Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

Many computer vision applications require robust estimation of the underlying geometry, in
terms of camera motion and 3D structure of the scene. These robust methods often rely on …

We present a massively parallel framework for computing tropicalizations of algebraic
varieties which can make use of symmetries using the workflow management system GPI …

Many new ciphers target a concise algebraic description for efficient evaluation in a proof
system or a multi-party computation. This new target for optimization introduces algebraic …

The new functions added in this version include dd MatrixCanonicalize to find a
nonredundant proper H-or V-representation, dd FindRelativeInterior to find a relative interior …

Polytropes are both ordinary and tropical polytopes. We show that tropical types of
polytropes in TP n− 1 are in bijection with cones of a certain Gröbner fan GF n in R n 2− n …

We consider the notions of Groebner fan and Newton non-degeneracy for an ideal on a toric
variety, extending the two existing notions for ideals on affine spaces. We prove, without …

We show that the tropical projective Grassmannian of planes is homeomorphic to a closed
subset of the analytic Grassmannian in Berkovich's sense by constructing a continuous …

The Gröbner walk is an algorithm for conversion between Gröbner bases for different term
orders. It is based on the polyhedral geometry of the Gröbner fan and involves tracking a line …

In this paper we propose a general functorial definition of the operation of\emph {local
tropicalization} in commutative algebra. Let $ R $ be a commutative ring, $\Gamma $ a …