[EXT] Solving Polynomial Equation Systems without Gröbner Bases

252 / BBB

2026-10-06

Akin Ünal

15:45

Solving Polynomial Systems over multiple Variables is a core aspect of Algebraic Cryptanalysis, and many other symbolic calculations.
A typical approach is to compute a degrevlex GB of the system, transform it to a lexicographic GB and apply the Shape-Lemma.
Can we do without GBs?

I will show here an approach that only utilizes Macaulay Matrices and Stickelberger's theorem.
This approach has the advantage that it descends well to quotients of polynomial rings (assuming that a GB of the defining ideal is known).