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Making presentation math computable : a context-sensitive approach for translating LaTeX to computer algebra systems / submitted by André Greiner-Petter. Wuppertal, 2021
Content
List of Figures
List of Tables
Abstract
Zusammenfassung
Acknowledgements
Introduction
Motivation & Problem
Research Gap
Research Objective
Thesis Outline
Publications
Research Path
Mathematical Information Retrieval
Background and Overview
Mathematical Formats and Their Conversions
Web Formats
Word Processor Formats
Computable Formats
Images and Tree Representations
Math Embeddings
From Presentation to Content Languages
Background
Benchmarking MathML
Evaluation of Context-Agnostic Conversion Tools
Summary of MathML Converters
Mathematical Information Retrieval for LaTeX Translations
Semantification of Mathematical LaTeX
Semantification via Math-Word Embeddings
Foundations and Related Work
Semantic Knowledge Extraction
On Overcoming the Issues of Knowledge Extraction Approaches
The Future of Math Embeddings
Semantification with Mathematical Objects of Interest
Related Work
Data Preparation
Frequency Distributions of Mathematical Formulae
Relevance Ranking for Formulae
Applications
Outlook
Semantification with Textual Context Analysis
Semantification, Translation & Evaluation Pipeline
From LaTeX to Computer Algebra Systems
Context-Agnostic Neural Machine Translation
Training Datasets & Preprocessing
Methodology
Evaluation of the Convolutional Network
Context-Sensitive Translation
Motivation
Related Work
Formal Mathematical Language Translations
Document Pre-Processing
Annotated Dependency Graph Construction
Semantic Macro Replacement Patterns
Qualitative and Quantitative Evaluations
Evaluations on the Digital Library of Mathematical Functions
The DLMF dataset
Semantic LaTeX to CAS translation
Evaluation of the DLMF using CAS
Results
Conclude Quantitative Evaluations on the DLMF
Evaluations on Wikipedia
Symbolic and Numeric Testing
Benchmark Testing
Results
Error Analysis & Discussion
Conclude Qualitative Evaluations on Wikipedia
Conclusion and Future Work
Summary
Contributions and Impact of the Thesis
Future Work
Improved Translation Pipeline
Improve LaTeX to MathML Converters
Enhanced Formulae in Wikipedia
Language Independence
BACK MATTER
Appendix
Branch Cut Position Problems in CAS
History of Mathematics in Wikipedia
An Example Proof by Isabelle
Summary of Bug Reports and Fixed Issues
Digital Library of Mathematical Functions
Maple
Mathematica
Wikipedia
DLMF Evaluations
DLMF Test Samples
Qualitative Symbolic and Numeric Evaluations
Wikipedia Evaluations
Noun Phrase Definitions
Example Translation Process
Evaluation Analysis
Benchmark Dataset
Glossary
Bibliography of Publications, Submissions & Talks
Bibliography