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
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
|
#############################################################################
##
#W tuples.gd GAP library Steve Linton
##
#H @(#)$Id: tuples.gd,v 4.18 2002/04/15 10:05:25 sal Exp $
##
#Y Copyright (C) 1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file declares the operations for tuples.
##
## Tuples are immutable finite type-safe lists.
##
Revision.tuples_gd :=
"@(#)$Id: tuples.gd,v 4.18 2002/04/15 10:05:25 sal Exp $";
#############################################################################
##
#C IsTuple( <obj> ) . . . . . . . . . . . . . . . . . . category of tuples
##
## `IsTuple' is a subcategory of the meet of `IsDenseList'
## (see~"IsDenseList"), `IsMultiplicativeElementWithInverse'
## (see~"IsMultiplicativeElementWithInverse"),
## and `IsAdditiveElementWithInverse' (see~"IsAdditiveElementWithInverse"),
#T and `IsCopyable' (see~"Mutability and Copyability"),
## where the arithmetic operations (addition, zero, additive inverse,
## multiplication, powering, one, inverse) are defined componentwise.
##
## Note that each of these operations will cause an error message if
## its result for at least one component cannot be formed.
##
#T For a tuple, `ShallowCopy' returns a mutable plain list with the same
#T entries.
## The sum and the product of a tuple and a list in `IsListDefault' is the
## list of sums and products, respectively.
## The sum and the product of a tuple and a non-list is the tuple of
## componentwise sums and products, respectively.
##
DeclareCategory( "IsTuple",
IsDenseList
and IsCopyable
and IsMultiplicativeElementWithInverse
and IsAdditiveElementWithInverse );
#############################################################################
##
#C IsTupleFamily( <family> ) . . . . . . . . . . category of tuples families
##
DeclareCategoryFamily( "IsTuple" );
#############################################################################
##
#C IsTupleCollection( <coll> ) . . . . . . category of tuples collections
##
DeclareCategoryCollections( "IsTuple" );
#############################################################################
##
#O TuplesFamily ( <famlist> ) . . . . . . . . family of tuples of elements
##
DeclareOperation( "TuplesFamily", [ IsCollection ] );
#############################################################################
##
#A ComponentsOfTuplesFamily( <tuplesfam> ) . . . . . . . component families
##
DeclareAttribute( "ComponentsOfTuplesFamily", IsTupleFamily );
#############################################################################
##
#V TUPLES_FAMILIES . . . . . . . . . . . all tuples families so far created
##
## `TUPLES_FAMILIES' is a list whose $i$-th component is a weak pointer
## object containing all currently known $i+1$ component tuples families.
##
DeclareGlobalVariable( "TUPLES_FAMILIES",
"list, at position i the list of known i+1 component tuples families" );
#############################################################################
##
#O Tuple ( <objlist> ) . . . . . . . . . . . . basic tuple making operation
#O Tuple ( <tuplesfam>, <objlist> ) . . . alternate form if family is known
##
## methods of this type have to be OtherMethods
##
#O TupleNC ( <tuplesfam>, <objlist> ) . . . omits check on object families
## and objlist length
DeclareOperation( "Tuple", [ IsList ]);
DeclareOperation( "TupleNC", [ IsTupleFamily, IsList ]);
#############################################################################
##
#E
|
