Related papers: Reconstructing Rational Functions with $\texttt{Fi…
We present the main improvements and new features in version $\texttt{2.0}$ of the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid…
We present FUEL (Fractional Universal Evaluation Library), a C++ library for performing rational function arithmetic with a flexible choice of third-party computer algebra systems as simplifiers. FUEL is an outgrowth of a C++ interface to…
In this paper the C++ version of FIRE is presented - a powerful program performing Feynman integral reduction to master integrals. All previous versions used only Wolfram Mathematica, the current version mostly uses Wolfram Mathematica as a…
FIRE is a program which performs integration-by-parts (IBP) reduction of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an…
Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…
We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…
FIRE is a program performing reduction of Feynman integrals to master integrals. The C++ version of FIRE was presented in 2014. There have been multiple changes and upgrades since then including the possibility to use multiple computers for…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
Rational Tracer (Ratracer) is a tool to simplify complicated arithmetic expressions using modular arithmetics and rational function reconstruction, with the main idea of separating the construction of expressions (via tracing, i.e.…
In this work, we introduce DeepFlame, an open-source C++ platform with the capabilities of utilising machine learning algorithms and pre-trained models to solve for reactive flows. We combine the individual strengths of the computational…
In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals. We extend existing approaches by using an…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic.…
We provide a small C++ library with Mathematica and Python interfaces for computing thermal functions, defined $$ J_\text{B/F}(y^2) \equiv \Re \int_0^\infty x^2 \log\left[1 \mp e^{-\sqrt{x^2 + y^2}} \right] \,\text{d}x, $$ which appear in…
Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional…
Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…