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TitleGröbner basis for an ideal of a polynomial ring over an algebraic extension over a field and its applications
Author(s) Sui Sun Cheng, Shugong Zhang
TypeArticle in Journal
AbstractAn algorithm for a Gröbner basis for an ideal of a polynomial ring over an algebraic extension over a field is presented. Algorithms for inverses of convertible level m(r1,r2,,rm)-block circulant matrices and minimal polynomials of level m(r1,r2,,rm)-block circulant matrices over a (s1,s2,,st)-generated algebra F(α1,α2,,αt) of degree (n1,n2,,nt) over a field F are given by the algorithm for the reduced Gröbner basis for an ideal of the polynomial ring F[y1,,yt,x1,,xm]. In particular, the inverses of convertible level m(r1,r2,,rm)-block circulant matrices and the minimal polynomials of level m(r1,r2,,rm)-block circulant matrices over a (s1,s2,,st)-generated algebra Q(α1,α2,,αt) of degree (n1,n2,,nt) over the field Q of all rational numbers can be transformed into those over Q, and then computed by CoCoA 4.1.
ISSN0096-3003
URL http://www.sciencedirect.com/science/article/pii/S0096300303006076
LanguageEnglish
JournalApplied Mathematics and Computation
Volume153
Number1
Pages27 - 58
Year2004
Edition0
Translation No
Refereed No
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