MeatAxe
2.4
Programs for working with modular representations

mkdotl [Options] [G] [nodup] Name
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 dottedlines from the output. If this option is specified, the program will calculate, for each dottedline, the maximal mountains contained in the span of the dottedline. If a dottedline has the same set of maximal mountains as an earlier dottedline, 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 dottedlines.