65.8 The Smash MeatAxe

The standard MeatAxe provided in the GAP library is is based on the MeatAxe in the sf Smash share package for GAP3, originally written by Derek Holt and Sarah Rees (HR94). It is accessible via the variable SMTX to which MTX is assigned by default. For the sake of completeness the remaining sections document more technical functions of this MeatAxe.

  • SMTX.RandomIrreducibleSubGModule(module) F

    returns the module action on a random irreducible submodule.

  • SMTX.GoodElementGModule(module) F

    finds an element with minimal possible nullspace dimension if module is known to be irreducible.

  • SMTX.SortHomGModule(module1,module2,homs) F

    Function to sort the output of Homomorphisms.

  • SMTX.MinimalSubGModules(module1,module2[,max])

    returns (at most max) bases of submodules of module2 which are isomorphic to the irreducible module module1.

  • SMTX.Setter(string)

    returns a setter function for the component smashMeataxe.(string).

  • SMTX.Getter(string)

    returns a getter function for the component smashMeataxe.(string).

  • SMTX.IrreducibilityTest(module)

    Tests for irreducibility and sets a subbasis if reducible. It neither sets an irreducibility flag, nor tests it. Thus the routine also can simply be called to obtain a random submodule.

  • SMTX.AbsoluteIrreducibilityTest(module)

    Tests for absolute irreducibility and sets splitting field degree. It neither sets an absolute irreducibility flag, nor tests it.

  • SMTX.MinimalSubGModule(module,cf,nr)

    returns the basis of a minimal submodule of module containing the indicated composition factor. It assumes Distinguish has been called already.

  • SMTX.MatrixSum(matrices1,matrices2)

    creates the direct sum of two matrix lists.

  • SMTX.CompleteBasis(module,pbasis)

    extends the partial basis pbasis to a basis of the full space by action of module. It returns whether it succeeded.

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    GAP 4 manual
    February 2000