The Hensel Lemma in Algebraic Manipulation
MASSACHUSETTS INST OF TECH CAMBRIDGE PROJECT MAC
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New and improved algorithms for computation in several fundamental polynomial operations are presented. The common basis for these algorithms are generalizations of the p-adic technique used in the constructive proof of the Hensel Lemma. Multivariate polynomial operations are stressed due to the special importance of the multivariate Hensel-type construction in replacing the modular evaluation-and-interpolation technique under certain conditions. Due to the availability of numerous methods for the computation of polynomial greatest common divisors GCD, the EZGCD Algorithm is given special emphasis. Both theoretically and by actual computing data, this new algorithm demonstrates promising efficiencies by taking advantage of the sparseness of multivariate polynomials.
- Theoretical Mathematics
- Computer Programming and Software