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Efficient p-adic Cell Decompositions for Univariate Polynomials

✍ Scribed by Michael Maller; Jennifer Whitehead

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
177 KB
Volume
15
Category
Article
ISSN
0885-064X

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✦ Synopsis

Cell decompositions are constructed for polynomials f (x) # Z p [x] of degree n, such that n< p, using O(n 2 ) cells. When f is square-free this yields a polynomialtime algorithm for counting and approximating roots in Z p . These results extend to give a polynomial-time algorithm in the bit model for f # Z[x].

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## Abstract In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for __p__‐adically closed fields. We work here with the notion of __P__‐minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a __P__‐minimal field __K__ admits cell decomposition if an