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|
#############################################################################
##
#W list.g GAP library Martin Schoenert
##
#H @(#)$Id: list.g,v 4.35.4.2 2006/08/22 09:56:12 gap 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 contains some list types and functions that have to be known
## very early in the bootstrap stage (therefore they are not in list.gi)
##
Revision.list_g :=
"@(#)$Id: list.g,v 4.35.4.2 2006/08/22 09:56:12 gap Exp $";
#############################################################################
##
#C IsListDefault( <list> ) . . . . . . . . methods for arithmetic operations
##
## For a list <list>, `IsListDefault' indicates that the default methods for
## arithmetic operations of lists, such as pointwise addition and
## multiplication as inner product or matrix product,
## shall be applicable to <list>.
##
## `IsListDefault' implies `IsGeneralizedRowVector' and
## `IsMultiplicativeGeneralizedRowVector'.
##
## All internally represented lists are in this category,
## and also all lists in the representations `IsGF2VectorRep',
## `Is8BitVectorRep', `IsGF2MatrixRep', and `Is8BitMatrixRep'
## (see~"Row Vectors over Finite Fields" and "Matrices over Finite Fields").
#T strings and blists:
#T It does not really make sense to have them in `IsGeneralizedRowVector'.
## Note that the result of an arithmetic operation with lists in
## `IsListDefault' will in general be an internally represented list,
## so most ``wrapped list objects'' will not lie in `IsListDefault'.
##
DeclareCategory( "IsListDefault", IsMultiplicativeGeneralizedRowVector );
#T IsListDefault should imply IsAdditiveElement and IsMultiplicativeElement,
#T probably IsGeneralizedRowVector should imply IsAdditiveElement, and
#T IsMultiplicativeGeneralizedRowVector should imply IsMultiplicativeElement.
InstallTrueMethod( IsListDefault, IsInternalRep and IsList );
#############################################################################
##
#P IsRectangularTable( <list> ) . . . . table with all rows the same length
##
## A list lies in `IsRectangularTable' when it is nonempty and its elements
## are all homogeneous lists of the same family and the same length.
##
## This filter is a Property, not a Category, because it is not
## always possible to determine cheaply the length of a row (which
## might be some sort of Enumerator). If the rows are plain lists
## then this property should always be known (the kernel type determination
## for plain lists handles this). Plain lists without mutable
## elements will remember their rectangularity once it is determined.
##
DeclareProperty( "IsRectangularTable", IsList );
InstallTrueMethod( IsTable, IsRectangularTable );
#############################################################################
##
#V TYPE_LIST_NDENSE_MUTABLE . . . . . . . . type of non-dense, mutable list
##
BIND_GLOBAL( "TYPE_LIST_NDENSE_MUTABLE", NewType( ListsFamily,
IsMutable and IsList and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_NDENSE_IMMUTABLE . . . . . . type of non-dense, immutable list
##
BIND_GLOBAL( "TYPE_LIST_NDENSE_IMMUTABLE", NewType( ListsFamily,
IsList and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_DENSE_NHOM_MUTABLE . . . type of dense, non-homo, mutable list
##
BIND_GLOBAL( "TYPE_LIST_DENSE_NHOM_MUTABLE", NewType( ListsFamily,
IsMutable and IsList and IsDenseList and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_DENSE_NHOM_IMMUTABLE . type of dense, non-homo, immutable list
##
BIND_GLOBAL( "TYPE_LIST_DENSE_NHOM_IMMUTABLE", NewType( ListsFamily,
IsList and IsDenseList and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_DENSE_NHOM_SSORT_MUTABLE . . .
## type of dense, non-homo, ssorted, mutable list
##
BIND_GLOBAL( "TYPE_LIST_DENSE_NHOM_SSORT_MUTABLE", NewType( ListsFamily,
IsMutable and IsList and IsDenseList and IsPlistRep and IsSSortedList ) );
#############################################################################
##
#V TYPE_LIST_DENSE_NHOM_NSORT_MUTABLE . . .
## type of dense, non-homo, nsorted, mutable list
##
BIND_GLOBAL( "TYPE_LIST_DENSE_NHOM_NSORT_MUTABLE", NewType( ListsFamily,
IsMutable and IsList and IsDenseList and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_DENSE_NHOM_SSORT_IMMUTABLE .
