Contents
Preface vii
Multivariate Ultrametric Root Counting
Mart´
ın
Avenda˜
no and Ashraf Ibrahim 1
A Parallel Endgame
Daniel J. Bates, Jonathan D. Hauenstein,
and Andrew J. Sommese 25
Efficient Polynomial System Solving by Numerical Methods
Carlos
Beltr´
an and Luis Miguel Pardo 37
Symmetric Determinantal Representation of Formulas and Weakly Skew
Circuits
Bruno Grenet, Erich L. Kaltofen, Pascal Koiran, and Natacha
Portier 61
Mixed Volume Computation in Solving Polynomial Systems
Tsung-Lin Lee and Tien-Yien Li 97
A Search for an Optimal Start System for Numerical Homotopy Continuation
Anton Leykin 113
Complex Tropical Localization, and Coamoebas of Complex Algebraic
Hypersurfaces
Mounir Nisse 127
Randomization, Sums of Squares, Near-Circuits, and Faster Real Root Counting
Osbert Bastani, Chris J. Hillar, Dimitar Popov, and J. Maurice
Rojas 145
Dense Fewnomials
Korben Rusek, Jeanette Shakalli, Frank Sottile 167
The Numerical Greatest Common Divisor of Univariate Polynomials
Zhonggang Zeng 187
v
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