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2 How to Start?


  1. Starting XGAP
  2. Starting ITC

2.1 Starting XGAP

You begin an ITC session by starting XGAP. On most systems this is done by completing the provided line



user@host:~> xgap

on the command line. Ask your system administrator if this does not work. This command will create a new window, the so called GAP Window, in which GAP is awaiting your input.

During a typical ITC session various windows will be opened to display the involved tables and further information. The size of the characters displayed in these windows and hence the sizes of the windows themselves are determined by the so-called fonts used.

The XGAP package knows five different fonts, tiny, small, normal, large, and huge (see the XGAP manual for details), but the ITC routines use only two of them, namely small and normal. So, if the default ITC window sizes are inconvenient for you, you need only to change the values of these two fonts. You may do this by starting XGAP with one or two additional arguments of the form "-small font" or "-normal font" where font has to be a font which is known to your system. You can get a list of all available fonts via the command

user@host:~> xlsfonts


user@host:~> xgap -small 6x12 -normal 8x13

In particular, you should use this option to change the fonts if the default fonts of XGAP do not work properly in your local installation (this may happen in some rare cases where there are too few or too many fonts).

2.2 Starting ITC

At the top of the GAP Window opened by XGAP you will see a ``title bar'' with three buttons: GAP, Run, and Help. Clicking either of these will pop up a menu, in which you may choose between several options.

You can always interrupt a computation by making the GAP Window active and pressing CTRL-C. You will get the same effect selecting Interrupt in the Run menu.

In the GAP Window, as usual, the GAP prompt


will indicate that GAP is awaiting your input.

If it is not loaded automatically, first load the ITC package by

gap> LoadPackage( "itc" );

See LoadPackage in the GAP Reference Manual.

Then you may input a finitely presented group, say g, and a subgroup, say h, of it, the cosets of which you want to enumerate using ITC. The format of this input is the same as usual in GAP, see Chapter Finitely Presented Groups of the GAP reference manual for the details.

ITC will in several of its windows have to display generators of the free group which is used to describe the presentation. Note that ITC will use the names of the generators of this free group, if these names consist of at most three symbols. Otherwise ITC will use names of the form g1, g2, ... up to at most g99 for the generators of the free group (if the group has more than 99 generators, an error message will be given). A choice of short and easily distinguishable names for the generators of the free group is hence advisable.

Now you are ready to start the ITC using the command InteractiveTC.

  • InteractiveTC( g, h ) F

    Called with a group g and a subgroup h, this will open the ``Coset Table Window'', which really serves a multiple purpose:

    It shows the Coset Table and allows certain operations by mouse click in this Coset Table. We will describe the details in Section The Coset Table of Chapter The Tables. In this chapter also a description of all other tables is given that can be shown on the screen by ITC.

    Directly below the Coset Table space is left for one row of text in which some warnings will be given (in red) by ITC if the user tries to invoke actions that in the present state are not possible, e. g. if the user tries to call the short-cut function while the tables have not yet closed (see Section Warnings).

    It provides up to date information on the state that an interactive coset enumeration has reached in the ``Information Line'' (see The Information Line).

    It also provides a number of buttons which can be used in the interactive handling of a coset enumeration by ITC. We will describe this aspect in a separate chapter ``Buttons and Menus'' (Chapter Buttons and Menus).

    The initial table size for the ITC Coset Table is set by default to 1000. You can change this default table size using the menu entry change default table size in the menu of the top button Settings, (see change default table size). If during a run of a CE the table size does not suffice, you can extend it using the menu entry extend table size (see extend table size) in the same menu.

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    ITC manual
    March 2022