Implement a new matrix object using flat lists in row-major form

lib/matobjflist.gd

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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.
+##
+
+############################################################################
+#
+# This is an implementation for nxm matrices 
+# stored as a flat n*m element list. In this 
+# file the representation, types and global 
+# functions are declared.
+
+
+#############################################################################
+##
+##  <#GAPDoc Label="IsFlistMatrixRep">
+##  <ManSection>
+##  <Filt Name="IsFlistMatrixRep" Arg='obj' Type="representation"/>
+##
+##  <Description>
+##  An object <A>obj</A> in <Ref Filt="IsFlistMatrixRep"/> describes
+##  a matrix object that stores the matrix entries as a flat list. It is 
+##  internally represented as a positional object
+##  (see <Ref Filt="IsPositionalObjectRep"/> that stores 4 entries:
+##  <Enum>
+##  <Item>
+##    its base domain
+##    (see <Ref Attr="BaseDomain" Label="for a matrix object"/>),
+##  </Item>
+##  <Item>
+##    the number of rows (see <Ref Attr="NumberRows" Label="for a matrix object"/>), 
+##  </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 entries.
+##  </Item>
+##  </Enum>
+##  </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+# Here we declare the new representation and tell GAP which properties it
+# implies. FListMatrices e.g. are positional objects and so on.
+DeclareRepresentation( "IsFlistMatrixRep",
+        IsMatrixObj and IsMatrixOrMatrixObj and IsPositionalObjectRep
+    and IsNoImmediateMethodsObject
+    and HasNumberRows and HasNumberColumns
+    and HasBaseDomain and HasOneOfBaseDomain and HasZeroOfBaseDomain,
+    [] );
+
+# If we implement our object a a positional object we often have to access its
+# properties in the code. To make that more readable we declare global
+# variables. If you do this too make sure you use variables that are unique and
+# unlikely to be used someplace else, even though that might mean using longer
+# names. Here we prefixed the names with the name of the representation. See
+# also Reference Manual Chapter 79 for more information about Objects.
+
+# Some constants for matrix access:
+# Position in the positional object of the base domain
+BindGlobal( "FLISTREP_BDPOS", 1 );
+# Position in the positional object of the number of rows
+BindGlobal( "FLISTREP_NRPOS", 2 );
+# Position in the positional object of the number of columns
+BindGlobal( "FLISTREP_NCPOS", 3 );
+# Position in the positional object of the list of entries
+BindGlobal( "FLISTREP_ELSPOS", 4 );