@techreport{RISC7249,
author = {Silvio Ghilardi and Cleo Pau (Editors)},
title = {{Proceedings of the 40th International Workshop on Unification, UNIF 2026}},
language = {english},
abstract = {This volume contains the extended abstract presented at the 40th edition of the annual international workshop on Unification (UNIF 2026), held on July 24th, 2026. The workshop was a part of the Federated Logic Conference (FLoC 2026), that unites the ten leading international conferences focused on mathematical logic and its applications in computer science, as well as over 30 satellite workshops. FLoC 2026 took place in Lisbon.},
year = {2026},
month = {July},
keywords = {unification},
length = {80},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7234,
author = {J. Ablinger and A. Behring and J.~Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The complete three-loop unpolarized and polarized massive operator matrix elements and asymptotic Wilson coefficients}},
language = {english},
abstract = {We report on the three-loop unpolarized and polarized massive operator matrix elements, with single- and two-mass corrections, and the associated deep-inelastic massive Wilson coefficients in the region $Q^2 gg m_Q^2$, the calculation of which has been completed recently. We also provide fast and precise numerical representations ofthe massless Wilson coefficients, splitting functions to tree-loop order, and target-mass corrections in $x$-space well suited for QCD-fitting codes.},
number = {26-01},
year = {2026},
month = {January},
keywords = { three-loop unpolarized and polarized massive operator matrix elements, deep-inelastic scattering, computer algebra, special functions},
length = {16},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7237,
author = {Wolfgang Schreiner},
title = {{Building a Logical Agent with LangChain ... and Quite Some Vibe Coding}},
language = {english},
abstract = {This document reports on our experience of building an “agentic AI” (Artificial Intelligence) that helps a human to answer logical questions in a trustworthy way. This agent combines a Large Language Model (LLM) (which interacts with the human in natural language) with a logical software (which automatically proves formal theorems). The LLM engages in a dialogue with the human in order to translate their logical question from natural language to a formal proof problem. Once the human is satisfied with the formalization, the LLM invokes the prover to automatically solve the problem and thus answer the question; then the LLM also offers the user the possibility to inspect the successful proof or the unsuccessful proof attempt by calling the prover in an interactive mode. Furthermore, we describe how much of the source code (which is based on on the agent construction framework LangChain) has been “vibe coded”, i.e., itself generated with the help of an LLM.},
number = {26-02},
year = {2026},
month = {March},
keywords = {large language models, automated theorem proving, agentic AI, logical formalization, vibe coding},
length = {73},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7239,
author = {Tereso del Río and Wolfgang Schreiner and Martina Seidl and Temur Kutsia and Wolfgang Windsteiger },
title = {{An Intermediate Representation Format for Industrial Optimization Problems - The Translation of OptDSL to MiniZinc}},
language = {english},
abstract = {This report presents the implementation of OptDSL, a Python-inspired domain-specific language for describing optimisation problems. The implementation is based on the translationof a high-level OptDSL formulation of the problem to an intermediate representation in the constraint modelling language MiniZinc, which can be used by multiple state-of-the-art solvers. The report also describes the translation software, illustrates its use on a simplified industrial example, discusses selected implementation details, and suggests directions for further development.},
number = {26-04},
year = {2026},
month = {April},
keywords = {industrial optimization, domain-specific languages, constraint solving, formal languages, translation},
sponsor = {Supported by the FFG project FO999923579 “InProSSA: Industrial Problem Solving Using Symbolic and Subsymbolic AI”},
length = {88},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7250,
author = {Bruno Buchberger},
title = {{Nakano’s Light Puzzle: A Correctness Proof for a Greedy Algorithm}},
language = {english},
abstract = {We consider Nakano’s Problem: Give a (simple and algorithmic) necessary and sufficient conditionfor a configuration of lights (on/off) in a cube to be transformable to the all-off configuration bycertain touches on the faces of the cube. In this paper, we provide a detailed correctness proof for a“greedy” algorithm for Nakano’s problem. With the same proof technique, we also get anotheralgorithmic criterion for Nakano’s problem, which is based on the notion of “parity of box sums”.We discuss the relevance of such proofs for the recent research on automating mathematicalinvention by a combination of Automated Reasoning techniques and Automated Search of Rele-vant Mathematical Literature through Machine Learning.},
