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#############################################################################
##
#W ringsc.gd GAP library Alexander Hulpke
##
##
#Y Copyright (C) 2008 The GAP Group
##
## This file contains declarations for elements of rings, given as Z-modules
## with structure constants for multiplication. Is is based on algsc.gd
##
#############################################################################
##
#C IsSCRingObj( <obj> )
#C IsSCRingObjCollection( <obj> )
#C IsSCRingObjFamily( <obj> )
##
## S.~c. ring elements may have inverses, in order to allow `One' and
## `Inverse' we make them scalars.
##
DeclareCategory( "IsSCRingObj", IsScalar );
DeclareCategoryCollections( "IsSCRingObj" );
DeclareCategoryCollections( "IsSCRingObjCollection" );
DeclareCategoryCollections( "IsSCRingObjCollColl" );
DeclareCategoryFamily( "IsSCRingObj" );
DeclareSynonym("IsSubringSCRing",IsRing and IsSCRingObjCollection);
#############################################################################
##
#F RingByStructureConstants( <moduli>, <sctable>[, <nameinfo>] )
##
## <#GAPDoc Label="RingByStructureConstants">
## <ManSection>
## <Func Name="RingByStructureConstants" Arg='moduli, sctable[, nameinfo]'/>
##
## <Description>
## returns a ring <M>R</M> whose additive group is described by the list
## <A>moduli</A>,
## with multiplication defined by the structure constants table
## <A>sctable</A>.
## The optional argument <A>nameinfo</A> can be used to prescribe names for
## the elements of the canonical generators of <M>R</M>;
## it can be either a string <A>name</A>
## (then <A>name</A><C>1</C>, <A>name</A><C>2</C> etc. are chosen)
## or a list of strings which are then chosen.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "RingByStructureConstants" );
#############################################################################
##
#F StandardGeneratorsSubringSCRing( <S> )
##
## for a subring <S> of an SC ring <R> this command returns a list of length 3.
## The first entry are generators for <S> as addive group, given with
## respect to the additive group basis for <R> and being in hermite normal
## form. The second entries are pivot positions for these generators. The third
## entry are the generators as actual ring elements.
DeclareAttribute("StandardGeneratorsSubringSCRing",IsSubringSCRing);
#############################################################################
##
#A Subrings( <R> )
##
## for a finite ring <R> this function returns a list of all subrings of <R>.
DeclareAttribute("Subrings",IsRing);
#############################################################################
##
#A Ideals( <R> )
##
## for a finite ring <R> this function returns a list of all ideals of <R>.
DeclareAttribute("Ideals",IsRing);
#############################################################################
##
#F NumberSmallRings( <s> )
##
## returns the number of (nonisomorphic) rings of order <s> stored in the
## library of small rings.
DeclareGlobalFunction("NumberSmallRings");
#############################################################################
##
#F SmallRing( <s>,<n> )
##
## returns the <n>-th ring of order <s> from a library of rings of small
## order (up to isomorphism).
DeclareGlobalFunction("SmallRing");
#############################################################################
##
#F DirectSum( <R>{, <S>} )
#O DirectSumOp( <list>, <expl> )
##
## <#GAPDoc Label="DirectSum">
## <ManSection>
## <Func Name="DirectSum" Arg='R{, S}'/>
## <Oper Name="DirectSumOp" Arg='list, expl'/>
##
## <Description>
## These functions construct the direct sum of the rings given as
## arguments.
## <C>DirectSum</C> takes an arbitrary positive number of arguments
## and calls the operation <C>DirectSumOp</C>, which takes exactly two
## arguments, namely a nonempty list of rings and one of these rings.
## (This somewhat strange syntax allows the method selection to choose
## a reasonable method for special cases.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "DirectSum" );
DeclareOperation( "DirectSumOp", [ IsList, IsRing ] );
DeclareAttribute( "DirectSumInfo", IsGroup, "mutable" );
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