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On Factor Refinement in Number Fields (1996)
| Content Provider | CiteSeerX |
|---|---|
| Author | Buchmann, Johannes Eisenbrand, Friedrich |
| Abstract | Let O be an order of an algebraic number field. It was shown by Ge [Ge93],[Ge94] that given a factorization of an O-ideal a into a product of O-ideals it is possible to compute in polynomial time an overorder O 0 of O and a gcd-free refinement of the input factorization, i.e. a factorization of aO 0 into a power product of O 0 -ideals such that the bases of that power product are all invertible and pairwise coprime and the extensions of the factors of the input factorization are products of the bases of the output factorization. In this paper we prove that the order O 0 is the smallest overorder of O in which such a gcd-free refinement of the input factorization exists. We also introduce a partial ordering on the gcd-free factorizations and prove that the factorization which is computed by Ge's algorithm is the smallest gcd-free refinement of the input factorization with respect to this partial ordering. 1 Introduction Let O be an order in an algebraic number field K and let ... |
| File Format | |
| Volume Number | 68 |
| Journal | Math. Comp |
| Language | English |
| Publisher Date | 1996-01-01 |
| Access Restriction | Open |
| Subject Keyword | Gcd-free Refinement Number Field Input Factorization Factor Refinement Partial Ordering Power Product Algebraic Number Field Output Factorization Input Factorization Exists Polynomial Time Introduction Let Pairwise Coprime Gcd-free Factorization Ge Ge93 |
| Content Type | Text |
| Resource Type | Article |
