Related papers: SNEG - Mathematica package for symbolic calculatio…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
While there exist many methods in machine learning for comparison of letter string data, most are better equipped to handle strings that represent natural language, and their performance will not hold up when presented with strings that…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and…
Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver…
A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
We explore using the Suggested Upper Merged Ontology (SUMO) to develop a semantic simulation. We provide two proof-of-concept demonstrations modeling transitions in a simulated gasoline engine using a general-purpose programming language.…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
I give in this lecture an overview of the features of the Mathematica package SARAH, and explain how it can be used together with other codes to study all aspects of a BSM model. The focus will be on the description of the analytical…
Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing…
We present two applications of egglog to mathematical optimization in JijModeling 2, a mathematical modeller whose internal representation is based on simply typed $\lambda$-calculus. First, we use egglog to improve $\LaTeX$ output for…
We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge…
We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second…
An early-stage version of simulation package is developed for electronic structure calculation and dynamics of atom process in large-scale systems, particularly, nm-scale or 10nm-scale systems. We adopted the Extensible Markup Language…
We tackle the problem of neural machine translation of mathematical formulae between ambiguous presentation languages and unambiguous content languages. Compared to neural machine translation on natural language, mathematical formulae have…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We report on a new version of FeynCalc, a well-known Mathematica package for symbolic computations in quantum field theory and provide some explicit examples for using the software in different types of calculations.