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Title	Applications of strong Gr\"obner bases over Euclidean domains.
Author(s)	Daniel Lichtblau
Type	Article in Journal
Abstract	Strong Gr ̈ obner bases over Euclidean domains and even more general rings were first defined in the 1980s. Since that time, efficient ways to compute them, and a variety of applications, have appeared. In this note we show, via simple examples, applications to solving equations in quotient rings, Hensel lifting, Hermite normal form computations, reduction of univariate polynomial lattices, and finding small generators in quadratic number rings
Keywords	Gr ̈ obner basis, Euclidean domain, Hensel lifting, Hermite normal form, linear diophantine systems, lattice reduction, Popov form
ISSN	1312-8868; 1314-7595/e
File
URL	http://www.m-hikari.com/ija/ija-2013/ija-5-8-2013/lichtblauIJA5-8-2013.pdf
Language	English
Journal	Int. J. Algebra
Volume	7
Number	5-8
Pages	369--390
Publisher	Hikari, Ruse
Year	2013
Edition	0
Translation	No
Refereed	No