Exploring Mathematica Function Names Network

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Author: Frederick Wu

1. Overview Function Names

Mathematica 7 has over 3000+ function names.

How to best learn those functions? Are they all important? What is the relations between those functions?
This Blog tries to answer those questions by exploring those functions networks from a graph prospective.

2. Database and Relationship

We use Wolfram Research defined Documenations "SEE ALSO" as functions relation. It' s an useful and available database.

For example, if we are looking for Table, it's related with 14 functios (Range, DiagonalMatrix ... and so on ) in red frame.

We take four Mathematica's functions for a tiny case study, They are Table, ParallelTable, NestList, NestWhileList.

3. Visualizing and Structure

4. Conclusion

According to above networks, we can find some interesting points.

1. Table still plays a key role in the networks.
2. ParallelTable is a Table related functions, but specialized for parallel computing.
3. NestList and NestWhileList are closely related but slight to different directions, they share another functions FixedPointList.

We can plot a bigger network, if we include more functions and data.

We could even plot the complete network, if we include all functions. One net to rule them all. (一网打尽)

5. Reference

[1] 吴飞，附录篇，Mathematica 演示项目记，清华大学出版社 2010.
[2] Yifan Hu, Case Study 3. Mathematica Seminar 2006 China, Wolfram Research Inc.
[3] Bing Ye, Mathematica Pocket Reference, Wolfram Research Inc.