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» The Complexity of the Annihilating Polynomial
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ANTS
2006
Springer
105views Algorithms» more  ANTS 2006»
15 years 1 months ago
A Modular Method for Computing the Splitting Field of a Polynomial
We provide a modular method for computing the splitting field Kf of an integral polynomial f by suitable use of the byproduct of computation of its Galois group Gf by p-adic Staudu...
Guénaël Renault, Kazuhiro Yokoyama
ISAAC
2010
Springer
233views Algorithms» more  ISAAC 2010»
14 years 8 months ago
Computing Sparse Multiples of Polynomials
We consider the problem of finding a sparse multiple of a polynomial. Given f F[x] of degree d, and a desired sparsity t, our goal is to determine if there exists a multiple h F[...
Mark Giesbrecht, Daniel S. Roche, Hrushikesh Tilak
TIT
2010
98views Education» more  TIT 2010»
14 years 4 months ago
QR decomposition of Laurent polynomial matrices sampled on the unit circle
Abstract--We consider Laurent polynomial (LP) matrices defined on the unit circle of the complex plane. QR decomposition of an LP matrix A(s) yields QR factors Q(s) and R(s) that, ...
Davide Cescato, Helmut Bölcskei
CSL
2010
Springer
14 years 10 months ago
Randomisation and Derandomisation in Descriptive Complexity Theory
We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic ...
Kord Eickmeyer, Martin Grohe
DAGSTUHL
2008
14 years 11 months ago
Real Algebraic Numbers: Complexity Analysis and Experimentation
Abstract. We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree d, with integer coefficients of bit size , using S...
Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsig...