#! @Chapter Miscellaneous useful functions
#! @Section Matrices and homomorphisms
#! @Arguments hom, func
#! @Returns Homomorphism g given by g(x) = func(hom(x)).
#! @Description This is mainly for convenience, since it handles all
#! GAP accounting issues regarding the range, ByImages vs ByFunction,
#! etc.
DeclareGlobalFunction( "ComposeHomFunction" );
#! @Section Representation theoretic functions
#! @Arguments list1, list2
#! @Returns All possible tensor products given by $\rho \otimes \tau$
#! where $\rho : G \to \mbox{GL}(V)$ is taken from <A>list1</A> and
#! $\tau : H \to \mbox{GL}(W)$ is taken from <A>list2</A>. The result
#! is then a list of representations of $G \times H$.
DeclareGlobalFunction( "TensorProductRepLists" );
#! @Arguments list
#! @Returns Direct sum of the list of representations <A>list</A>
DeclareGlobalFunction( "DirectSumOfRepresentations" );
#! @Arguments rho
#! @Returns Degree of the representation <A>rho</A>. That is,
#! $\mbox{Tr}(\rho(e_G))$, where $e_G$ is the identity of the group
#! $G$ that <A>rho</A> has as domain.
DeclareGlobalFunction( "DegreeOfRepresentation" );
#! @Arguments rho
#! @Returns Linear representation $\rho$ isomorphic to the permutation
#! representation <A>rho</A>.
DeclareGlobalFunction( "PermToLinearRep" );
#! @Arguments S, prod
#! @Returns Whether <A>S</A> is an orthonormal set with respect to the
#! inner product <A>prod</A>.
DeclareGlobalFunction( "IsOrthonormalSet" );
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