Polynomial system solving: Properties and algorithms - Part 4 | Vidéo

Polynomial system solving: Properties and algorithms - Part 4

computer algebra
linear algebra
Algebraic systems
Equation solving
Algebraic combinatorics
Resultant
Mixed volume
Algebraic algorithms

Appears in collection : 2023 - T3 - WS2 - Special Week

Τhe study of polynomial systems is a centerpiece in solving a wide variety of scientific and engineering problems. We are interested in understanding the power of alternative approaches, which complement the traditional tools of algebraic geometry, namely techniques emanating from combinatorics and linear algebra. Two basic concepts have established themselves as primary ways of addressing such questions, namely mixed volume and sparse resultants, the main ingredients of toric elimination theory. We wish to examine recent progress in both directions, including extensions such as new resultant formulae and randomized algorithms, while also considering specific application domains such as Voronoi diagrams, structural bioinformatics, or game theory.