P-adic root isolation.

Sturm, Thomas, and Weispfenning, Volker. "P-adic root isolation.." RACSAM 98.1 (2004): 239-258. <http://eudml.org/doc/41636>.

@article{Sturm2004,
abstract = {We present an implemented algorithmic method for counting and isolating all p-adic roots of univariate polynomials f over the rational numbers. The roots of f are uniquely described by p-adic isolating balls, that can be refined to any desired precision; their p-adic distances are also computed precisely. The method is polynomial space in all input data including the prime p. We also investigate the uniformity of the method with respect to the coefficients of f and the primes p. Our method thus provides information analogous to that provided by well-established real methods as, e.g., Cauchy bounds and Sturm sequences over the reals.},
author = {Sturm, Thomas, Weispfenning, Volker},
journal = {RACSAM},
keywords = {p-adic fields; root isolation; root counting; algorithm},
language = {eng},
number = {1},
pages = {239-258},
title = {P-adic root isolation.},
url = {http://eudml.org/doc/41636},
volume = {98},
year = {2004},
}

TY - JOUR
AU - Sturm, Thomas
AU - Weispfenning, Volker
TI - P-adic root isolation.
JO - RACSAM
PY - 2004
VL - 98
IS - 1
SP - 239
EP - 258
AB - We present an implemented algorithmic method for counting and isolating all p-adic roots of univariate polynomials f over the rational numbers. The roots of f are uniquely described by p-adic isolating balls, that can be refined to any desired precision; their p-adic distances are also computed precisely. The method is polynomial space in all input data including the prime p. We also investigate the uniformity of the method with respect to the coefficients of f and the primes p. Our method thus provides information analogous to that provided by well-established real methods as, e.g., Cauchy bounds and Sturm sequences over the reals.
LA - eng
KW - p-adic fields; root isolation; root counting; algorithm
UR - http://eudml.org/doc/41636
ER -