文档准备系统与计算机代数系统之间数学公式的语义保持双射映射
Semantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems
摘要：
像LaTeX这样的文档准备系统提供了渲染数学表达式的能力，就像人们在纸上写这些一样。使用LaTeX、LaTeXML和为在国家标准研究所（NIST）数学函数数字图书馆中使用而生成的工具，通过使用语义宏集来实现语义增强的数学LaTeX标记（语义LaTeX）。计算机代数系统（CAS），如Maple和Mathematica使用替代标记来表示数学表达式。通过利用Youssef的部分数学标记和CAS内部表示，我们开发的算法来翻译数学表达式表示在语义LaTeX相应的CAS表示，反之亦然。我们还开发了用于翻译整个Wolfram编码连分数知识和安特卫普大学特殊函数连分数数据集的工具，用于NIST数学公式数字库。这些努力的总体目标是为数字数学图书馆中的公式向公众提供语义丰富的符合标准的MathML表示。这些表示包括表示MathML，内容MathML，通用LaTeX，语义LaTeX，现在还有CAS表示。
英文摘要：
Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) is achieved by using a semantic macro set. Computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. By taking advantage of Youssef's Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic LaTeX to corresponding CAS representations and vice versa. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. These representations include presentation MathML, content MathML, generic LaTeX, semantic LaTeX, and now CAS representations as well.
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