## type of dense, non-homo, ssorted, immutable list
##
BIND_GLOBAL( "TYPE_LIST_DENSE_NHOM_SSORT_IMMUTABLE", NewType( ListsFamily,
IsList and IsDenseList and IsPlistRep and IsSSortedList ) );
#############################################################################
##
#V TYPE_LIST_DENSE_NHOM_NSORT_IMMUTABLE .
## type of dense, non-homo, nsorted, immutable list
##
BIND_GLOBAL( "TYPE_LIST_DENSE_NHOM_NSORT_IMMUTABLE", NewType( ListsFamily,
IsList and IsDenseList and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_EMPTY_MUTABLE . . . . . . . . . type of the empty, mutable list
##
BIND_GLOBAL( "TYPE_LIST_EMPTY_MUTABLE", NewType( ListsFamily,
IsMutable and IsList and IsDenseList and IsHomogeneousList
and IsEmpty and IsString and IsPlistRep ) );
#############################################################################
##
#V TYPE_LIST_EMPTY_IMMUTABLE . . . . . . . type of the empty, immutable list
##
BIND_GLOBAL( "TYPE_LIST_EMPTY_IMMUTABLE", NewType( ListsFamily,
IsList and IsDenseList and IsHomogeneousList
and IsEmpty and IsString and IsPlistRep ) );
#############################################################################
##
#V TYPE_BLIST_*
##
BIND_GLOBAL( "TYPE_BLIST_MUT",
NewType( CollectionsFamily(BooleanFamily),
IsMutable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP ) );
BIND_GLOBAL( "TYPE_BLIST_IMM",
NewType( CollectionsFamily(BooleanFamily),
IsCopyable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP ) );
BIND_GLOBAL( "TYPE_BLIST_NSORT_MUT",
NewType( CollectionsFamily(BooleanFamily),
IsMutable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP and Tester(IsSSortedList) ) );
BIND_GLOBAL( "TYPE_BLIST_NSORT_IMM",
NewType( CollectionsFamily(BooleanFamily),
IsCopyable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP and Tester(IsSSortedList) ) );
BIND_GLOBAL( "TYPE_BLIST_SSORT_MUT",
NewType( CollectionsFamily(BooleanFamily),
IsMutable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP and Tester(IsSSortedList) and IsSSortedList ) );
BIND_GLOBAL( "TYPE_BLIST_SSORT_IMM",
NewType( CollectionsFamily(BooleanFamily),
IsCopyable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP and Tester(IsSSortedList) and IsSSortedList ) );
BIND_GLOBAL( "TYPE_BLIST_EMPTY_MUT",
NewType( CollectionsFamily(BooleanFamily),
IsMutable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP and IsEmpty and Tester(IsEmpty) ) );
BIND_GLOBAL( "TYPE_BLIST_EMPTY_IMM",
NewType( CollectionsFamily(BooleanFamily),
IsCopyable and IsInternalRep and IsDenseList and IsHomogeneousList and
IS_BLIST_REP and IsEmpty and Tester(IsEmpty) ) );
#############################################################################
##
#F TYPE_LIST_HOM( <family>, <kernel_number> ) . . return the type of a list
##
## For <kernel_number> see "objects.h" and "plist.c":
##
## 1: T_PLIST_HOM
## 2: T_PLIST_HOM + IMMUTABLE
## 3: T_PLIST_HOM_NSORT
## 4: T_PLIST_HOM_NSORT + IMMUTABLE
## 5: T_PLIST_HOM_SSORT
## 6: T_PLIST_HOM_SSORT + IMMUTABLE
## 7: T_PLIST_TAB
## 8: T_PLIST_TAB + IMMUTABLE
## 9: T_PLIST_TAB_NSORT
## 10: T_PLIST_TAB_NSORT + IMMUTABLE
## 11: T_PLIST_TAB_SSORT
## 12: T_PLIST_TAB_SSORT + IMMUTABLE
## 13: T_PLIST_TAB_RECT
## 14: T_PLIST_TAB_RECT + IMMUTABLE
## 15: T_PLIST_TAB_RECT_NSORT
## 16: T_PLIST_TAB_RECT_NSORT + IMMUTABLE
## 17: T_PLIST_TAB_RECT_SSORT
## 18: T_PLIST_TAB_RECT_SSORT + IMMUTABLE
## 19: T_PLIST_CYC
## 20: T_PLIST_CYC + IMMUTABLE
## 21: T_PLIST_CYC_NSORT
## 22: T_PLIST_CYC_NSORT + IMMUTABLE
## 23: T_PLIST_CYC_SSORT
## 24: T_PLIST_CYC_SSORT + IMMUTABLE
## 25: T_PLIST_FFE
## 26: T_PLIST_FFE + IMMUTABLE
##
BIND_GLOBAL( "TYPE_LIST_HOM", function ( family, knr )
