8 citations · 24 across the 17 of their papers we have counts for
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A Polyhedral Homotopy Algorithm For Real Zeros
Alperen A. Ergür, Timo de Wolff
We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is…
The algebraic boundary of the sonc cone
Jens Forsgård, Timo de Wolff
In this article, we explore the connections between nonnegativity, the theory of -discriminants, and tropical geometry. For an integral support set , we…
The Lattice of Amoebas
Jens Forsgård, Timo de Wolff
We study amoebas of exponential sums as functions of the support set . To any amoeba, we associate a set of approximating sections of amoebas, which we call caissons. We show th…
A Positivstellensatz for Sums of Nonnegative Circuit Polynomials
Mareike Dressler, Sadik Iliman, Timo de Wolff
Recently, the second and the third author developed sums of nonnegative circuit polynomials (SONC) as a new certificate of nonnegativity for real polynomials, which is independent…
Imaginary projections of polynomials
Thorsten Jörgens, Thorsten Theobald, Timo de Wolff
We introduce the imaginary projection of a multivariate polynomial as the projection of the variety of onto its imaginary part, $\mathcal{I}(f) \…
Norms of Roots of Trinomials
Thorsten Theobald, Timo de Wolff
The behavior of norms of roots of univariate trinomials for fixed support with respect to the choice of…
Amoebas, Nonnegative Polynomials and Sums of Squares Supported on Circuits
Sadik Iliman, Timo de Wolff
We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on circuits, a genuine class of spars…
The Boundary of Amoebas
Franziska Schroeter, Timo de Wolff
The computation of amoebas has been a challenging open problem for the last dozen years. The most natural approach, namely to compute an amoeba via its boundary, has not been pract…
Separating inequalities for nonnegative polynomials that are not sums of squares
Sadik Iliman, Timo de Wolff
Ternary sextics and quaternary quartics are the smallest cases where there exist nonnegative polynomials that are not sums of squares (SOS). A complete classification of the differ…
Amoebas of genus at most one
Thorsten Theobald, Timo de Wolff
The amoeba of a Laurent polynomial $f \in \C[z_1^{\pm 1},\ldots,z_n^{\pm 1}]$ is the image of its zero set under the log-absolute-value map. Understanding the spac…
Approximating amoebas and coamoebas by sums of squares
Thorsten Theobald, Timo de Wolff
Amoebas and coamoebas are the logarithmic images of algebraic varieties and the images of algebraic varieties under the arg-map, respectively. We present new techniques for computa…