number = {26-05},
year = {2026},
month = {May},
howpublished = {RISC Report},
keywords = {Nakano's problem, light puzzle problem, greedy algorithm, correctness proof, automated mathematical invention, canonical simplification, parity lemma, THEOREMA},
length = {58},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7247,
author = {J. Ablinger and A. Behring and J.~Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The variable flavor number scheme to three-loop order}},
language = {english},
abstract = {We describe the variable flavor number scheme to three-loop order, which modifies the massless parton densities by single- and two-mass effects and introduces heavy-quark parton distribution functions for charm and bottom. A renormalization group analysis shows the validity of this picture at large scales $Q^2$, where it resembles the non-power-suppressed heavy-flavor corrections completely. We also provide numerical implementations of a series of charged and neutral current Wilson coefficients.},
number = {26-06},
year = {2026},
month = {July},
note = {DESY 26--064, RISC Report number 26-06, CERN-TH-2026-113, MPP-2026-89, PoS (LL2026) 025},
keywords = {variable flavor number scheme, heavy-quark parton distribution function, computer algebra, numerical implementation},
length = {11},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7242,
author = {C. Schneider},
title = {{A Survey on Symbolic Summation in Difference Rings}},
language = {english},
abstract = {This survey article provides an overview of the fundamental principles used to simplify multi-sums into indefinite nested sums over hypergeometric products in the setting of difference rings. We place special emphasis on the algorithmic translation between hypergeometric sums and the formal difference ring setting. Furthermore, we detail the core summation paradigms of telescoping, creative telescoping, and recurrence solving within difference rings, illustrating these techniques and their underlying algorithms with concrete examples.},
number = {26-07},
year = {2026},
month = {May},
keywords = {Difference ring, telescoping, creative telescoping, parameterized telescoping, recurrence solving.},
length = {31},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7245,
author = {Besik Dundua and Georg Ehling and Santiago Escobar and Maribel Fernández and Temur Kutsia},
title = {{Quantitative Equational Rewriting}},
language = {english},
abstract = {Rewriting logic is a logical framework for expressing both concurrent computation and logical deduction using equations and re-write rules. Quantitative equational reasoning enriches equations with quantitative measures, expressing concepts such as similarity or proximity rather than mere equality of terms. In this article, we bring these two approaches together and propose a quantitative extension of rewriting logic as a flexible formalism for quantitative deduction and computation.},
number = {26-09},
year = {2026},
month = {June},
keywords = {Quantitative rewriting, quantitative equational reasoning, quantitative matching},
length = {39},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7248,
author = {Silvio Ghilardi and Cleo Pau (Editors)},
title = {{Proceedings of the 40th International Workshop on Unification, UNIF 2026}},
language = {english},
abstract = {This volume contains the extended abstract presented at the 40th edition of the annual international workshop on Unification (UNIF 2026), held on July 24th, 2026. The workshop was a part of the Federated Logic Conference (FLoC 2026), that unites the ten leading international conferences focused on mathematical logic and its applications in computer science, as well as over 30 satellite workshops. FLoC 2026 took place in Lisbon.},
number = {26-10},
year = {2026},
month = {July},
keywords = {unification},
length = {80},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7257,
author = {J. Bluemlein and A.M. Gavrilik and O. Mykhailiv and C. Schneider},
title = {{The $q$-extension of iterated integrals and nested sums in quantum field theory}},
language = {english},
abstract = {Analytic calculations of zero- and single-scale quantities in perturbative quantum fieldtheory result into special numbers and functions, the first of which have been revealed during the last decades. These are generalizations of the polylogarithm in form of Kummer-Poincar'e iterative integrals over special alphabets and extensions thereof.With growing order in the coupling constant, the polylogarithms, Nielsen integrals, the iterated integrals over linear denominator terms, cyclotomic letters, letters induced by quadratic forms, square-root valued letters, and more general functions contribute. For the nested sums we consider nested harmonic sums, generalized harmonic sums,nested sums implied by quadratic forms, cyclotomic harmonic sums, and nested sumscontaining central binomials. We construct the $q$-extensions of these special functions and of the nested sums, which are associated to them by the series expansion at $x=0$, and their Mellin transform in the $q$-free case. These functions are expected to play a role in perturbative calculations in the case of $q$-deformed commutation relations. For the simpler function spaces closed form solutions are presented. For more involvedalphabets we present the algorithmic steps leading to the $q$-extension for the individual cases. We also derive the determining differential and difference equations of these higher transcendental functions. The $q$-extended special functions arequite different form the corresponding $mu$-extended functions.},
