MeatAxe: mkinc - Find Mountains

MeatAxe 2.4

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mkinc - Find Mountains

## Command Line

    mkinc [Options] [-G] Name

Options
  Standard options, see Standard Command Line Options

-G
  Produce output in GAP format.

Name
  Name of the representation.

## Input Files

Name.cfinfo
  Constituent info file.

NameCf.1, NameCf.2, ...
  Generators on the irreducible constituents.

NameCf.1k, NameCf.2k, ...
  Generators on the corresponding condensed modules.

NameCf.v
  Cyclic submodules, generated by mkcycl.

NameCf.im
  Peak word images.

NameCf.k
  Uncondense matrices.

## Output Files

Name.v
  Mountains.

Name.mnt
  Mountain dimensions and classes of cyclic submodules corresponding to the mountains.

Name.inc
  Incidence matrix.

## Description

This program runs in two steps. During the first step, all cyclic cyclic submodules found by mkcycl are uncondensed, giving the local submodules, the "mountains", of the original module. Then, each local submodule is projected back to the condensed module, and all cyclic vectors which are contained in the image are found. At the end of this step, there is a list of local submodules and, for each local submodule, a list of cyclic subspaces in the condensed module. This information is written to Name.mnt.

In the second step, mkinc computes the incidence relation between local submodules. The result is a matrix which contains a 1 for each incidence. This matrix is written to the file Name.inc.

## Implementation Details

The whole calculation of step 2 is done in the condensed modules. This is possible because incidences between local submodules do not change if they are condensed. Usually this saves a lot of both memory and CPU time because one does not have to keep all mountains simultaneously, and the condensed modules have a smaller dimension.