Bounding the Number of Common Zeros of Multivariate Polynomials and Their Consecutive Derivatives
Bounding the Number of Common Zeros of Multivariate Polynomials and Their Consecutive Derivatives
We upper-bound the number of common zeros over a finite grid of multivariate polynomials and an arbitrary finite collection of their consecutive Hasse derivatives (in a coordinate-wise sense). To that end, we make use of the tool from Gröbner basis theory known as footprint. Then we establish and prove extensions …