number = {26-11},
year = {2026},
month = {August},
note = {arXiv:2608.02702[math-ph]},
keywords = {q-difference equations, q-differential eqations, q-iterative integrals, q-iterative sums, holonomic closure properties, recurrence solving, quantum field theory},
length = {40},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7134,
author = {Ralf Hemmecke and Peter Paule and Cristian-Silviu Radu},
title = {{Computer-assisted construction of Ramanujan-Sato series for 1 over pi}},
language = {english},
abstract = {Referring to ideasof Takeshi Sato, Yifan Yang in~cite{YangDE} described a construction ofseries for $1$ over $pi$ startingwith a pair $(g,h)$, where $g$ is a modular formof weight $2$ and $h$ is a modular function; i.e.,a modular form of weight zero. In this article we present an algorithmicversion,called ``Sato construction''. Series for $1/pi$ obtained this way will becalled ``Ramanujan-Sato''series. Famous series fit into this definition, for instance, Ramanujan'sseries used by Gosperand the series used by the Chudnovsky brothersfor computing millions of digits of $pi$. Weshow that these series are induced by membersof infinite families of Sato triples $(N, gamma_N,tau_N)$ where $N>1$ is an integer and $gamma_N$ a $2times 2$ matrixsatisfying $gamma_N tau_N=N tau_N$ for$tau_N$ being an element from the upper half of thecomplex plane.In addition to procedures for guessingand proving from the holonomic toolbox togetherwiththe algorithm ``ModFormDE'', as describedin~cite{PPSR:ModFormDE1}, a central roleis played by the algorithm ``MultiSamba'',an extension ofSamba (``subalgebra module basis algorithm'') originating fromcite{Radu_RamanujanKolberg_2015} and cite{Hemmecke}.With thehelp of MultiSamba one canfind and prove evaluations of modular functions,at imaginary quadratic points, in terms of nested algebraic expressions.As a consequence,all the series for $1/pi$ constructed withthe help of MultiSamba are proven completelyin a rigorous non-numerical manner.},
number = {25-01},
year = {2025},
month = {January},
keywords = {modular forms and functions, holonomic differential equations, Ramanujan-Sato series for 1 over pi, MultiSamba algorithm},
length = {58},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7136,
author = {Wolfgang Schreiner and William Steingartner},
title = {{Semantics-Based Rapid Prototyping of a Subset of SQL}},
language = {english},
abstract = {This report documents the application of our semantics-based language generator SLANG to developing a rapid prototype of a non-trivial domain-specific language, a substantial subset of the Structured Query Language SQL that we have named SubSQL. After developing a mathematical/logical formulation of the language’s abstract syntax, formal type system, and denotational semantics, we have translated this formulation into a SLANG specification from which the SLANG software generates Java code that implements a parser, a printer, a type-checker, and an executor of the language. This implementation is based on several manually created Java classes that implement the mathematical domains and operations used in the formalization, a simple persistent database, and a high-level application programming interface that allows to execute complete SubSQL scripts from file or individual SubSQL commands within Java programs. The results represent a blueprint for the semantics-based development of other domain-specific languages of similar complexity.},
number = {25-02},
year = {2025},
month = {February},
keywords = {formal semantics of programming languages, domain specific languages, rapid prototyping, interpreters},
sponsor = {Aktion Österreich–Slowakei project 2024-05-15-001, KEGA project 030TUKE-4/2023},
length = {179},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7141,
author = {Besik Dundua and Temur Kutsia},
title = {{Higher-Order Pattern Unification Modulo Similarity Relations}},
language = {english},
abstract = {The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient reasoning and computational techniques for such a combined formalism presents a significant challenge. In this paper, we adopt a more straightforward approach aiming at integrating two well-established and computationally well-behaving components: higher-order patterns on one side and fuzzy equivalences expressed through similarity relations based on minimum T-norm on the other. We propose a unification algorithm for higher-order patterns modulo these similarity relations and prove its termination, soundness, and completeness. This unification problem, like its crisp counterpart, is unitary. The algorithm computes the most general unifier with the highest degree of approximation when the given terms are unifiable.},
