ISSAC 2006 Poster Committee di erent weights and the sets of initial Hensel factors are the same, then the sets of resulting Hensel factors are also the same. Theorem 2: in the case that Newton polynomials are di erent, there is a procedure to convert one set of Hensel factors to another set, so long as there is a one-to-one correspondence among the sets of initial Hensel factors. Theorem 3: all the di erent sets of Hensel factors are classi ed by a fan in the weight space. In deriving the last theorem, we referred to the theory of polytope [Zig95]. These theorems lead us to a concept of Hensel fan", just as the concept of Gr bner fan is introduced for classifying Gr bner bases w.r.t. di erent term ordering [MR88],[Stu95]. o o REFERENCES [Kuo89] T.-C. Kuo: Generalized Newton-Puiseux theory and Hensel s lemma in C[[x, y]]. Canad. J. Math. XLI, 1101-1116 (1989). [MR88] F. Mora and L. Robbiano: The Gr bner fan of an ideal. J. Symbolic Comput. 6, no.2-3, 183-208 (1988). o [SI00] T. Sasaki and D. Inaba: Hensel construction of F (x, u1 , . . . , u ), tions. ACM SIGSAM Bulletin
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Towards collaboration across display diversity
Krandick, Werner; Pierce, Shawn S.; Wan, Zhendong
Follow ACM Communications in Computer Algebra
, Volume 40 (2)
Association for Computing Machinery – Jun 1, 2006
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