Related papers: Rings: an efficient Java/Scala library for polynom…
In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings $A$ in…
We present release 2.0 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…
The recent series 5 of the ASP system clingo provides generic means to enhance basic Answer Set Programming (ASP) with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints, discuss the…
We show that the $\imath$Hall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism from this $\imath$Hall algebra to…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
We present QuantumToolbox$.$jl, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of QuTiP (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast…
This paper introduces the Encog library for Java and C#, a scalable, adaptable, multiplatform machine learning framework that was 1st released in 2008. Encog allows a variety of machine learning models to be applied to datasets using…
Combinatorial algorithms such as those that arise in graph analysis, modeling of discrete systems, bioinformatics, and chemistry, are often hard to parallelize. The Combinatorial BLAS library implements key computational primitives for…
In this work, we present MOLPIPx, a versatile library designed to seamlessly integrate Permutationally Invariant Polynomials (PIPs) with modern machine learning frameworks, enabling the efficient development of linear models, neural…
Let $A$ be a finite dimensional algebra over an algebraically closed field. We present a relationship between simple-minded systems and coherent rings.
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
We study the set of algebraic objects known as vanishing polynomials (the set of polynomials that annihilate all elements of a ring) over general commutative rings with identity. These objects are of special interest due to their close…
General revision. In particular the parts concerning involutive bases over rings have been significantly changed. In addition some proofs have been improved.
On many parallel machines, the time LQCD applications spent in communication is a significant contribution to the total wall-clock time, especially in the strong-scaling limit. We present a novel high-performance communication library that…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
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…
The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting correlative and term sparsity to obtain a new moment-SOS…