Constructive lifting in graded structures: A unified view of Buchberger and Hensel methods

Authors:
A. Miola;T. Mora
Affiliations:
Dipartimento di Informatica e Sistemistica dell'Università degli Studi di Roma La Sapienza, Italy;Dipartimento di Matematica dell'Università di Genova, Italy
Venue:
Journal of Symbolic Computation
Year:
1988

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Abstract

This paper discusses a general lifting technique for solving polynomial equations in gradedstructures A, where the solution is understood to lie in the completion A^@^ of A. It shows that the classical Hensel lifting and the main constructions related to the Buchberger algorithm for Grobner bases are both instances of this technique. So, while the setting of it is too general to allow for an effective solution of equations, this technique stresses a theoretical relation between two basic algorithms in computer algebra and could be used as a theoretical model to attack computation problems under the same viewpoint.