number = {25-03},
year = {2025},
month = {February},
keywords = {Unification, higher-order patterns, fuzzy similarity relations},
length = {20},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7181,
author = {J. Ablinger and A. Behring and J. Blümlein and d and A. De Freitas and A. von Manteuffel and C. Schneider and and K. Schönwald},
title = {{The Single-Mass Variable Flavor Number Scheme at Three-Loop Order}},
language = {english},
abstract = {The matching relations in the unpolarized and polarized variable flavor number scheme at three-loop order are presented in the single-mass case. They describe the process of massive quarks becoming light at large virtualities $Q^2$. In this framework, heavy-quark parton distributions can be defined. Numerical results are presented on the matching relations in the case of the single-mass variable flavor number scheme for the light parton, charm and bottom quark distributions. These relations are process independent. In the polarized case we generally work in the Larin scheme. To two-loop order we present the polarized massive OMEs also in the $overline{rm MS}$ scheme. Fast numerical codes for the single-mass massive operator matrix elements are provided. },
number = {25-04},
year = {2025},
month = {October},
note = {arXiv:2510.02175 [hep-ph]},
keywords = {QCD, Feynman diagrams, computer algebra},
length = {27},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7151,
author = {S. Chen and Y. Gao and H. Huang and C. Schneider},
title = {{Telescoping Algorithms for $Sigma^*$-Extensions via Complete Reductions}},
language = {english},
abstract = {A complete reduction on a difference field is a linear operator that enables one to decompose an element of the field as the sum of a summable part and a remainder such thatthe given element is summable if and only if the remainder is equal to zero.In this paper, we present a complete reduction in a tower of $Sigma^*$-extensions that turns to a new efficient framework for the parameterized telescoping problem. Special instances of such $Sigma^*$-extensions cover iterative sums such as the harmonic numbers and generalized versions that arise, e.g., in combinatorics, computer science or particle physics. Moreover, we illustrate how these new ideas can be used to reduce the depth of the given sum and provide structural theorems that connect complete reductions to Karr's Fundamental Theorem of symbolic summation.},
number = {25-05},
year = {2025},
month = {June},
note = {arXiv:2506.08767 [cs.SC]},
keywords = {symbolic summation, difference fields, complete reductions, paramaterized telescoping},
length = {35},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7153,
author = {Jack Heseltine},
title = {{Theorema Project: Document Processing}},
language = {english},
abstract = {This work explores the Wolfram Language as a Software Engineering tool, with a particular focus on the Theorema mathematical software package, in combination with the LATEX typesetting system. It delves into the advanced functionalities and paradigms of Wolfram Language, including high-level programming, functional programming, and pattern matching, to showcase these capabilities beyond object oriented programming languages in particular, as applied to mathematical document transformation. Through Theorema, package development using Wolfram Language is demonstrated from conception through execution to the point that the new package can be easily integrated with the existing Theorema system: the associated analysis touches on the workings of Theorema but the focus is on an implementational bridge between computational mathematics and document preparation, aiming to provide easy extensibility and delivering on further Software Engineering principles to make for a rounded Wolfram Language and Theorema package, as the final project output.The thesis also addresses the challenges and methodologies associated with the LATEX typesetting of mathematical content, emphasizing the transformation of Wolfram Language/Theorema notebooks using a Wolfram-Language-native approach. This includes an examination of first-order predicate logic symbols, to ensure coverage at the output side, and the role of (mathematical) expressions in Wolfram Language, the input side, showcasing back-and-forth between typesetting and (symbolic) computational languages, and particularly, recursive parsing of entire notebook expressions as the basic working principle in this approach.},
number = {25-06},
year = {2025},
month = {March 02},
note = {Bachelor Thesis at University of Applied Sciences Hagenberg, bachelor program Software Engineering},
keywords = {Theorema, LaTeX},
length = {76},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7182,
author = {J. Ablinger and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and Kay Schoenwald},
