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GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation

1989
*
Journal of symbolic computation
*

A

doi:10.1016/s0747-7171(89)80004-5
fatcat:sqjk4aow3ncixa4kbn2p2rtrom
*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. ...##
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Evaluation of the heuristic polynomial GCD

1995
*
Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95
*

The

doi:10.1145/220346.220376
dblp:conf/issac/LiaoF95
fatcat:aox7tsovordg7ky6v3l5bt4zcm
*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. ...##
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In-place arithmetic for polynomials over Zn
[chapter]

1993
*
Lecture Notes in Computer Science
*

These

doi:10.1007/3-540-57272-4_21
fatcat:cnum46gw4bbkhjy7tvuae6uenq
*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. ...##
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Page 1192 of Mathematical Reviews Vol. , Issue Index
[page]

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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*. ...

##
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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*. ...

##
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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. ...