Related papers: Implementing p-adic numbers in Macaulay2 using its…
In problems of mathematical physics, to study the structures of spaces using the Cayley-Klein models in theoretical calculations, the use of generalized complex numbers is required. In the case of computational experiments, such tasks…
Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously…
The Macaulay2 package NumericalSchubertCalculus provides methods for the numerical computation of Schubert problems on Grassmannians. It implements both the Pieri homotopy algorithm and the Littlewood-Richardson homotopy algorithm. Each…
New cloud programming and deployment models pose challenges to software application engineers who are looking, often in vain, for tools to automate any necessary code adaptation and transformation. Function-as-a-Service interfaces are…
Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has…
The $M_2$ variables are devised to extend $M_{T2}$ by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible…
The emergence of data-driven computational materials science offers unprecedented opportunities to explore complex material landscapes, complementing experimental research with the discovery of novel compounds. To enable these developments,…
Plyades: A Python Library for Space Mission Design Designing a space mission is a computation-heavy task. Software tools that conduct the necessary numerical simulations and optimizations are therefore indispensable. The usability of…
Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different…
In this thesis, work is undertaken towards the design in hardware description languages and implementation in FPGA of an out-of-order execution engine of floating-point arithmetic operations for the Lagarto II core. A first proposal covers…
AI assistants can now carry out tasks for users by directly interacting with website UIs. Current semantic parsing and slot-filling techniques cannot flexibly adapt to many different websites without being constantly re-trained. We propose…
This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over…
AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter…
The program ftint is introduced which numerically evaluates dimensionally regulated integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to…
This paper presents Favalon, a functional programming language built on the premise of a lambda calculus for use as an interactive shell replacement. Favalon seamlessly integrates with typed versions of existing libraries and commands using…