local colls;
colls := CollectionsFamily( family );
# The Cyclotomic types behave just like the corresponding
# homogenous types
if knr > 18 then
if knr < 25 then
knr := knr -18;
# The FFE types behave just like the corresponding
# homogenous types
else
knr := knr -24;
fi;
fi;
# T_PLIST_HOM
if knr = 1 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
IsPlistRep );
# T_PLIST_HOM + IMMUTABLE
elif knr = 2 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
IsPlistRep );
# T_PLIST_HOM_NSORT
elif knr = 3 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and
IsPlistRep );
# T_PLIST_HOM_NSORT + IMMUTABLE
elif knr = 4 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and
IsPlistRep );
# T_PLIST_HOM_SSORT
elif knr = 5 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and
IsSSortedList and
IsPlistRep );
# T_PLIST_HOM_SSORT + IMMUTABLE
elif knr = 6 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and
IsSSortedList and
IsPlistRep );
# T_PLIST_TAB
elif knr = 7 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
IsTable and IsPlistRep );
# T_PLIST_TAB + IMMUTABLE
elif knr = 8 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
IsTable and IsPlistRep );
# T_PLIST_TAB_NSORT
elif knr = 9 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsTable
and IsPlistRep );
# T_PLIST_TAB_NSORT + IMMUTABLE
elif knr = 10 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsTable
and IsPlistRep );
# T_PLIST_TAB_SSORT
elif knr = 11 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and
IsSSortedList and IsTable and IsPlistRep );
# T_PLIST_TAB_SSORT + IMMUTABLE
elif knr = 12 then
return NewType( colls,
IsList and IsDenseList and IsHomogeneousList
and Tester(IsSSortedList)
and IsCollection and IsSSortedList and IsTable
and IsPlistRep );
# T_PLIST_TAB_RECT
elif knr = 13 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
IsTable and HasIsRectangularTable and IsRectangularTable and IsPlistRep );
# T_PLIST_TAB_RECT + IMMUTABLE
elif knr = 14 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
IsTable and HasIsRectangularTable and IsRectangularTable and IsPlistRep );
# T_PLIST_TAB_RECT_NSORT
elif knr = 15 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsTable and HasIsRectangularTable and IsRectangularTable
and IsPlistRep );
# T_PLIST_TAB_RECT_NSORT + IMMUTABLE
elif knr = 16 then
return NewType( colls,
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsTable and HasIsRectangularTable and IsRectangularTable
and IsPlistRep );
# T_PLIST_TAB_RECT_SSORT
elif knr = 17 then
return NewType( colls,
IsMutable and IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and
IsSSortedList and IsTable and HasIsRectangularTable and IsRectangularTable and IsPlistRep );
# T_PLIST_TAB_RECT_SSORT + IMMUTABLE
elif knr = 18 then
return NewType( colls,
IsList and IsDenseList and IsHomogeneousList
and Tester(IsSSortedList)
and IsCollection and IsSSortedList and IsTable and HasIsRectangularTable
and IsRectangularTable
and IsPlistRep );
else
Error( "what? Unknown kernel number ", knr );
fi;
end );
#############################################################################
##
#M ASS_LIST( <plist>, <pos>, <obj> ) . . . . . . . . . . default assignment
##
InstallMethod( ASS_LIST,
"for plain list and external objects",
true,
[ IsMutable and IsList and IsPlistRep,
IsPosInt,
IsObject ],
0,
ASS_PLIST_DEFAULT );
#############################################################################
##
#C IsRange( <obj> )
##
## tests if the object <obj> is a range, i.e. is a dense list of integers
## that is also a range (see~"Ranges" for a definition of ``range'').
#T shouldn't this better be a property?
