Related papers: Implementing p-adic numbers in Macaulay2 using its…
We introduce FunKit, a Mathematica package for the derivation and tracing of functional equations from arbitrary master equations. FunKit provides an expression vocabulary and a set of rules that allow for derivations in any given field…
Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes…
The advent of modern data processing has led to an increasing tendency towards interdisciplinarity, which frequently involves the importation of different technical approaches. Consequently, there is an urgent need for a unified data…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as…
Massively parallel Fourier transforms are widely used in computational sciences, and specifically in computational fluid dynamics which involves unbounded Poisson problems. In practice the latter is usually the most time-consuming operation…
Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…
Aggregate programming is a field-based coordination paradigm with over a decade of exploration and successful applications across domains including sensor networks, robotics, and IoT, with implementations in various programming languages,…
We introduce the VirtualResolution package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating…
Processing-in-memory (PIM) promises to alleviate the data movement bottleneck in modern computing systems. However, current real-world PIM systems have the inherent disadvantage that their hardware is more constrained than in conventional…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
A supplemental paper detailing the QuillenSuslin package for Macaulay2. The QuillenSuslin package for Macaulay2 provides the ability to compute a free basis for a projective module over a polynomial ring with coefficients in Q, Z or Z/p for…
In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code,…
Normaliz is a tool for the computation of Hilbert bases of normal affine monoids and related tasks. We describe the Macaulay 2 interface to Normaliz. It makes Normaliz accessible for operations on monoid algebras in Macaulay 2 and,…
Exterior calculus with its three operations meet, join and hodge star complement, is used for the representation of fermion-hole systems and for fermionic analogues of logical gates. Two different schemes that implement fermionic quantum…
The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. While several mixed integer programming (MIP)…
This introduces Rees algebras and some of their uses with illustrations via version 2.0 of the Macaulay2 package ReesAlgebra.m2.
Recently, Transformer-based models have achieved promising results in various vision tasks, due to their ability to model long-range dependencies. However, transformers are computationally expensive, which limits their applications in…