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» Comparing Real Algebraic Numbers of Small Degree
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ISSAC
2005
Springer
105views Mathematics» more  ISSAC 2005»
15 years 5 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»
14 years 11 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»
15 years 4 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
15 years 4 months 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
15 years 5 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