VMEXT：一个数学表达式树的可视化工具
VMEXT: A Visualization Tool for Mathematical Expression Trees
摘要：
数学表达式可以表示为由终端符号组成的树，例如标识符或数字（叶节点）以及函数或运算符（非叶节点）。表达式树是存储和处理数学表达式的重要机制，也是最常用的数学表达式结构可视化方法。通常，研究人员和从业者使用通用工具手动可视化表达树。这种方法是费力的、冗余的并且容易出错。手动可视化表示用户对表达式的标记应该是什么的概念，但不一定是实际的标记。本文介绍了VMEXT -一个免费的开源工具，直接可视化表达式树从并行MathML。VMEXT同时可视化数学表达式的表示元素和语义结构，使用户能够快速发现Content MathML标记中不影响表达式表示的缺陷。以前，识别这种差异需要阅读冗长而复杂的MathML标记。VMEXT还允许可视化两个表达式的相似和相同元素。可视化表达式相似性可以支持开发人员设计检索方法，并为数学信息检索系统的用户实现改进的交互概念。我们展示了VMEXT的可视化在两个基于Web的应用程序。第一个应用程序单独呈现可视化。第二个应用程序显示了一个可能的整合系统中的数学知识管理和数学信息检索的可视化。该应用程序将LaTeX输入转换为并行MathML，计算数学表达式的基本相似性度量，并使用VMEXT可视化结果。
英文摘要：
Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is laborious, redundant, and error-prone. Manual visualizations represent a user's notion of what the markup of an expression should be, but not necessarily what the actual markup is. This paper presents VMEXT - a free and open source tool to directly visualize expression trees from parallel MathML. VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content MathML markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex MathML markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can support support developers in designing retrieval approaches and enable improved interaction concepts for users of mathematical information retrieval systems. We demonstrate VMEXT's visualizations in two web-based applications. The first application presents the visualizations alone. The second application shows a possible integration of the visualizations in systems for mathematical knowledge management and mathematical information retrieval. The application converts LaTeX input to parallel MathML, computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.
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