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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Andrew Solomon.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains declarations for magma homomorphisms.
##
#############################################################################
##
#P IsMagmaHomomorphism( <mapp> )
##
## <#GAPDoc Label="IsMagmaHomomorphism">
## <ManSection>
## <Filt 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]);
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