Factoring Polynomials Over Algebraic Number Fields
ACM Transactions on Mathematical Software (TOMS)
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EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
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EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
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SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
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ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
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ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
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The calculation of radical ideals in positive characteristic
Journal of Symbolic Computation
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This paper considers the problem of factoring polynomials over a variety of domains. We first describe the current methods of factoring polynomials over the integers, and extend them to the integers mod p. We then consider the problem of factoring over algebraic domains. Having produced several negative results, showing that, if the domain is not properly specified, then the problem is insoluble, we then show that, for a properly specified finitely generated extension of the rationals or the integers mod p, the problem is soluble. We conclude by discussing the problems of factoring over algebraic closures.