Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Efficient factorization of polynomials over local fields |
| Συγγραφείς: |
Chistov, A. L. |
| Στοιχεία εκδότη: |
American Mathematical Society (AMS), Providence, RI |
| Θεματικοί όροι: |
Computational methods for problems pertaining to field theory, local field, polynomial time, Newton polygon, Symbolic computation and algebraic computation, algorithm for factorizing a multivariate polynomial, Polynomials |
| Περιγραφή: |
The author gives an algorithm for factorizing a multivariate polynomial \(f\) over a local field \(K\) in time polynomial in the length of the input data and the characteristic of the field. He reduces the problem to the case of a separable polynomial in one variable, for which the theorem was already proven by himself [J. Sov. Math. 34, 1838--1882 (1986); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 137, 124--188 (1984; Zbl 0561.12010)]. He uses the Newton polygon to embed \(K[X]/(f)\) into a product \(\prod_{\ell \in L}K_{\ell}[X]/(f_{\ell}),\) where \(K_{\ell}/K\) is tamely ramified and \(f_{\ell}\) is irreducible over \(K_{\ell}\). Finally he uses the Newton polygon to compute the roots of \(f\) in \(K_{\ell}[X]/(f_{\ell})\). Finally he computes the irreducible factors by taking norms. |
| Τύπος εγγράφου: |
Article |
| Περιγραφή αρχείου: |
application/xml |
| Σύνδεσμος πρόσβασης: |
https://zbmath.org/4035950 |
| Αριθμός Καταχώρησης: |
edsair.c2b0b933574d..dd3c071cf283038b1a61ecb28ca6080f |
| Βάση Δεδομένων: |
OpenAIRE |