The desktop group theory visualization software Group Explorer was ported to the web in 2019. It is available online at https://nathancarter.github.io/group-explorer. It has some software-as-a-service features that let its pages be opened by other applications, with parameters indicating which groups to display and in which ways. This package provides a GAP API for doing exactly that.
Group Explorer has many features that this package does not expose, because its primary intended use case is (as the name suggests) interactive exploration of visualizations (rather than generating them programmatically). The reader may wish to investigate the Group Explorer manual for a full list of its features.
The subset of those features exposed by this package include:
displaying a multiplication table for a given group
displaying a Cayley graph for a given group
displaying a cycle graph for a given group
letting the user interact with any of these visualizations after they have been displayed
These visualizations have natural limitations; it becomes impossible to gain any benefit from, for example, a Cayley graph that is so huge that its structure is unreadable to the human eye. And the computer would have difficulty constructing and rendering such an object as well. Thus this package's utility decreases with group size, roughly as follows.
groups of order 1-30: ideal
groups of order 31-60: still useful
groups of order 61-200: renderable but not very useful (as in the example in Section 2.10)
groups of order 201+: slow to render, not very useful
Note that Group Explorer is a separate application from this package, and if bugs are discovered within Group Explorer, they should be reported on its issue tracker on GitHub, rather than within the issue tracker for this GAP package. Bugs for this package's connection to Group Explorer can be reported to this package's issue tracker.
The remaining sections of this chapter cover some illustrative examples to help get you started using the package. Comprehensive reference documentation for the few functions exposed by the package appears in Chapter 3.
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