Related papers: FunGrim: a symbolic library for special functions
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide 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…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
This paper reports on the development of a Web platform to host the Mizar Mathematical Library (MML). In recent years, the size of formalized mathematical libraries has been drastically increasing, and this has led to a growing demand for…
GXWeb is the free browser based version of the symbolic geometry software Geometry Expressions. We demonstrate its use in an educational setting with examples from theorem proving, mathematical modelling and loci and envelopes.
Mathematicians and computer scientists are increasingly using proof assistants to formalize and check correctness of complex proofs. This is a non-trivial task in itself, however, with high demands on human expertise. Can we lower the bar…
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra…
We give a brief introduction to FORM, a symbolic programming language for massive batch operations, designed by J.A.M. Vermaseren. In particular, we stress various methods to efficiently use FORM under the UNIX operating system. Several…
Functional programming languages are seen by many as instrumental to effectively utilizing the computational power of multi-core platforms. As a result, there is growing interest to introduce functional programming and functional thinking…
We introduce $\texttt{cuSkyrmion}$, a 3-dimensional Skyrme model computation and visualization software, that is written in $\texttt{CUDA C}$ for rapid computation and visualization of especially the arrested Newton flow algorithm. The…
An extensive table of pairs of functions linked by the Legendre transformation is presented. Many special functions and formulas that are used in the sciences are included in the pairs. Formulations are provided for finding the Legendre…
In this paper we introduce the Functional Modelling System (FMS). The system introduces the Functional Modelling Language (FML), which is a modelling language for NP-complete search problems based on concepts of functional programming.…
PhyloFrame is a Python library for phylogenetic computation targeting the gap between specialist, compiler-optimized operations and flexible, script-based workflows -- with emphasis on fast, memory-efficient operations for very large tree…
Creative coding is an experimentation-heavy activity that requires translating high-level visual ideas into code. However, most languages and libraries for creative coding may not be adequately intuitive for beginners. In this paper, we…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
FunnyQT is a model querying and model transformation library for the functional Lisp-dialect Clojure providing a rich and efficient querying and transformation API. This paper describes the FunnyQT solution to the TTC 2013 Flowgraphs…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Processing-in-memory (PIM) promises to alleviate the data movement bottleneck in modern computing systems. However, current real-world PIM systems have the inherent disadvantage that their hardware is more constrained than in conventional…