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TitleAn efficient algorithm for factoring polynomials over algebraic extension field.
Author(s) Yao Sun, Dongming Wang
TypeArticle in Journal
AbstractAn efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Gröbner basis, no extra Gröbner basis computation is needed for factoring a polynomial over this extension field. Nothing more than linear algebraic technique is used to get a characteristic polynomial of a generic linear map. Then this polynomial is factorized over the ground field. From its factors, the factorization of the polynomial over the extension field is obtained. The algorithm has been implemented in Magma and computer experiments indicate that it is very efficient, particularly for complicated examples.
Keywordsalgorithm, factorization, algebraic extension field
ISSN1674-7283; 1869-1862/e
URL http://link.springer.com/article/10.1007%2Fs11425-013-4586-0
JournalSci. China, Math.
PublisherSpringer, Berlin/Heidelberg; Science in China Press, Beijing
Translation No
Refereed No