相关论文: Toric Geometry in OSCAR
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
Celeste is a procedure for inferring astronomical catalogs that attains state-of-the-art scientific results. To date, Celeste has been scaled to at most hundreds of megabytes of astronomical images: Bayesian posterior inference is…
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…
We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of…
The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it…
We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
To any toric ideal $I_A$, encoded by an integer matrix $A$, we associate a matroid structure called {\em the bouquet graph} of $A$ and introduce another toric ideal called {\em the bouquet ideal} of $A$. We show how these objects capture…
We study the abelian sub-C*-algebra of the CAR algebra generated by the start and face opertors of Kitaev's toric code. We show that it is a C*-diagonal equivalent to the canonical diagonal of the CAR algebra.
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of…
Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this thesis we explore this correspondence to classify smooth lattice…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
We study whether a given tropical curve $\Gamma$ in $\mathbb{R}^n$ can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented by $\Gamma$. We give an affirmative answer to this…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
Toric varieties are perhaps the most accessible class of algebraic varieties. They often arise as varieties parameterized by monomials, and their structure may be completely understood through objects from geometric combinatorics. While…