soc man page

soc — Socle series


soc [Options] <Name>


This program determines the Loewy structure of a module by calculating the socles. Before using the program, you must run chop(1) and pwkond(1) 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.


Quiet, no messages.
Verbose, more messages.
-T <MaxTime>
Set CPU time limit
-l <length>
Calculate only the first<length> layers.

Implementation Details

The algorithm used by this program was developed by Magdolna Szöke; see "Examining Green Correspondents of Weight Modules", Aachener Beiträge zur Mathematik, Band 24, Wissenschaftsverlag Mainz, Aachen, 1998.

Input Files

Constituent info file.
Generators on constituents.
Spin-up script for the standard basis.
Uncondense matrix.

Output Files

Constituent info file.
Matrix for basis change.

See Also

chop(1), pwkond(1)

Referenced By


Explore man page connections for soc(1).

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