VMEXT: A Visualization Tool for Mathematical Expression Trees

  • Moritz SchubotzEmail author
  • Norman MeuschkeEmail author
  • Thomas HeppEmail author
  • Howard S. CohlEmail author
  • Bela GippEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10383)


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 represents 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 Open image in new window . VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content Open image in new window markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex Open image in new window markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can 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 Open image in new window input to parallel Open image in new window , computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.


Mathematical information retrieval Expression tree Open image in new window Open image in new window Visualization 



We thank Ludwig Goohsen and Stefan Kaufhold for their support in developing VMEXT. Furthermore, we thank the Wikimedia Foundation for providing a server to run the VMEXT demo.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany
  2. 2.Applied and Computational Mathematics DivisionNational Institute of Standards and TechnologyGaithersburgUSA

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