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#############################################################################
##
#W tuples.gd GAP library Steve Linton
##
##
#Y Copyright (C) 1997, Lehrstuhl D für 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 direct product elements.
##
## Direct product elements are immutable finite type-safe lists.
##
#############################################################################
##
#V InfoDirectProductElements . . . . . . . . . . . . . . . . . . Info Class
##
DeclareInfoClass( "InfoDirectProductElements" );
#############################################################################
##
#C IsDirectProductElement( <obj> ) . . category of direct product elements
##
## <#GAPDoc Label="IsDirectProductElement">
## <ManSection>
## <Filt Name="IsDirectProductElement" Arg='obj' Type='Category'/>
##
## <Description>
## <Ref Func="IsDirectProductElement"/> is a subcategory of the meet of
## <Ref Func="IsDenseList"/>,
## <Ref Func="IsMultiplicativeElementWithInverse"/>,
## <Ref Func="IsAdditiveElementWithInverse"/>,
## and <Ref Func="IsCopyable"/>,
## where the arithmetic operations (addition, zero, additive inverse,
## multiplication, powering, one, inverse) are defined componentwise.
## <P/>
## Note that each of these operations will cause an error message if
## its result for at least one component cannot be formed.
## <P/>
## For an object in the filter <Ref Func="IsDirectProductElement"/>,
## <Ref Func="ShallowCopy"/> returns a mutable plain list with the same
## entries.
## The sum and the product of a direct product element and a list in
## <Ref Func="IsListDefault"/> is the list of sums and products,
## respectively.
## The sum and the product of a direct product element and a non-list
## is the direct product element of componentwise sums and products,
## respectively.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsDirectProductElement",
IsDenseList
and IsCopyable
and IsMultiplicativeElementWithInverse
and IsAdditiveElementWithInverse );
#############################################################################
##
#C IsDirectProductElementFamily( <family> ) . . . category of direct product
#C element families
##
## <ManSection>
## <Filt Name="IsDirectProductElementFamily" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategoryFamily( "IsDirectProductElement" );
#############################################################################
##
#C IsDirectProductElementCollection( <coll> ) . category of direct product
#C element collections
##
## <ManSection>
## <Filt Name="IsDirectProductElementCollection" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategoryCollections( "IsDirectProductElement" );
#############################################################################
##
#O DirectProductElementsFamily( <famlist> ) . . . . family of direct product
#O elements
##
## <ManSection>
## <Oper Name="DirectProductElementsFamily" Arg='famlist'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation( "DirectProductElementsFamily", [ IsCollection ] );
#############################################################################
##
#A ComponentsOfDirectProductElementsFamily( <fam> ) . . component families
##
## <ManSection>
## <Attr Name="ComponentsOfDirectProductElementsFamily" Arg='fam'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareAttribute( "ComponentsOfDirectProductElementsFamily",
IsDirectProductElementFamily );
#############################################################################
##
#R IsDefaultDirectProductElementRep( <obj> ) . . . . . representation as a
#R component object
##
DeclareRepresentation( "IsDefaultDirectProductElementRep",
IsPositionalObjectRep and IsDirectProductElement, [] );
#############################################################################
##
#V EmptyDirectProductElementsFamily
##
BindGlobal( "EmptyDirectProductElementsFamily",
NewFamily( "DirectProductElementsFamily([])", IsDirectProductElement,
IsDirectProductElement ) );
#############################################################################
##
#V DIRECT_PRODUCT_ELEMENT_FAMILIES . . . all direct product element families
#V so far created
##
## <ManSection>
## <Var Name="DIRECT_PRODUCT_ELEMENT_FAMILIES"/>
##
## <Description>
## <Ref Var="DIRECT_PRODUCT_ELEMENT_FAMILIES"/> is a list whose <M>i</M>-th
## component is a weak pointer object containing all currently known
## families of <M>i+1</M> component direct product elements.
## </Description>
## </ManSection>
##
DeclareGlobalVariable( "DIRECT_PRODUCT_ELEMENT_FAMILIES",
"list, at position i the list of known i+1 component \
direct product elements families" );
#############################################################################
##
#O DirectProductElement( [<fam>, ]<objlist> )
#O DirectProductElementNC( <fam>, <objlist> ) . . . . omits check on object
#O families and objlist length
##
## <ManSection>
## <Oper Name="DirectProductElement" Arg='[fam, ]objlist'/>
## <Oper Name="DirectProductElementNC" Arg='fam, objlist'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation( "DirectProductElement", [ IsList ]);
DeclareOperation( "DirectProductElementNC",
[ IsDirectProductElementFamily, IsList ]);
#############################################################################
##
#E
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