1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
|
#############################################################################
##
#W addgphom.gi GAP library Scott Murray
#W Alexander Hulpke
##
##
#Y (C) 2000 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains declarations for mappings between groups and additive
## groups.
##
#############################################################################
##
#F GroupToAdditiveGroupHomomorphismByFunction( <S>, <R>, <fun> )
#F GroupToAdditiveGroupHomomorphismByFunction( <S>, <R>, <fun>, <invfun> )
##
InstallGlobalFunction(GroupToAdditiveGroupHomomorphismByFunction,function(arg)
local map;
# no inverse function given
if Length(arg) = 3 then
# make the general mapping
map:= Objectify(
NewType(GeneralMappingsFamily(ElementsFamily(FamilyObj(arg[1])),
ElementsFamily(FamilyObj(arg[2]))),
IsSPMappingByFunctionRep
and IsSingleValued
and IsTotal
and IsGroupToAdditiveGroupHomomorphism ),
rec( fun:= arg[3] ) );
# inverse function given
elif Length(arg) = 4 then
# make the mapping
map:= Objectify(
NewType(GeneralMappingsFamily(ElementsFamily(FamilyObj(arg[1])),
ElementsFamily(FamilyObj(arg[2]))),
IsSPMappingByFunctionWithInverseRep
and IsBijective
and IsGroupToAdditiveGroupHomomorphism ),
rec( fun := arg[3],
invFun := arg[4] ) );
# otherwise signal an error
else
Error(
"usage: GroupToAdditiveGroupHomomorphismByFunction(<D>,<E>,<fun>[, <inv>])");
fi;
SetSource(map,arg[1]);
SetRange(map,arg[2]);
# return the mapping
return map;
end );
#############################################################################
##
#E
|