##
#DeclareCategory(IsRange,IsCollection and IsDenseList);
DeclareCategoryKernel( "IsRange",
IsCollection and IsDenseList and IsCyclotomicCollection, IS_RANGE );
#############################################################################
##
#R IsRangeRep( <obj> )
##
## For internally represented ranges, there is a special representation
## which requires only a small amount of memory.
##
DeclareRepresentationKernel( "IsRangeRep",
IsInternalRep, [], IS_OBJECT, IS_RANGE_REP );
#############################################################################
##
#F ConvertToRangeRep( <list> )
##
## For some lists the {\GAP} kernel knows that they are in fact ranges.
## Those lists are represented internally in a compact way instead of the
## ordinary way.
##
## If <list> is a range then `ConvertToRangeRep' changes the representation
## of <list> to this compact representation.
##
## This is important since this representation needs only 12 bytes for
## the entire range while the ordinary representation needs $4 length$
## bytes.
##
## Note that a list that is represented in the ordinary way might still be a
## range.
## It is just that {\GAP} does not know this.
## The following rules tell you under which circumstances a range is
## represented in the compact way,
## so you can write your program in such a way that you make best use of
## this compact representation for ranges.
##
## Lists created by the syntactic construct
## `[ <first>, <second> .. <last> ]' are of course known to be ranges and
## are represented in the compact way.
##
## If you call `ConvertToRangeRep' for a list represented the ordinary way
## that is indeed a range, the representation is changed from the ordinary
## to the compact representation.
## A call of `ConvertToRangeRep' for a list that is not a range is
## ignored.
##
## If you change a mutable range that is represented in the compact way,
## by assignment, `Add' or `Append', the range will be converted to the
## ordinary representation, even if the change is such that the resulting
## list is still a proper range.
##
## Suppose you have built a proper range in such a way that it is
## represented in the ordinary way and that you now want to convert it to
## the compact representation to save space.
## Then you should call `ConvertToRangeRep' with that list as an argument.
## You can think of the call to `ConvertToRangeRep' as a hint to {\GAP}
## that this list is a proper range.
##
BIND_GLOBAL( "ConvertToRangeRep", function( list )
IsRange( list );
end );
#N
#N This must change -- a range is NOT is IS_PLIST_REP
#N
#############################################################################
##
#V TYPE_RANGE_SSORT_MUTABLE . . . . . . . . . type of sorted, mutable range
##
BIND_GLOBAL( "TYPE_RANGE_SSORT_MUTABLE",
NewType(CollectionsFamily(CyclotomicsFamily),
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsRange and IsMutable and
IsSSortedList
and IsRangeRep and IsInternalRep));
#############################################################################
##
#V TYPE_RANGE_NSORT_MUTABLE . . . . . . . . type of unsorted, mutable range
##
BIND_GLOBAL( "TYPE_RANGE_NSORT_MUTABLE",
NewType(CollectionsFamily(CyclotomicsFamily),
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsRange and IsMutable
and IsRangeRep and IsInternalRep));
#############################################################################
##
#V TYPE_RANGE_SSORT_IMMUTABLE . . . . . . . type of sorted, immutable range
##
BIND_GLOBAL( "TYPE_RANGE_SSORT_IMMUTABLE",
NewType(CollectionsFamily(CyclotomicsFamily),
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsRange and
IsSSortedList
and IsRangeRep and IsInternalRep));
#############################################################################
##
#V TYPE_RANGE_NSORT_IMMUTABLE . . . . . . type of unsorted, immutable range
##
BIND_GLOBAL( "TYPE_RANGE_NSORT_IMMUTABLE",
NewType(CollectionsFamily(CyclotomicsFamily),
IsList and IsDenseList and
IsHomogeneousList and IsCollection and
Tester(IsSSortedList) and IsRange
and IsRangeRep and IsInternalRep));
#############################################################################
##
#C IsBlist(<obj>)
