65.1 MeatAxe Modules

  • GModuleByMats(gens,field)
  • GModuleByMats(emptygens,dim,field)

    creates a MeatAxe module over field from a list of invertible matrices gens which reflect a group's action. If the list of generators is empty, the dimension must be given as second argument.

    MeatAxe routines are on a level with Gaussian elimination. Therefore they do not deal with GAP modules but essentially with lists of matrices. For the MeatAxe, a module is a record with components

    generators
    A list of matrices which represent a group operation on a finite dimensional row vector space.

    dimension
    The field over which the vector space is defined.

    field
    The field over which the vector space is defined.
    Once a module has been created its entries may not be changed. A MeatAxe may create a new component NameOfMeatAxe in which it can store private information. By a MeatAxe ``submodule'' or ``factor module'' we denote actually the induced action on the submodule, respectively factor module. Therefore the submodules or factor modules are again MeatAxe modules. The arrangement of generators is guaranteed to be the same for the induced modules, but to obtain the complete relation to the original module, the bases used are needed as well.

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    GAP 4 manual
    February 2000