mkhom_old man page
mkhom_old — calculate homomorphisms between modules
Synopsis
mkhom_old [Options] <M> <N> <Hom>
Description
This program calculates a basis for the vector space of homomorphisms between two kG-modules, Hom_kG(M,N). In the case M=N the program optionally finds a generating set for the algebra of endomoprhisms, End_kG(M), and calculates the corresponding left or right regular representation.
If used without any options, mkhom_old writes the standard basis of M to M.std, and a k-basis of the homomorphism space to Hom.1, Hom.2, .... The latter are given with respect to the standard basis of M and the original basis of N. To get the homomorphisms with respect to the original bases of M and N]fP, multiply the matrices from the left with the inverse of Hom.
Mkhom_old uses peak words of the first module. Thus, before using the program, chop(1) and pwkond(1) must have been run on the first module.
Options
- -Q
Quiet, no messages.
- -V
Verbose, more messages.
- -T <MaxTime>
Set CPU time limit
- -t
Calculate generators for <M> in the standard basis.
- -s
When M=N, calculate endomorphisms in the standard basis.
- -r <Side>
When M=N, find a generating set of End(M), and calculate the left (Side=1) or right (Side=2) regular representation.
- -b <Mode>
Save memory, Mode=0..2.
- -H <Dim>
If the radical is given, Dim is the dimension of the head.
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
Output Files
- M.std
The standard basis for M.
- Hom.{1,2,...}
A k-basis of Hom(M,N).
- M.std.{1,2,...}
Generators in the standard basis (with -t).