Related papers: HyperFORM -- a FORM package for parametric integra…
A transformation on homogeneous polynomials is proposed, which is further applied to parametric Feynman integrals. The two representations related through this transformation are dual to each other. It naturally leads to dualities of Landau…
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in…
DeepLog is an operational neurosymbolic framework that unifies logic and deep learning within standard PyTorch workflows. While existing neurosymbolic systems focus on a particular paradigm and semantics, DeepLog serves as a universal…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…
We introduce FORM 4.2, a new minor release of the symbolic manipulation toolkit. We demonstrate several new features, such as a new pattern matching option, new output optimization, and automatic expansion of rational functions.
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
ALHEP is the symbolic algebra program for high-energy physics. It deals with amplitudes calculation, matrix element squaring, Wick theorem, dimensional regularization, tensor reduction of loop integrals and simplification of final…
The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to…
This work deals with special nested objects arising in massive higher order perturbative calculations in renormalizable quantum field theories. On the one hand we work with nested sums such as harmonic sums and their generalizations…
Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work done by Formal…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
Generative AI, particularly Large Language Models, increasingly integrates graph-based representations to enhance reasoning, retrieval, and structured decision-making. Despite rapid advances, there remains limited clarity regarding when,…
We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…
Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation.…
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric…
The remarkable growth and significant success of machine learning have expanded its applications into programming languages and program analysis. However, a key challenge in adopting the latest machine learning methods is the representation…
Formal Laurent-Puiseux series are important in many branches of mathematics. This paper presents a {\it Mathematica} implementation of algorithms developed by the author for converting between certain classes of functions and their…