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GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation

Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet
1989 Journal of symbolic computation  
A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers.  ...  The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme.  ...  For example, the GCDHEU algorithm presented in this paper is based on evaluation at integer values and the solver may compute a GCD which is a multiple of the true GCD, but never a sub-multiple.  ... 
doi:10.1016/s0747-7171(89)80004-5 fatcat:sqjk4aow3ncixa4kbn2p2rtrom

Evaluation of the heuristic polynomial GCD

Hsin-Chao Liao, Richard J. Fateman
1995 Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95  
The Heuristic Polynomial GCD procedure (GCDHEU) is Richard Zippel, Effective Polynomial Computation, Kluwer Academic Publishers, Boston 1993.  ...  Acknowledgments We thank Daniel Lichtblau of Wolfram Research Inc. for his information on the GCD methods used in Mathematical.  ...  The end result is a pair of fairly large integers. A guess at the polynomial GCD is then constructed one variable at a time using rn-adic interpolations starting from the GCD of these two numbers.  ... 
doi:10.1145/220346.220376 dblp:conf/issac/LiaoF95 fatcat:aox7tsovordg7ky6v3l5bt4zcm

In-place arithmetic for polynomials over Zn [chapter]

Michael Monagan
1993 Lecture Notes in Computer Science  
These algorithms provide the key tools for the efficient implementation of polynomial resultant gcd and factorization computation over Z, without having to write large amounts of code in a systems implementation  ...  We present space and time efficient algorithms for univariate polynomial arithmetic operations over Z mod n where the modulus n does not necessarily fit into is not a machine word.  ...  The first method [17] is a heuristic method that reduces the problem to a single Gcd computation over Zn for a large possibly composite modulus n.  ... 
doi:10.1007/3-540-57272-4_21 fatcat:cnum46gw4bbkhjy7tvuae6uenq

Page 1192 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
GCDHEU: heuristic polynomical GCD algorithm based on integer GCD computation. 90g:68073 Dvornicich, Roberto (with Traverso, Carlo) Newton symmetric functions and the arithmetic of algebraically closed  ...  minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial.  ... 

Page 423 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
GCDHEU: heuristic polynomical GCD algorithm based on integer GCD computation. J. Symbolic Comput. 7 (1989), no. 1, 31-48. (Michael Clausen) 90g:68073 68Q40 (11Y16, 12-04) Gonor, A. L.  ...  Heuristic methods for operations with algebraic numbers (extended abstract). Symbolic and algebraic computation (Rome, 1988), 475-480, Lecture Notes in Comput.  ... 

Page 139 of Mathematical Reviews Vol. 17, Issue Index [page]

Mathematical Reviews  
GCDHEU: heuristic polynomial GCD algorithm based on integer GCD computation. EUROSAM 84 (Cambridge, 1984), 285-296, Lecture Notes in Comput. Sci., 174, Springer, Berlin-New York, 1984.  ...  Algorithms for univalence of polynomial mappings of domains. (Russian) Trudy Vychisl. Tsentra Akad. Nauk Gruzin. SSR 22 (1982), no. 1, 65-76. (W. C. Royster) 85e:30019 30045 (30C35) Chanturia, Z. A.  ...