Knotscape 1.01

Fork Notes:

• This is still very unstable but somewhat works if we ignore some random error boxes that sometimes pop up when resizing the window.

• Some actions like "Draw Knot" for some reason don't work or hang for now.

Usage

To run Knotscape, you need to have Tcl/Tk installed on your system. Then you can build and run it with the following commands:

$ https://github.com/aziis98/knotscap
$ make
$ ./knotscape

Project Structure

Knotscape is primarily a Tcl/Tk application that provides a graphical user interface for exploring knot theory concepts. Its structure can be understood at a high level as follows:

• Main Application (knotscape script & tcl/ directory):

  • The knotscape shell script is the main entry point, which launches the Tcl/Tk-based GUI.

  • The tcl/ directory contains numerous Tcl scripts (.tcl files). These scripts define the user interface elements, event handling, and the core logic of the application. They are organized into various procedures (Tcl procs) that manage different functionalities like displaying knots, handling user input, and orchestrating calls to backend programs.

• Computational Backend (C Programs in src/):

  • Knotscape offloads computationally intensive tasks to a suite of external programs written in C. The source code for these programs resides in the src/ directory.

  • Upon compilation (using the Makefile), these C programs are placed as executables in the bin/ directory.

  • Examples of such programs include:

    • poly1 and poly2: Used for computing various knot polynomials.

    • draw: Handles the generation of knot diagrams.

    • knotfind, locate_a, locate_n: Used for searching and identifying knots in the database.

    • Other specialized programs for tasks like calculating hyperbolic invariants, checking knot properties, etc.

• Data and Resources:

  • knotTable/: Contains the database of knots.

  • doc/: Provides documentation, including conversion tables for knot notations.

  • help/: Stores help files accessible from the application.

  • gif/: Contains images used in the GUI.

  • lib/: Includes auxiliary data files used by some of the backend programs.

This separation allows the Tcl/Tk frontend to remain responsive while the C programs perform complex calculations.

Help Outline

The help/ directory contains plain text files that provide guidance on various aspects of Knotscape. The help/help.toc file serves as a table of contents for these help files. Here's a brief overview of the key help topics:

• help.tutorial: A step-by-step guide for new users to learn the basics of Knotscape.

• help.notation: Explains the different systems of notation used to describe knots within the program (e.g., Dowker-Thistlethwaite, Alexander-Briggs).

• help.enter: Instructions on how to manually input knots into the application, typically using a specific notation.

• help.linksmith: Detailed guide on using LinkSmith, the graphical tool for drawing and editing knot and link diagrams with the mouse.

• help.locate: How to search for and identify knots within Knotscape's extensive database.

• help.draw: Information on generating and customizing visual diagrams of knots.

• help.hyperbolic: Covers the calculation and interpretation of hyperbolic invariants for knots, a key feature for studying knot geometry.

• help.polynomials: Describes the various knot polynomials (e.g., Alexander, Jones, HOMFLY) that Knotscape can compute and their significance.

• help.homomorphisms: Details on working with representations of knot groups and their homomorphisms.

• help.shortcuts: A list of keyboard shortcuts to speed up common operations.

• help.limits: Outlines the operational boundaries of the software, such as the maximum number of crossings it can handle.

• help.editing: Provides tips and instructions for text editing within Knotscape's various windows and input fields.

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4-1-99 by Jim Hoste and Morwen Thistlethwaite, with help from Bruce Ewing, Ken Millett, Ken Stephenson and Jeff Weeks.

Features added since Version 1.0:

1. LinkSmith has a new "Export" menu, with two options:

   1. save the current link diagram in Ewing-Millett format;

   2. save the underlying link complement as an ideal triangulation, in SnapPea-readable format.

2. The horoball and drawing windows now have an option invoking a file-save dialogue box for saving the picture as a PostScript file.

3. Hyperbolic invariants now occupy a separate (tear-off) submenu of the Action menu. There are two new features:

   1. "Save Triangulation", which produces an ideal triangulation of the (hyperbolic) knot complement, and writes it to a file in SnapPea-readable format;
   2. "Canonical Cell Decomposition", which displays the canonical cell decomposition of the knot complement, as viewed from the cusp. The canonical cell decomposition can be saved as a PostScript file. It is a complete invariant of cusped hyperbolic manifolds. For further details, see the Help file on hyperbolic invariants.

