65.7 Module Homomorphisms

  • MTX.IsEquivalent(module1,module2) F

    tests two irreducible modules for equivalence.

  • MTX.Isomorphism(module1,module2) F

    returns an isomorphism from module1 to module2 (if one exists) and fail otherwise. It requires that one of the modules is known to be irreducible. It implicitly assumes that the same group is acting, otherwise the results are unpredictable. The isomorphism is given by a matrix M, whose rows give the images of the standard basis vectors of module2 in the standard basis of module1. That is, conjugation of the generators of module2 with M yields the generators of module1.

  • MTX.Homomorphisms(module1,module2) F

    returns a basis of all homomorphisms from the irreducible module module1 to module2.

  • MTX.Distinguish(cf,nr) F

    Let cf be the output of MTX.CollectedFactors. This routine tries to find a group algebra element that has nullity zero on all composition factors except number nr.

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    GAP 4 manual
    February 2000