Solving decomposable sparse polynomial systems

Algebra Seminar
Monday, September 26, 2022 - 1:30pm for 1 hour (actually 50 minutes)
Clough 125 Classroom
Thomas Yahl – TAMU – thomasjyahl@math.tamu.edu
Papri Dey

Polynomial systems can be effectively solved by exploiting structure present in their Galois group. Esterov determined two conditions for which the Galois group of a sparse polynomial system is imprimitive, and showed that the Galois group is the symmetric group otherwise. A system with an imprimitive Galois group can be decomposed into simpler systems, which themselves may be further decomposed. Esterov's conditions give a stopping criterion for decomposing these systems and leads to a recursive algorithm for efficient solving.