title = {{The two-mass contributions to the three-loop massive operator matrix elements $tilde{A}_{Qg}^{(3)}$ and $Delta tilde{A}_{Qg}^{(3)}$}},
language = {english},
abstract = {We calculate the two-mass three-loop contributions to the unpolarized and polarized massive operator matrix elements $tilde{A}_{Qg}^{(3)}$ and $Delta tilde{A}_{Qg}^{(3)}$ in $x$-space for a general mass ratio by using a semi-analytic approach. We also compute Mellin moments up to $N = 2000 (3000)$ by an independent method, to which we compare the results in $x$-space. In the polarized case, we work in the Larin scheme. We present numerical results. The two-mass contributions amount to about $50 %$ of the full textcolor{blue}{$O(T_F^2)$} and textcolor{blue}{$O(T_F^3)$} terms contributing to the operator matrix elements. The present result completes the calculation of all unpolarized and polarized massive three-loop operator matrix elements.},
number = {25-07},
year = {2025},
month = {November},
keywords = {operator matrix elements,3-loop massive Feynman diagrams, two masses, symbolic computation},
length = {50},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7178,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schönwald},
title = {{The three-loop single-mass heavy-flavor corrections to the structure functions $F_2(x,Q^2)$ and $g_1(x,Q^2)$}},
language = {english},
abstract = {We report quantitative results on the single-mass heavy-flavor contributions up to three-loop order to the unpolarized structure function $F_2(x,Q^2)$ and the polarized structure function $g_1(x,Q^2)$ for the first time. These results are relevant for precision QCD analyses of the World deep-inelastic data and the data taken at future colliders, such as the Electron--Ion Collider, in order to measure the strong coupling constant $alpha_s(M_Z^2)$, and the twist-2 parton distribution functions consistently at next-to-next-to-leading order.},
number = {25-08},
year = {2025},
month = {September},
keywords = {single-mass heavy-flavor contributions, QCD, Feynman diagrams, computer algebra},
length = {6},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7197,
author = {Ralf Hemmecke and Peter Paule and Cristian-Silviu Radu},
title = {{An Algorithm to Compute Algebraic Relations Between Modular Functions}},
language = {english},
abstract = {The existence of an algebraic relation between two modular functions,in short: a modular equation, is implied by a classical fact from thetheory of compact Riemann surfaces. In this article, we present a new,purely algebraic proof of the existence of modular equations. Oursetting consists of an algorithmic framework which is based on areduction procedure for tuples of formal Laurent series. The resultingalgorithm MultiSamba (“sub-algebra module basis algorithm”) is part ofHemmecke's computer algebra package QEta which has been implemented inFriCAS, a general purpose computer algebra system which is freelyavailable as open source. QEta is a powerful tool-box for actualcomputations. For example, MultiSamba has been used forcomputer-assisted discovery and proofs of Ramanujan-Sato series. Inthis article, we describe the mathematics underlying the MultiSambaalgorithm. Moreover, we explain in detail how MultiSamba works for thederivationof a well-known modular equation betweenthe modular $\lambda$-function and the Klein $j$function.Other examples of the automatic discovery and proving of modularequations include identities by Alladi and others, which suggestrelations of Ramanujan-G\"ollnitz-Gordon type as another promisingarea of MultiSamba application.},
number = {25-09},
year = {2025},
month = {November},
keywords = {modular functions, multisamba, modular equations},
length = {23},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7210,
author = {A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The heavy quark-antiquark asymmetry in the variable flavor number scheme}},
language = {english},
abstract = {The twist-2 heavy-quark and antiquark distributions, as defined in the variable flavor number scheme, turn out to be different due to QCD corrections from three-loop onward. This is caused by terms containing the color factor $d_{abc} d^{abc}$ in the heavy-flavor massive pure-singlet operator matrix elements (OMEs) $A^{rm PS, s, (3)}_{Qq}$ for odd moments in the unpolarized case and for $Delta A^{rm PS, s, (3)}_{Qq}$ for even moments in the polarized case. The dependence on the factorization scale of the OMEs is ruled by the anomalous dimensions $gamma^{rm NS, s, (2)}_{qq}$ and $Delta gamma^{rm NS, s, (2)}_{qq}$. The polarized calculations are performed in the Larin scheme. We compute the corresponding three-loop heavy-flavor distributions $(Delta) f_Q(x,Q^2) - (Delta) f_{overline{Q}}(x,Q^2)$. Compared to the sum of the heavy-quark and antiquark parton distributions, their difference is small, however, non-vanishing. },
number = {25-10},
year = {2025},
month = {December},
note = {arXiv:2512.13508 [hep-ph]},
keywords = {particle physics, QCD, massive 3-loop eynman integrals, computer algebra, solving recurrences},
length = {17},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}