Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Computing the Radical of an Ideal in Positive Characteristic
Journal of Symbolic Computation
Local Decomposition Algorithms
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
An Algorithm for the Computation of the Radical of an Ideal in the Ring of Polynomials
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Jacobian Matrices and Constructions in Algebra
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Yet Another Ideal Decomposition Algorithm
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Properties of Gröbner bases under specializations
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Quantum automata and algebraic groups
Journal of Symbolic Computation
Decomposing polynomial sets into simple sets over finite fields: The positive-dimensional case
Theoretical Computer Science
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The purpose of this paper is to give a complete effective solution to the problem of computing radicals of polynomial ideals over general fields of arbitrary characteristic. We prove that Seidenberg's "Condition P" is both a necessary and sufficient property of the coefficient field in order to be able to perform this computation. Since Condition P is an expensive additional requirement on the ground field, we use derivations and ideal quotients to recover as much of the radical as possible. If we have a basis for the vector space of derivations on our ground field, then the problem of computing radicals can be reduced to computing pth roots of elements in finite dimensional algebras.