# Introduction

®ina; is a software package for low-dimensional topologists. Historically, its main strengths lie in 3-manifold topology: it has a highly optimised toolkit with a focus on normal surface theory, angle structures, and the combinatorial structures of triangulations, and it now performs many high-level topological algorithms for 3-manifolds. ®ina; also offers rich toolkits for knots and links and triangulated 4-manifolds, and offers more basic combinatorial support for manifolds of dimension 5–15. For more on these and its many other features, see the full feature set later in this introduction.

## Getting Started

Not sure how to start ®ina;? You can find it in your main applications or programs menu; follow this link for details and screenshots.

The best way to become familiar with ®ina; is simply to play around with it. ®ina; ships with several example files, including a number of censuses of 3-manifold triangulations. Most of these examples can be accessed through the File Open Example menu when running ®ina;.

For an excellent starting point, try File Open Example Introductory Examples , which illustrates most of the structures that ®ina; can work with. The users' handbook (which you are reading now) also includes a number of sample &python; sessions that illustrate how ®ina;'s in-built &python; scripting can be used.

The graphical user interface offers extensive assistance through tooltips and "What's This?" texts. If you ever want to know what element of the user interface means (such a button or a text field), just press &Shift;F1 and click on the thing you would like to know more about.

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## Genealogy

In 1997 in Melbourne, David Letscher, Richard Rannard and Ben Burton under the guidance of J. Hyam Rubinstein planned out a program that would do normal surface theory and everything else besides. Much groundwork planning was done, epsilon code was written and then things kind of faded away. David Letscher revived the project on his own and in 1999 presented Normal 1.0. This program performed triangulation simplification and found vertex normal surfaces, was written in &java; and was a proof-of-concept program that normal surface theory was computationally feasible.

In March 1999, David and Ben sat down to write a new version of the program from scratch. The new version would have a calculation engine written in &cpp; for speed and would have a &java; GUI for portability. It would be carefully designed and written with rigour and extensibility in mind, allowing for the possibility of add-ons written by other people.

David however leads a busy life and pulled out of the project in late 2000, but remained to offer technical advice. In late 2000 a prerelease of the new program was ready and ®ina; 2.0 was uploaded to the web.

Since then, many more people have been involved in both small ways and large. ®ina; has also undergone some major structural changes over the years: In late 2003 the old &java; user interface was completely removed in favour of a faster and cleaner native &cpp; user interface (written using the excellent &kde; libraries), and the scripting interface switched from &jython; to standard &python; support. By 2012 the user interface had been ported from &kde; to the more portable &qt;, offering a much cleaner experience on &macosx; and supporting &windows; for the first time. In 2016 the underlying &cpp; code was redeveloped in a much more generic style, merging the existing 3-manifolds code with a long-running project with Ryan Budney on 4-manifolds, and creating a new infrastructure for exploring triangulations in dimensions as high as 15.

## Citing Regina

If you find ®ina; useful in your research, please consider citing it as you would any other paper that you use. A suggested form of reference is:

> Benjamin A. Burton, Ryan Budney, William Pettersson, et al., Regina: Software for low-dimensional topology, `http://regina-normal.github.io/`, 1999–2021.

A &bibtex; entry for this reference is included below.

    @misc{regina,
        author = {Benjamin A. Burton and Ryan Budney and William Pettersson and others},
        title = {Regina: Software for low-dimensional topology},
        howpublished = {{\tt http://\allowbreak regina-normal.\allowbreak
            github.\allowbreak io/}},
        year = {1999--2021}
    }

## Who is Regina?

This normal surface theory software has been named after Regina Basman who once told me she was the most normal person I knew. She's studied mathematics, reads interesting books, has a gorgeous child and likes running around rainforests in the dark.