30 citations · 93 across the 23 of their papers we have counts for
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Sparse systems with high local multiplicity
Frédéric Bihan, Alicia Dickenstein, Jens Forsgård
Consider a sparse system of n Laurent polynomials in n variables with complex coefficients and support in a finite lattice set A. The maximal number of isolated roots of the system…
New bounds for the number of connected components of fewnomial hypersurfaces
Frédéric Bihan, Tristan Humbert, Sébastien Tavenas
We prove that the number of connected components of a smooth hypersurface in the positive orthant of defined by a real polynomial with monomials, where $…
Optimal Descartes' Rule of Signs for Circuits
Frédéric Bihan, Alicia Dickenstein, Jens Forsgård
We present an optimal version of Descartes' rule of signs to bound the number of positive real roots of a sparse system of polynomial equations in n variables with n+2 monomials. T…
Sign conditions for the existence of at least one positive solution of a sparse polynomial system
Frédéric Bihan, Alicia Dickenstein, Magalí Giaroli
We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real ro…
Descartes' Rule of Signs for Polynomial Systems supported on Circuits
Frédéric Bihan, Alicia Dickenstein
We give a multivariate version of Descartes' rule of signs to bound the number of positive real roots of a system of polynomial equations in n variables with n+2 monomials, in term…
Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes
Frédéric Bihan, Pierre-Jean Spaenlehauer
Consider a regular triangulation of the convex-hull of a set of points in , and a real matrix of size . A version of Viro's method…