##
## A boolean list (``blist'') is a list that has no holes and contains only
## `true' and `false'. If a list is known to be a boolean list by a test
## with `IsBlist' it is stored in a compact form. See "More about Boolean
## Lists".
##
DeclareCategoryKernel( "IsBlist", IsHomogeneousList, IS_BLIST );
#############################################################################
##
#R IsBlistRep( <obj> )
##
DeclareRepresentationKernel( "IsBlistRep",
IsInternalRep, [], IS_OBJECT, IS_BLIST_REP );
#############################################################################
##
#F BlistList(<list>,<sub>)
##
## returns a new boolean list that describes the list <sub> as a sublist of
## the dense list <list>.
## That is `BlistList' returns a boolean list <blist> of the same length as
## <list> such that `<blist>[<i>]' is `true' if `<list>[<i>]' is in
## <sub> and `false' otherwise.
##
## <list> need not be a proper set (see~"Sorted Lists and Sets"),
## even though in this case `BlistList' is most efficient.
## In particular <list> may contain duplicates.
## <sub> need not be a proper sublist of <list>,
## i.e., <sub> may contain elements that are not in <list>.
## Those elements of course have no influence on the result of `BlistList'.
##
DeclareSynonym( "BlistList", BLIST_LIST );
#############################################################################
##
#F UniteBlistList( <list>, <blist>,<sub> )
##
## works like `UniteBlist(<blist>,BlistList(<list>,<sub>))'. As no
## intermediate blist is created, the performance is better than the
## separate function calls.
##
DeclareSynonym( "UniteBlistList", UNITE_BLIST_LIST );
#############################################################################
##
#O ListBlist(<list>,<blist>)
##
## returns the sublist <sub> of the list <list>, which must have no holes,
## represented by the boolean list <blist>, which must have the same
## length as <list>. <sub> contains the element `<list>[<i>]' if
## `<blist>[<i>]' is `true' and does not contain the element
## if `<blist>[<i>]' is `false'. The order of the elements in <sub> is
## the same as the order of the corresponding elements in <list>.
##
DeclareSynonym( "ListBlist", LIST_BLIST );
#############################################################################
##
#F SizeBlist(<blist>)
##
## returns the number of entries of the boolean list <blist> that are
## `true'. This is the size of the subset represented by the boolean
## list <blist>.
##
DeclareSynonym( "SizeBlist", SIZE_BLIST );
#############################################################################
##
#F IsSubsetBlist(<blist1>,<blist2>)
##
## returns `true' if the boolean list <blist2> is a subset of the boolean
## list <list1>, which must have equal length, and `false' otherwise.
## <blist2> is a subset of <blist1> if `<blist1>[<i>] =
## <blist1>[<i>] or <blist2>[<i>]' for all <i>.
##
DeclareSynonym( "IsSubsetBlist", IS_SUB_BLIST );
#############################################################################
##
#F UniteBlist( <blist1>, <blist2> )
##
## `UniteBlist' unites the boolean list <blist1> with the boolean
## list <blist2>, which must have the same length. This is
## equivalent to assigning `<blist1>[<i>] := <blist1>[<i>] or
## <blist2>[<i>]' for all <i>. `UniteBlist' returns nothing, it is only
## called to change <blist1>.
##
DeclareSynonym( "UniteBlist", UNITE_BLIST );
#############################################################################
##
#F IntersectBlist( <blist1>, <blist2> )
##
## intersects the boolean list <blist1> with the boolean list <blist2>,
## which must have the same length. This is equivalent to assigning
## `<blist1>[<i>]:= <blist1>[<i>] and <blist2>[<i>]' for all <i>.
## `IntersectBlist' returns nothing, it is only called to change <blist1>.
##
DeclareSynonym( "IntersectBlist", INTER_BLIST );
#############################################################################
##
#F SubtractBlist( <blist1>, <blist2> )
##
## subtracts the boolean list <blist2> from the boolean list <blist1>,
## which must have equal length. This is equivalent to assigning
## `<blist1>[<i>] := <blist1>[<i>] and not <blist2>[<i>]' for all
## <i>. `SubtractBlist' returns nothing, it is only called to change
## <blist1>.
##
DeclareSynonym( "SubtractBlist", SUBTR_BLIST );
#############################################################################
##
#E list.g . . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
##
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