Some bug fixes are listed in the file FIXES.

README for Version 1.0

Please see the file Credits.ps for details on contributors to Knotscape.

This version is an upgrade to Knotscape 1.0-BETA.

The main enhancement is the incorporation of LinkSmith, a program enabling the user to draw a knot with a mouse. Also, Knotscape now includes in its database all knots up to 16 crossings. Various other minor improvements have been made since the beta version.

The original purpose of Knotscape was to provide convenient access to tables of knots. Its purpose has expanded somewhat, particularly with the inclusion of the hyperbolic invariants. The binaries which calculate hyperbolic invariants were compiled against SnapPea 2.0; we are very grateful to Jeff Weeks, the author of SnapPea, for making this possible. We'd like to emphasize that we take full responsibility for any bugs that there might be in the hyperbolic part of Knotscape.

At present, Knotscape will deal with knots up to 49 crossings. A database containing all prime knots of up to 16 crossings is included. Dictionaries are included in the doc directory for converting between classical numbering of knots and Dowker-Thistlethwaite numbering. The doc directory also has a subdirectory "symmetric_knots" containing all highly symmetric knots up to 16 crossings. These can be loaded into Knotscape and investigated.

The program requires Tcl 7.4, 7.5, 7.6 or 8.0 / Tk 4.0, 4.1 4.2 or 8.0.

Binaries of the executables are provided for the following two platforms:

i386 linux sunos

Source code is also provided in each version for all but one of the executables.

The procedures not dependant on SnapPea can be compiled in a straightforward manner, using the Makefile in Knotscape's home directory. But we have not yet tested Knotscape on any platform except those listed above, so it is likely that there would be problems.

The program knotscape_hyp.c can also be compiled against Snappea-2.0, downloadable from Jeff Weeks's home page at http://thames.northnet.org/weeks/ . knotscape_hyp.c provides all the SnapPea functions in Knotscape except for the computation of fixed point sets of symmetries, and the computation of the canonical dell decomposition. The program knotscape_hyp.c refers to procedures in decode_new_DT.c, also in the src directory.

The source code for computation of fixed point sets and the canonical decomposition is not yet supplied, as the two programs in question have to be compiled against non-standard versions of the SnapPea kernel. Hopefully these will also be available in the near future.

We welcome any suggestions for improvements, and also of course reports of bugs.

Jim Hoste jhoste@calvin.pitzer.edu Morwen Thistlethwaite morwen@math.utk.edu

Installation.

1. Download the file knotscape-1.0.<platform>.tar.gz, where <platform> is appropriate for your computer, and copy to the directory where you wish Knotscape to be installed.

2. Untar by typing tar zxvf knotscape-1.0.<platform>.tar.gz. On some systems the file has to be decompressed with gunzip before untarring with "tar xvf ... " A new directory "knotscape" will appear.

3. Change directory to the new directory "knotscape".

4. If necessary edit the shell script, also called "knotscape", to suit your system. The environment variable KSHOME should be set to the present directory. You may want to choose a different temporary directory from $KSHOME/tmp . This temporary directory is a scratch directory containing all the input and output files generated by the executables. It also contains any PostScript files generated by Knotscape. On some systems the command "wish" needs to be made more specific, as several different versions of Tk might be installed. Knotscape will not run on any version of Tk prior to 4.0. Finally, ensure that all files have the correct permissions.

5. Run Knotscape by typing "./knotscape", or simply "knotscape" if the current working directory is in your PATH variable.

Getting started.

The easiest way of getting started is to use the browser window to enter one or more knots in the input window. A tutorial can be accessed by clicking on "HELP" followed by "Tutorial".

It's possible that machines with no swap partition or machines with a small amount of memory will produce a segmentation violation when some of Knotscape's options are invoked. If you are using a Linux machine, the solution is to create a suitably large swap partition.