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» Comparing Real Algebraic Numbers of Small Degree
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ISSAC
2005
Springer
105views Mathematics» more  ISSAC 2005»
14 years 1 months ago
Computing the rank and a small nullspace basis of a polynomial matrix
We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n×n matrix of degree d over ...
Arne Storjohann, Gilles Villard
CORR
2008
Springer
125views Education» more  CORR 2008»
13 years 7 months ago
Simultaneous Modular Reduction and Kronecker Substitution for Small Finite Fields
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform sever...
Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy
ESA
2001
Springer
61views Algorithms» more  ESA 2001»
13 years 12 months ago
A Separation Bound for Real Algebraic Expressions
Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for int...
Christoph Burnikel, Stefan Funke, Kurt Mehlhorn, S...
STACS
2009
Springer
14 years 1 days ago
Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials ...
Mahdi Cheraghchi, Amin Shokrollahi
VISUALIZATION
2005
IEEE
14 years 1 months ago
Build-by-Number: Rearranging the Real World to Visualize Novel Architectural Spaces
We present Build-by-Number, a technique for quickly designing architectural structures that can be rendered photorealistically at interactive rates. We combine image-based capturi...
Daniel R. Bekins, Daniel G. Aliaga