Making Presentation Math Computable

This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book

Making Presentation Math Computable

This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book

Natural Language Processing: Integration of Automatic and Manual Analysis

There is a current trend to combine natural language analysis with research questions from the humanities. This requires an integration of automatic analysis with manual analysis, e.g. to develop a theory behind the analysis, to test the theory against a corpus, to generate training data for automatic analysis based on machine learning algorithms, and to evaluate the quality of the results from automatic analysis. Manual analysis is traditionally the domain of linguists, philosophers, and researchers from other humanities disciplines, who are often not expert programmers. Automatic analysis, on the other hand, is traditionally done by expert programmers, such as computer scientists and more recently computational linguists. It is important to bring these communities, their tools, and data closer together, to produce analysis of a higher quality with less effort. However, promising cooperations involving manual and automatic analysis, e.g. for the purpose of analyzing a large corpus, are hindered by many problems: - No comprehensive set of interoperable automatic analysis components is available. - Assembling automatic analysis components into workflows is too complex. - Automatic analysis tools, exploration tools, and annotation editors are not interoperable. - Workflows are not portable between computers. - Workflows are not easily deployable to a compute cluster. - There are no adequate tools for the selective annotation of large corpora. - In automatic analysis, annotation type systems are predefined, but manual annotation requires customizability. - Implementing new interoperable automatic analysis components is too complex. - Workflows and components are not sufficiently debuggable and refactorable. - Workflows that change dynamically via parametrization are not readily supported. - The user has no control over workflows that rely on expert skills from a different domain, undocumented knowledge, or third-party infrastructures, e.g. web services. In cooperation with researchers from the humanities, we develop innovative technical solutions and designs to facilitate the use of automatic analysis and to promote the integration of manual and automatic analysis. To address these issues, we set foundations in four areas: - Usability is improved by reducing the complexity of the APIs for building workflows and creating custom components, improving the handling of resources required by such components, and setting up auto-configuration mechanisms. - Reproducibility is improved through a concept for self-contained, portable analysis components and workflows combined with a declarative modeling approach for dynamic parametrized workflows, that facilitates avoiding unnecessary auxiliary manual steps in automatic workflows. - Flexibility is achieved by providing an extensive collection of interoperable automatic analysis components. We also compare annotation type systems used by different automatic analysis components to locate design patterns that allow for customization when used in manual analysis tasks. - Interactivity is achieved through a novel "annotation-by-query" process combining corpus search with annotation in a multi-user scenario. The process is supported by a web-based tool. We demonstrate the adequacy of our concepts through examples which represent whole classes of research problems. Additionally, we integrated all our concepts into existing open-source projects, or we implemented and published them within new open-source projects

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Conférence Nationale d'Intelligence Artificielle Année 2020

National audienc