Related papers: Integer formula encoding SageTeX package
Symbolic computation techniques are used to derive some closed form expressions for an analytic continuation of the Euler-Zagier zeta function evaluated at the negative integers as recently proposed by B. Sadaoui. This approach allows to…
Coherence has been used as a resource for optical communications since its earliest days. It is widely used for multiplexing of data, but not for encoding of data. Here we introduce a coding scheme, which we call \textit{mutual coherence…
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…
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…
In this paper, we present a new approach to the semantic enrichment of mathematical expression problem. Our approach is a combination of statistical machine translation and disambiguation which makes use of surrounding text of the…
We consider representing of natural numbers by arithmetical expressions using ones, addition, multiplication and parentheses. The (integer) complexity of n -- denoted by ||n|| -- is defined as the number of ones in the shortest expressions…
This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition…
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…
We encode/decode Prolog terms as unique natural numbers. Our encodings have the following properties: a) are bijective b) natural numbers always decode to syntactically valid terms c) they work in low polynomial time in the bitsize of the…
Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved…
A source code summary of a subroutine is a brief description of that subroutine. Summaries underpin a majority of documentation consumed by programmers, such as the method summaries in JavaDocs. Source code summarization is the task of…
In this paper, the term formula code refers to fragments of source code that implement a mathematical formula. We present empirical studies that analyze the diversity and frequency of formula code in open-source-software projects. In an…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
This article explores a generic framework of well-typed and well-scoped syntaxes, with a signature-axiom approach resembling traditional abstract algebra. The boilerplate code needed in defining operations on syntaxes is identified and…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS…
We propose a novel framework of program and invariant synthesis called neural network-guided synthesis. We first show that, by suitably designing and training neural networks, we can extract logical formulas over integers from the weights…
Finding desired information from large data set is a difficult problem. Information retrieval is concerned with the structure, analysis, organization, storage, searching, and retrieval of information. Index is the main constituent of an IR…
This document defines the mathematical backbone of the Statebox programming language. In the simplest way possible, Statebox can be seen as a clever way to tie together different theoretical structures to maximize their benefits and limit…
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects…