Details:
Title  Conquering inseparability: Primary decomposition and multivariate factorization over algebraic function fields of positive characteristic  Author(s)  Allan K. Steel  Type  Article in Journal  Abstract  Algebraic function fields of positive characteristic are nonperfect fields, and many standard algorithms for solving some fundamental problems in commutative algebra simply do not work over these fields. This paper presents practical algorithms for the first time for (1) computing the primary decomposition of ideals of polynomial rings defined over such fields and (2) factoring arbitrary multivariate polynomials over such fields. Difficulties involving inseparability and the situation where the transcendence degree is greater than one are completely overcome, while the algorithms avoid explicit construction of any extension of the input base field. As a corollary, the problem of computing the primary decomposition of a positivedimensional ideal over a finite field is also solved. The algorithms perform very effectively in an implementation within the Magma Computer Algebra System, and an analysis of their practical performance is given.  Keywords  Algebraic function field, Nonperfect field, Inseparability, Primary decomposition, Polynomial factorization, Gröbner basis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717105000751 
Language  English  Journal  Journal of Symbolic Computation  Volume  40  Number  3  Pages  1053  1075  Year  2005  Edition  0  Translation 
No  Refereed 
No 
