1############################################################################# 2## 3## This file is part of GAP, a system for computational discrete algebra. 4## This file's authors include Andrew Solomon. 5## 6## Copyright of GAP belongs to its developers, whose names are too numerous 7## to list here. Please refer to the COPYRIGHT file for details. 8## 9## SPDX-License-Identifier: GPL-2.0-or-later 10## 11## This file contains declarations for magma homomorphisms. 12## 13 14############################################################################# 15## 16#P IsMagmaHomomorphism( <mapp> ) 17## 18## <#GAPDoc Label="IsMagmaHomomorphism"> 19## <ManSection> 20## <Filt Name="IsMagmaHomomorphism" Arg='mapp'/> 21## 22## <Description> 23## A <E>magma homomorphism</E> is a total single valued mapping 24## which respects multiplication. 25## </Description> 26## </ManSection> 27## <#/GAPDoc> 28## 29DeclareSynonymAttr( "IsMagmaHomomorphism", 30 IsMapping and RespectsMultiplication ); 31 32 33############################################################################# 34## 35#F MagmaHomomorphismByFunctionNC( <G>, <H>, <fn> ) 36## 37## <#GAPDoc Label="MagmaHomomorphismByFunctionNC"> 38## <ManSection> 39## <Func Name="MagmaHomomorphismByFunctionNC" Arg='G, H, fn'/> 40## 41## <Description> 42## Creates the homomorphism from <A>G</A> to <A>H</A> without checking 43## that <A>fn</A> is a homomorphism. 44## </Description> 45## </ManSection> 46## <#/GAPDoc> 47## 48DeclareGlobalFunction( "MagmaHomomorphismByFunctionNC"); 49 50############################################################################# 51## 52#F MagmaIsomorphismByFunctionsNC( <G>, <H>, <fn>, <inv> ) 53## 54## <ManSection> 55## <Func Name="MagmaIsomorphismByFunctionsNC" Arg='G, H, fn, inv'/> 56## 57## <Description> 58## Creates the isomorphism from <A>G</A> to <A>H</A> without checking 59## that <A>fn</A> or <A>inv</A> are homomorphisms or bijective or inverse. 60## </Description> 61## </ManSection> 62## 63DeclareGlobalFunction( "MagmaIsomorphismByFunctionsNC"); 64 65 66############################################################################ 67## 68#O NaturalHomomorphismByGenerators( <f>, <s> ) 69## 70## <#GAPDoc Label="NaturalHomomorphismByGenerators"> 71## <ManSection> 72## <Oper Name="NaturalHomomorphismByGenerators" Arg='f, s'/> 73## 74## <Description> 75## returns a mapping from the magma <A>f</A> with <M>n</M> generators to the 76## magma <A>s</A> with <M>n</M> generators, 77## which maps the <M>i</M>-th generator of <A>f</A> to the 78## <M>i</M>-th generator of <A>s</A>. 79## </Description> 80## </ManSection> 81## <#/GAPDoc> 82## 83DeclareOperation("NaturalHomomorphismByGenerators",[IsMagma, IsMagma]); 84