Related papers: TaylUR 3, a multivariate arbitrary-order automatic…
We present a new version of TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding…
We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives w.r.t. several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic…
TauREx 3 is the next generation of the TauREx exoplanet atmospheric retrieval framework for Windows, Mac, and Linux. It is a complete rewrite with a full Python stack that makes it easy-to-use, high-performance, dynamic, and flexible. The…
ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
dlordinal is a new Python library that unifies many recent deep ordinal classification methodologies available in the literature. Developed using PyTorch as underlying framework, it implements the top performing state-of-the-art deep…
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of…
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…
\texttt{aurel} is an open-source Python package designed to \emph{au}tomatically calculate \emph{rel}ativistic quantities. It uses an efficient, flexible and user-friendly caching and dependency-tracking system, ideal for managing the…
We present a new Fortran library to evaluate all harmonic polylogarithms up to weight four numerically for any complex argument. The algorithm is based on a reduction of harmonic polylogarithms up to weight four to a minimal set of basis…
While Large Language Models (LLMs) have demonstrated impressive capabilities, their output quality remains inconsistent across various application scenarios, making it difficult to identify trustworthy responses, especially in complex tasks…
ARC 3.0 is a modular, object-oriented Python library combining data and algorithms to enable the calculation of a range of properties of alkali and divalent atoms. Building on the initial version of the ARC library [N. \v{S}ibali\'c et al,…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
The scaling of large language models (LLMs) is currently bottlenecked by the rigidity of distributed programming. While high-performance libraries like CuBLAS and NCCL provide optimized primitives, they lack the flexibility required for…
Modern astronomical potentials modeling galaxies or stellar systems can be rather involved, and deriving their first derivatives (accelerations) and second derivatives (variational equations) in order to compute orbits and their chaoticity…
PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms.…
Simflowny is an open platform which automatically generates efficient parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support simultaneously a quite…
We present the Macaulay2 package Resultants, which provides commands for the effective computation of multivariate resultants, discriminants, and Chow forms. We provide some background for the algorithms implemented and show, with a few…