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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
# represent vectors/matrices over Z/nZ by nonnegative integer lists
# in the range [0..n-1], but reduce after
# arithmetic. This way avoid always wrapping all entries separately
#############################################################################
##
#R IsZmodnZVectorRep( <obj> )
##
## <#GAPDoc Label="IsZmodnZVectorRep">
## <ManSection>
## <Filt Name="IsZmodnZVectorRep" Arg='obj' Type='Representation'/>
##
## <Description>
## An object <A>obj</A> in <Ref Filt="IsZmodnZVectorRep"/> describes
## a vector object (see <Ref Filt="IsVectorObj"/>) with entries in a
## residue class ring of the ring of integers (see <Ref Func="ZmodnZ"/>).
## This ring is the base domain
## (see <Ref Attr="BaseDomain" Label="for a vector object"/>)
## of <A>obj</A>.
## <P/>
## <Ref Filt="IsZmodnZVectorRep"/> implies <Ref Filt="IsCopyable"/>,
## thus matrix objects in this representation can be mutable.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
## <A>obj</A> is internally represented as a positional object
## (see <Ref Filt="IsPositionalObjectRep"/>) which stores the base domain
## (see <Ref Attr="BaseDomain" Label="for a vector object"/>)
## at position <M>1</M> and a plain list of integers at position <M>2</M>.
##
DeclareRepresentation( "IsZmodnZVectorRep",
IsVectorObj and IsPositionalObjectRep
and IsCopyable
and IsNoImmediateMethodsObject
and HasBaseDomain and HasOneOfBaseDomain and HasZeroOfBaseDomain,
[] );
#############################################################################
##
#R IsZmodnZMatrixRep( <obj> )
##
## <#GAPDoc Label="IsZmodnZMatrixRep">
## <ManSection>
## <Filt Name="IsZmodnZMatrixRep" Arg='obj' Type='Representation'/>
##
## <Description>
## An object <A>obj</A> in <Ref Filt="IsZmodnZMatrixRep"/> describes
## a matrix object (see <Ref Filt="IsMatrixObj"/>) that behaves like the
## list of its rows (see <Ref Filt="IsRowListMatrix"/>).
## The matrix entries lie in a residue class ring of the ring of integers
## (see <Ref Func="ZmodnZ"/>).
## This ring is the base domain
## (see <Ref Attr="BaseDomain" Label="for a vector object"/>)
## of <A>obj</A>.
## <P/>
## <Ref Filt="IsZmodnZMatrixRep"/> implies <Ref Filt="IsCopyable"/>,
## thus matrix objects in this representation can be mutable.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
## <A>obj</A> is internally represented as a positional object
## (see <Ref Filt="IsPositionalObjectRep"/>) with <M>4</M> entries.
## <Enum>
## <Item>
## its base domain
## (see <Ref Attr="BaseDomain" Label="for a matrix object"/>),
## </Item>
## <Item>
## an empty vector in the representation of each row,
## </Item>
## <Item>
## the number of columns
## (see <Ref Attr="NumberColumns" Label="for a matrix object"/>), and
## </Item>
## <Item>
## a plain list (see <Ref Filt="IsPlistRep"/> of its rows,
## each of them being an object in <Ref Filt="IsZmodnZVectorRep"/>.
## </Item>
## </Enum>
##
DeclareRepresentation( "IsZmodnZMatrixRep",
IsRowListMatrix and IsPositionalObjectRep
and IsCopyable
and IsNoImmediateMethodsObject
and HasNumberRows and HasNumberColumns
and HasBaseDomain and HasOneOfBaseDomain and HasZeroOfBaseDomain,
[] );
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