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A criterion for detecting unnecessary reductions in the construction of Groebner bases
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On radical zero-dimensional ideals
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On the complexity of computing a Gröbner basis for the radical of a zero dimensional ideal
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Gröbner bases and the defining polynomial of a context-free grammar generating function
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An algorithm for the computation of the radical of an ideal
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On approximate triangular decompositions in dimension zero
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Gröbner bases for polynomial systems with parameters
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New algorithms for computing primary decomposition of polynomial ideals
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Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
Journal of Symbolic Computation
Parallelization of Modular Algorithms
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On the computation of matrices of traces and radicals of ideals
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We present an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic ideal theoretic operations can be performed using Grobner bases and we exploit these constructions to inductively reduce the problem to zero dimensional ideals. Here we again exploit the structure of Grobner bases to directly compute the primary decomposition using polynomial factorization. We also show how the reduction process can be applied to computing radicals and testing ideals for primality.