دانلود کتاب Making Presentation Math Computable: A Context-Sensitive Approach for Translating LaTeX to Computer Algebra Systems

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Contents List of Figures List of Tables Abstract Zusammenfassung Acknowledgements CHAPTER 1 Introduction 1.1 Motivation & Problem 1.2 Research Gap 1.3 Research Objective 1.4 Thesis Outline 1.4.1 Publications 1.4.2 Research Path CHAPTER 2 Mathematical Information Retrieval 2.1 Background and Overview 2.2 Mathematical Formats and Their Conversions 2.2.1 Web Formats 2.2.1.1 MathML 2.2.1.2 OpenMath 2.2.1.3 OMDoc 2.2.2 Word Processor Formats 2.2.2.1 LATEX 2.2.2.2 Semantic/Content LaTeX 2.2.2.3 sTeX 2.2.2.4 Template Editors 2.2.3 Computable Formats 2.2.3.1 Computer Algebra Systems 2.2.3.2 Theorem Prover 2.2.4 Images and Tree Representations 2.2.5 Math Embeddings 2.3 From Presentation to Content Languages 2.3.1 Background 2.3.1.1 Related Work 2.3.2 Benchmarking MathML 2.3.2.1 Collection 2.3.2.2 Gold Standard 2.3.2.3 Evaluation Metrics 2.3.3 Evaluation of Context-Agnostic Conversion Tools 2.3.3.1 Tool Selection 2.3.3.2 Testing framework 2.3.3.3 Results 2.3.4 Summary of MathML Converters 2.4 Mathematical Information Retrieval for LaTeX Translations CHAPTER 3 Semantification of Mathematical LaTeX 3.1 Semantification via Math-Word Embeddings 3.1.1 Foundations and Related Work 3.1.1.1 Word Embedding 3.1.2 Semantic Knowledge Extraction 3.1.2.1 Evaluation of Math-Embedding-Based Knowledge Extraction 3.1.2.2 Improvement by Considering the Context 3.1.2.3 Visualizing Our Model 3.1.3 On Overcoming the Issues of Knowledge Extraction Approaches 3.1.4 The Future of Math Embeddings 3.2 Semantification with Mathematical Objects of Interest 3.2.1 Related Work 3.2.2 Data Preparation 3.2.2.1 Data Wrangling 3.2.2.2 Complexity of Math 3.2.3 Frequency Distributions of Mathematical Formulae 3.2.3.1 Zipf’s Law 3.2.3.2 Analyzing and Comparing Frequencies 3.2.4 Relevance Ranking for Formulae 3.2.5 Applications 3.2.6 Outlook 3.3 Semantification with Textual Context Analysis 3.3.1 Semantification, Translation & Evaluation Pipeline CHAPTER 4 From LaTeX to Computer Algebra Systems 4.1 Context-Agnostic Neural Machine Translation 4.1.1 Training Datasets & Preprocessing 4.1.2 Methodology 4.1.3 Evaluation of the Convolutional Network 4.1.3.1 Results 4.1.3.2 Qualitative Analysis and Discussion 4.2 Context-Sensitive Translation 4.2.1 Motivation 4.2.2 Related Work 4.2.3 Formal Mathematical Language Translations 4.2.3.1 Example of a Formal Translation 4.2.4 Document Pre-Processing 4.2.5 Annotated Dependency Graph Construction 4.2.6 Semantic Macro Replacement Patterns 4.2.6.1 Common Knowledge Pattern Recognition CHAPTER 5 Qualitative and Quantitative Evaluations 5.1 Evaluations on the Digital Library of Mathematical Functions 5.1.1 The DLMF dataset 5.1.2 Semantic LaTeX to CAS translation 5.1.2.1 Constraint Handling 5.1.2.2 Parse sums, products, integrals, and limits 5.1.2.3 Lagrange’s notation for differentiation and derivatives 5.1.3 Evaluation of the DLMF using CAS 5.1.3.1 Symbolic Evaluation 5.1.3.2 Numerical Evaluation 5.1.4 Results 5.1.4.1 Error Analysis 5.1.5 Conclude Quantitative Evaluations on the DLMF 5.1.5.1 Future Work 5.2 Evaluations on Wikipedia 5.2.1 Symbolic and Numeric Testing 5.2.2 Benchmark Testing 5.2.3 Results 5.2.3.1 Descriptive Term Extractions 5.2.3.2 Semantification 5.2.3.3 Translations from LATEX to CAS 5.2.4 Error Analysis & Discussion 5.2.4.1 Defining Equations 5.2.4.2 Missing Information 5.2.4.3 Non-Matching Replacement Patterns 5.2.5 Conclude Qualitative Evaluations on Wikipedia CHAPTER 6 Conclusion and FutureWork 6.1 Summary 6.2 Contributions and Impact of the Thesis 6.3 Future Work 6.3.1 Improved Translation Pipeline 6.3.2 Improve LaTeX to MathML Converters 6.3.3 Enhanced Formulae in Wikipedia 6.3.4 Language Independence Glossary Bibliography of Publications, Submissions & Talks Bibliography