Related papers: Groebner.jl: A package for Gr\"obner bases computa…
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…
Solving multihomogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance. Experimentally, solving these systems with Gr\"obner bases algorithms seems to be easier…
Portable GPU frameworks such as Kokkos and RAJA reduce the burden of cross-architecture development but typically incur measurable overhead on fundamental parallel primitives relative to vendor-optimized libraries. We present…
This habilitation (German variant of a PhD on top of a PhD) thesis presents the quintessence of the ideas and experiences with Groebner Bases of Birgit Reinert. She died unexpectedly without providing an abstract. As arXiv requires an…
This paper presents a high-performance framework for three-dimensional gravity modeling and inversion implemented in Julia, addressing key challenges in geophysical modeling such as computational complexity, ill-posedness, and the…
We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gr\"obner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also present two accompanying software packages named…
One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…
In this paper we present an algorithm for construction of minimal involutive polynomial bases which are Groebner bases of the special form. The most general involutive algorithms are based on the concept of involutive monomial division…
The theory of Groebner Bases originated in the work of Buchberger and is now considered to be one of the most important and useful areas of symbolic computation. A great deal of effort has been put into improving Buchberger's algorithm for…
An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…
Let T(x) in k[x] be a monic non-constant polynomial and write R=k[x] / (T) the quotient ring. Consider two bivariate polynomials a(x, y), b(x, y) in R[y]. In a first part, T = p^e is assumed to be the power of an irreducible polynomial p. A…
We investigate the use of noncommutative Groebner bases in solving partially prescribed matrix inverse completion problems. The types of problems considered here are similar to those in [BLJW]. There the authors gave necessary and…
We introduce monomial divisibility diagrams (MDDs), a data structure for monomial ideals that supports insertion of new generators and fast membership tests. MDDs stem from a canonical tree representation by maximally sharing equal…
PowerSimulations.jl is a Julia-based BSD-licensed power system operations simulation tool developed as a flexible and open source software for quasi-static power systems simulations including Production Cost Models. PowerSimulations.jl…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
This paper presents a performant and portable recursive implementation of triangular matrix-matrix multiplication (TRMM) and triangular solve (TRSM) in Julia for GPUs, two kernels that underlie many linear-algebra algorithms. We restructure…
Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze…
TypedMatrices.jl is a Julia package to organize test matrices. By default, the package comes with a number of built-in matrices and interfaces to help users select test cases based on their properties. The package is designed to be…
Jet reconstruction remains a critical task in the analysis of data from HEP colliders. We describe in this paper a new, highly performant, Julia package for jet reconstruction, JetReconstruction.jl, which integrates into the growing…
The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as…