MeatAxe: soc - Socle Series

MeatAxe 2.4

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soc - Socle Series

## Command Line

    soc Options [-l MaxLength] Module

Options
  Standard options, see Standard Command Line Options

-l MaxLength
  Maximum number of layers to compute.

Module
  Module name.

## Input Files

Name.cfinfo.
  Constituent information.

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

NameCf.op
  Spin-up script for the standard basis.

NameCf.k
  Uncondense matrix

## Output Files

Name.cfinfo.
  Socle information, see description.

Name.soc.
  A basis reflecting the Loewy structure.

## Description

This program determines the Loewy structure of a module by calculating the socles. Before using the program, you must run chop and pwkond with the "-t" option. For example,

    chop m11
    pwkond -t m11
    soc m11

For each layer of the socle series, the program prints the dimension and the multiplicities of the irreducible constituents in this layer. This information is also written to the cfinfo file. The following example shows the relevant portion of the cfinfo file:

    CFInfo.NSocles := 5;
    CFInfo.Socles := [[1,0,0],[0,1,1],[2,0,0],[0,1,1],[1,0,0]];

The numbers in `CFInfo.socles` are the multiplicities of the irreducible constituents for each layer of the socle series.

Using the "-l" option, you can specify a maximum length. After MaxLength socles have been calculated, the program prints a warning and stops.

A basis basis reflecting the Loewy structure of the module is written to Name.soc. Note: soc always writes a basis of the full space. If the socle series is not calculated completely because the maximum length has been reached, the partial basis found so far is extended with random vectors to form a complete basis.

## Implementation Details

This program uses an algorithm by Magdolna Szöke, see [Sz98].