some finite extension field L (which is chosen such that V(f) has a smooth point with coordinates in L). Then a minimal extension field is determined making use of the Rothstein-Trager partial fraction decomposition algorithm. absFactorizeBCG uses the algorithm of Bertone, Cheze and Galligo for bivariate polynomials and similar ideas as above to reduce to this case.

References:
  G. Cheze, G. Lecerf: Lifting and recombination techniques for absolute factorization. Journal of Complexity, 23(3):380-420, 2007. C. Bertone, G. Cheze, and A. Galligo: Modular las vegas algorithms for polynomial absolute factorization. J. Symb. Comput., 45(12):1280-1295, December 2010

Procedures:

> D.4.1.1 absFactorize |  | absolute factorization of poly
> D.4.1.2 absFactorizeBCG |  | absolute factorization of poly

See also: factorize.

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