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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:
See also:
factorize.
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