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##############################################################################
##
#W maps.gd GAP4 package `Utils' Stefan Kohl
## Chris Wensley
#Y Copyright (C) 2015-2019, The GAP Group
#############################################################################
## these three functions were in RCWA and were initially transferred but,
## to simplify the situation, just EpimorphismByGenerators has been retained
##
#O EpimorphismByGenerators( <D1>, <D2> ) . epi: gen's of <D1>->gen's of <D2>
#O EpimorphismByGeneratorsNC( <D1>, <D2> ) . . NC version as underlying oper
#M EpimorphismByGeneratorsNC( <G>, <H> ) . . . . . . . . . . . . for groups
##
DeclareOperation( "EpimorphismByGenerators", [ IsDomain, IsDomain ] );
#############################################################################
##
#O Pullback( <nu>, <mu> )
#A PullbackInfo( <pb> )
##
DeclareOperation( "Pullback", [ IsGroupHomomorphism, IsGroupHomomorphism ] );
DeclareAttribute( "PullbackInfo", IsGroup, "mutable" );
#############################################################################
##
#O CentralProduct( <G1>, <G2>, <Z1>, <Phi> )
#A CentralProductInfo( <cp> )
##
DeclareOperation( "CentralProduct",
[ IsGroup, IsGroup, IsGroup, IsGroupHomomorphism ] );
DeclareAttribute( "CentralProductInfo", IsGroup, "mutable" );
#############################################################################
## these functions compute idempotent endomorphisms on G with image R
##
#O IdempotentEndomorphisms( <G> )
#A IdempotentEndomorphismsWithImage( <genG>, <R> )
#A IdempotentEndomorphismsData( <G> )
##
DeclareOperation( "IdempotentEndomorphisms", [ IsGroup ] );
DeclareOperation( "IdempotentEndomorphismsWithImage", [ IsList, IsGroup ] );
DeclareAttribute( "IdempotentEndomorphismsData", IsGroup );
#############################################################################
##
#O DirectProductOfFunctions( <G>, <H>, <f1>, <f2> )
#O DirectProductOfAutomorphismGroups( <A1>, <A2> )
##
DeclareOperation( "DirectProductOfFunctions",
[ IsGroup, IsGroup, IsGroupHomomorphism, IsGroupHomomorphism ] );
DeclareOperation( "DirectProductOfAutomorphismGroups", [ IsGroup, IsGroup ] );
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