Related papers: HyperFORM -- a FORM package for parametric integra…
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…
We present a new systematic method for evaluating generalized log-sine integrals in terms of polylogarithms. Our approach is based on an identity connecting ordinary generating functions of polylogarithms to integrals involving the sine…
Symbol letters are crucial for analytically calculating Feynman integrals in terms of iterated integrals. We present a novel method to construct the symbol letters for a given integral family without prior knowledge of the canonical…
Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms,…
In this paper we compare three different formalisms that can be used in the area of models for distributed, concurrent and mobile systems. In particular we analyze the relationships between a process calculus, the Fusion Calculus, graph…
This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of…
We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a…
In this paper we present a unification-based lexical platform designed for highly inflected languages (like Roman ones). A formalism is proposed for encoding a lemma-based lexical source, well suited for linguistic generalizations. From…
In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums…
An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…
Since language processing systems generally allocate/discard memory with complex reference relationships, including circular and indirect references, their implementation is often not trivial. Here, the allocated memory and the references…
The increasing complexity of computing systems places a tremendous burden on optimizing compilers, requiring ever more accurate and aggressive optimizations. Machine learning offers significant benefits for constructing optimization…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
This article describes the REDUCE package ZEILBERG implemented by Gregor St\"olting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of…
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by…
We introduce SOFIA, a Mathematica package that automatizes the computation of singularities of Feynman integrals, based on new theoretical understanding of their analytic structure. Given a Feynman diagram, SOFIA generates a list of…
After an introduction to the sequential version of FORM and the mechanisms behind it we report on the status of our ongoing project of its parallelization. An analysis of the parallel platforms used is given and the structure of a parallel…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…