The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On the substitution of polynomial forms
ACM '73 Proceedings of the ACM annual conference
ACM '73 Proceedings of the ACM annual conference
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
Factoring multivariate polynomials over the integers
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Multivariate quotient by power-series division
ACM SIGSAM Bulletin
Algebraic algorithms using p-adic constructions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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A new algorithm for division with remainder of univariate and multivariate polynomials over the integers is reported. This division algorithm relies on a p-adic construction which is closely related to the Hensel-type constructions used for polynomial factorization and greatest common divisor computations. It furnishes a new and systematic way of looking at the classical problem of division (with or without remainder). Due to the sparseness-preserving property of p-adic constructions, it appears useful as an alternative division algorithm in suitable cases when the polynomials are sparse. Detailed discussion and a more complete computing time analysis will be deferred until a later time as the work progresses further. An hope, in the meantime, is to attract comments and criticism on the algorithm and its significance.