Related papers: HyperFORM -- a FORM package for parametric integra…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
We evaluate integrals of certain polynomials over spheres and balls in real or complex spaces. We also promote the use of the Pochhammer symbol which gives the values of our integrals in compact forms.
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
Multimodal Small-to-Medium sized Language Models (MSLMs) have demonstrated strong capabilities in integrating visual and textual information but still face significant limitations in visual comprehension and mathematical reasoning,…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…
We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a wide range of combinatorial theories, can numerically…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
Some of the new features of the symbolic manipulation system FORM are discussed. Then some recent results running its multithreaded version TFORM are shown. Finally the plans for the future are presented.
Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…
We describe the implementation of facilities for the communication with external resources in the Symbolic Manipulation System FORM. This is done according to the POSIX standards defined for the UNIX operating system. We present a number of…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic…
Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize…
Applying Gr\"obner basis theory to concrete problems in Lean 4 remains difficult since the current formalization of multivariate polynomials is based on a non-computable representation and is therefore not suitable for efficient symbolic…
The rational Landen transformations are used to produce a highly efficient numerical method for the integration of rational functions.
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…