Related papers: Implementing p-adic numbers in Macaulay2 using its…
The complexity of Gr\"{o}bner computations has inspired many improvements to Buchberger's algorithm over the years. Looking for further insights into the algorithm's performance, we offer a threaded implementation of classical Buchberger's…
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
With the proliferation of embedded systems requiring intelligent behavior, custom number systems to optimize performance per Watt of the entire system become essential components for successful commercial products. We present the Universal…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this…
We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schemes.
We present PackLib^2, the first fully integrated benchmark library for multi-dimensional packing instances. PackLib^2 combines a systematic collection of all benchmark instances from previous literature with a well-organized set of new and…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
FinInG is a package for computation in Finite Incidence Geometry. It provides users with the basic tools to work in various areas of finite geometry from the realms of projective spaces to the flat lands of generalised polygons. The…
We continuously interact with computerized systems to achieve goals and perform tasks in our personal and professional lives. Therefore, the ability to program such systems is a skill needed by everyone. Consequently, computational thinking…
Large software systems often comprise programs written in different programming languages. In the case when cross-language interoperability is accomplished with a Foreign Function Interface (FFI), for example pybind11, Boost.Python,…
Astronomers are increasingly using Massively Parallel Network of Workstations (MP-NOW) to address their most challenging computing problems. Fully exploiting these systems is made more difficult as more and more modeling and data analysis…
In this paper we focus on the integration of high-performance numerical libraries in ab initio codes and the portability of performance and scalability. The target of our work is FLEUR, a software for electronic structure calculations…
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…
The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degrees and projective degrees of rational maps without any…
Ising machines can solve combinatorial optimization problems by representing them as energy minimization problems. A common implementation is the probabilistic Ising machine (PIM), which uses probabilistic (p-) bits to represent coupled…
This paper documents Int2Int, an open source code base for using transformers on problems of mathematical research, with a focus on number theory and other problems involving integers. Int2Int is a complete PyTorch implementation of a…
The FFT of three-dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on a large number of processors. Performance of many scientific…
I present new features of the open-source Python package lips, which leverages the newly developed pyadic and syngular libraries. These developments enable the generation and manipulation of massless phase-space configurations beyond real…