MeatAxe: mkdotl - Find Dotted-lines

MeatAxe 2.4

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mkdotl - Find Dotted-lines

## Command Line

    mkdotl [Options] [-G] [--nodup] Name

Options
  Standard options, see Standard Command Line Options

-G
  Produce output in GAP format.

--nodup
  Eliminate redundant dotted-lines.

Name
  Name of the representation.

## Input Files

Name.cfinfo
  Constituent info file.

NameCf.v
  Cyclic submodules, generated by mkcycl.

Name.inc
  Incidence matrix, created by mkinc.

Name.mnt
  Mountain data, created by mkinc.

## Output Files

Name.dot
  Dotted-lines.

## Description

This program calculates a set of dotted lines between the local submodules. More precisely, it computes one dotted line for each submodule with head isomoprphic to S⊕S, S irreducible. It can be shown that this set of dotted lines is sufficient to determine the complete submodule lattice as described by Benson and Conway.

Input for this program are the incidence matrix calculated by mkinc and the cyclic submodules from mkcycl. Again, the whole calculation takes place in the condensed modules, so there is no need to uncondense the cyclic submodules.

It is known that all dotted lines have length q+1, where q is the order of the splitting field. This information is used by the program to determine if a dotted line is complete.

A list of all dotted lines is written to Name.dot.

Using the option "--nodup" eliminates redundant dotted-lines from the output. If this option is specified, the program will calculate, for each dotted-line, the maximal mountains contained in the span of the dotted-line. If a dotted-line has the same set of maximal mountains as an earlier dotted-line, it is considered as redundant and dropped. Note that "--nodup" increases both memory and CPU time usage. However, the subsequent step, mkgraph, will benefit from a reduction of the number of dotted-lines.