/usr/share/gap/lib/mgmhom.gd is in gap-libs 4r7p9-1.
This file is owned by root:root, with mode 0o644.
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#W mgmhom.gd GAP library Andrew Solomon
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#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
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## This file contains declarations for magma homomorphisms.
##
#############################################################################
##
#P IsMagmaHomomorphism( <mapp> )
##
## <#GAPDoc Label="IsMagmaHomomorphism">
## <ManSection>
## <Prop Name="IsMagmaHomomorphism" Arg='mapp'/>
##
## <Description>
## A <E>magma homomorphism</E> is a total single valued mapping
## which respects multiplication.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareSynonymAttr( "IsMagmaHomomorphism",
IsMapping and RespectsMultiplication );
#############################################################################
##
#F MagmaHomomorphismByFunctionNC( <G>, <H>, <fn> )
##
## <#GAPDoc Label="MagmaHomomorphismByFunctionNC">
## <ManSection>
## <Func Name="MagmaHomomorphismByFunctionNC" Arg='G, H, fn'/>
##
## <Description>
## Creates the homomorphism from <A>G</A> to <A>H</A> without checking
## that <A>fn</A> is a homomorphism.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "MagmaHomomorphismByFunctionNC");
#############################################################################
##
#F MagmaIsomorphismByFunctionsNC( <G>, <H>, <fn>, <inv> )
##
## <ManSection>
## <Func Name="MagmaIsomorphismByFunctionsNC" Arg='G, H, fn, inv'/>
##
## <Description>
## Creates the isomorphism from <A>G</A> to <A>H</A> without checking
## that <A>fn</A> or <A>inv</A> are homomorphisms or bijective or inverse.
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "MagmaIsomorphismByFunctionsNC");
############################################################################
##
#O NaturalHomomorphismByGenerators( <f>, <s> )
##
## <#GAPDoc Label="NaturalHomomorphismByGenerators">
## <ManSection>
## <Oper Name="NaturalHomomorphismByGenerators" Arg='f, s'/>
##
## <Description>
## returns a mapping from the magma <A>f</A> with <M>n</M> generators to the
## magma <A>s</A> with <M>n</M> generators,
## which maps the <M>i</M>-th generator of <A>f</A> to the
## <M>i</M>-th generator of <A>s</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation("NaturalHomomorphismByGenerators",[IsMagma, IsMagma]);
#############################################################################
##
#E
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