Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
A completion procedure for computing canonical basis for a k-Subalgebra
Proceedings of the third conference on Computers and mathematics
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Deciding linear disjointness of finitely generated fields
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Basic algorithms for rational function fields
Journal of Symbolic Computation
Gröbner bases applied to finitely generated field extensions
Journal of Symbolic Computation - Special issue on applications of the Gröbner basis method
Computing the Intersection of finitely generated fields
ACM SIGSAM Bulletin
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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Grobner bases can be used to solve various algorithmic problems in the context of finitely generated field extensions. One key idea is the computation of a certain kind of restriction of an ideal to a subring. With this restricted ideal many problems concerning function fields reduce to ideal theoretic problems which can be solved by means of Buchberger's algorithm. In this contribution this approach is generalized to allow the computation of the restriction of an arbitrary ideal to a subring.