Related papers: Libra: a package for transformation of differentia…
Integration by parts (IBP) has acquired a bad reputation. While it allows us to compute a wide variety of integrals when other methods fall short, its implementation is often seen as plodding and confusing. Readers familiar with tabular IBP…
We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…
The rapid progress in quantum computing witnessed in recent years has sparked widespread interest in developing scalable quantum information theoretic methods to work with large quantum systems. For instance, several approaches have been…
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…
Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
This preprint contains a description of a package for Mathematica called EinS. This package allows one to perform various calculations with indexed objects.
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
Probing is an important presolving technique in mixed-integer programming solvers. It selects binary variables, tentatively fixes them to 0 and 1, and performs propagation to deduce additional variable fixings, bound tightenings,…
The library of practical abstractions (LIBPA) provides efficient implementations of conceptually simple abstractions, in the C programming language. We believe that the best library code is conceptually simple so that it will be easily…
Driven by increasing compute requirements for deep learning models, compiler developers have been looking for ways to target specialised hardware and heterogeneous systems more efficiently. The MLIR project has the goal to offer…
We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software…
In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…
This work presents MLIR, a novel approach to building reusable and extensible compiler infrastructure. MLIR aims to address software fragmentation, improve compilation for heterogeneous hardware, significantly reduce the cost of building…
We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…
Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
Hybrid systems are increasingly used in critical applications such as medical devices, infrastructure systems, and autonomous vehicles. Lince is an academic tool for specifying and simulating such systems using a C-like language with…