11 citations · 38 across the 15 of their papers we have counts for
5 papers · 1 filter
Metric Estimates and Membership Complexity for Archimedean Amoebae and Tropical Hypersurfaces
Martin Avendano, Roman Kogan, Mounir Nisse +1
Given any complex Laurent polynomial , is the image of its complex zero set under the coordinate-wise log absolute value map. We give an efficiently constru…
Interpolation of Ideals
Martin Avendano, Jorge Ortigas-Galindo
Let K denote an algebraically closed field. We study the relation between an ideal I in K[x1,...,xn] and its cross sections I_a=I+<x1-a>. In particular, we study under what conditi…
Multivariate ultrametric root counting
Martin Avendano, Ashraf Ibrahim
Let be a field, complete with respect to a discrete non-archimedian valuation and let be the residue field. Consider a system of polynomial equations in $K\vars$. O…
Ultrametric Root Counting
Martin Avendano, Ashraf Ibrahim
Let be a complete non-archimedean field with a discrete valuation, a polynomial with non-vanishing discriminant, the valuation ring of , and $\M$ the maximal…
The number of real roots of a bivariate polynomial on a line
Martin Avendano
We prove that a bivariate polynomial f with exactly t non-zero terms, restricted to a real line {y=ax+b}, either has at most 6t-4 zeroes or vanishes over the whole line. As a conse…