Related papers: Integer formula encoding SageTeX package
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer…
An \emph{indeterminate string} $x = x[1..n]$ on an alphabet $\Sigma$ is a sequence of nonempty subsets of $\Sigma$; $x$ is said to be \emph{regular} if every subset is of size one. A proper substring $u$ of regular $x$ is said to be a…
We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like…
This is an expository article on recent developments in the theory of group relaxations in integer programming from an algebraic perspective.
(This is only a first preliminary version, any suggestions about it will be welcome.) In this paper it is shown how to compute Riemann's zeta function $\zeta(s)$ (and Riemann-Siegel $Z(t)$) at any point $s\in\mathbf C$ with a prescribed…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
We present an elliptic version of Selberg's integral formula.
Previous works have demonstrated the effectiveness of utilising pre-trained sentence encoders based on their sentence representations for meaning comparison tasks. Though such representations are shown to capture hidden syntax structures,…
The theory of computational complexity is used to underpin a recent model of neocortical sensory processing. We argue that encoding into reconstruction networks is appealing for communicating agents using Hebbian learning and working on…
In the task of machine translation, context information is one of the important factor. But considering the context information model dose not proposed. The paper propose a new model which can integrate context information and make…
We have implemented a machine translation system, the PolyMath Translator, for LaTeX documents containing mathematical text. The current implementation translates English LaTeX to French LaTeX, attaining a BLEU score of 53.5 on a held-out…
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…
Large information sizes in samples and features can be encoded to speed up the learning of statistical models based on linear algebra and remove unwanted signals. Encoding information can reduce both sample and feature dimension to a…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
This document explains how to create or modify an existing LATEX document with commands enabling computations in the HTML5 output: when the reader opens the HTML5 output, he can run a computation in his browser, or modify the command to be…
We catalog and describe Google's key software engineering practices.
Assessing the degree of similarity of code fragments is crucial for ensuring software quality, but it remains challenging due to the need to capture the deeper semantic aspects of code. Traditional syntactic methods often fail to identify…
We present a mathematica package that performs the symbolic calculation of integrals of the form \int^{\infty}_0 e^{-x/u} x^n j_{\nu} (x) j_{\mu} (x) dx where $j_{\nu} (x)$ and $j_{\mu} (x)$ denote spherical Bessel functions of integer…
Mathematical formulae carry complex and essential semantic information in a variety of formats. Accessing this information with different systems requires a standardized machine-readable format that is capable of encoding presentational and…
In this paper, we reformulated the spell correction problem as a machine translation task under the encoder-decoder framework. This reformulation enabled us to use a single model for solving the problem that is traditionally formulated as…