mktree man page

mktree — enumerate elements of a finitely generated matrix group

Synopsis

mksub [Options] <Name>

Description

This program enumerates all elements of a finitely generated matrix group.  By default, the program assumes that the group has two generators, which are read from Name.1 and Name.2.  A different number of generators can be specified with -g.

Unless the -n option is used, the program writes the element tree to Name.elt.  The element tree describes how the group elements can be calculated as products of generators.  It is actually a matrix with two columns and one row for each group element.  The ith row of this matrix describes how the ith element is calculated:

The following example shows the output for a group of the order 10 with two generators, a and b:

Line Contents Meaning
1 -1 -1 identity matrix
2 0 0 a
3 0 1 b
4 1 0 aa
5 1 1 ab
6 3 0 aaa
7 3 1 aab
8 5 0 aaaa
9 5 1 aaab
10 7 1 aaaab

Options

-Q

Quiet, no messages.

-V

Verbose, more messages.

-T <MaxTime>

Set CPU time limit

-g <NGen>

Set the number of generators.  Default: 2.

-n

Don't write the element file, just print the order.

Implementation Details

The program holds all group elements in memory.  This limits the application of the program to fairly small groups and representations of small degree.

Input Files

Name.{1,2,...}

Generators

Output Files

Name.elt

Element tree.

Info

2.4.24 MeatAxe User Commands