Related papers: FunGrim: a symbolic library for special functions
Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
Detailed notes on the functions included in the DMRjulia library are included here. This discussion of how to program functions for a tensor network library are intended to be a supplement to the other documentation dedicated to explaining…
The Imaging Computational Microscope (ICM) is a suite of computational tools for automated analysis of functional imaging data that runs under the cross-platform MATLAB environment (The Mathworks, Inc.). ICM uses a semi-supervised…
We present FabSim, a toolkit developed to simplify a range of computational tasks for researchers in diverse disciplines. FabSim is flexible, adaptable, and allows users to perform a wide range of tasks with ease. It also provides a…
The purpose of this project is to collect symbol information in the Mizar Mathematical Library and manipulate it into practical and organized documentation. Inspired by the MathWiki project and API reference systems for computer programs,…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
In this position paper, we present a prototype of a visualizer for functional programs. Such programs, whose evaluation model is the reduction of an expression to a value through repeated application of rewriting rules, and which tend to…
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…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
magnum.np is a micromagnetic finite-difference library completely based on the tensor library PyTorch. The use of such a high level library leads to a highly maintainable and extensible code base which is the ideal candidate for the…
functionalObjects.h allows the C++ programmer performing common mathematical calculations to use a more symbolic syntax rather than an algorithmic syntax. This is not as ambitious as a symbolic manipulation program such as Mathematica; it…
MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database…
In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…
Deep learning models typically use single-precision (FP32) floating point data types for representing activations and weights, but a slew of recent research work has shown that computations with reduced-precision data types (FP16, 16-bit…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…