Matrix object type: upper triangular matrices

lib/matobjtriangularmatrices.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 nxn triangular matrices 
+ # stored as a flat element list. In this 
+ # file the representation, types and global 
+ # functions are declared.
+
+
+ #############################################################################
+ ##
+ ##  <#GAPDoc Label="IsUpperTriangularMatrixRep">
+ ##  <ManSection>
+ ##  <Filt Name="IsUpperTriangularMatrixRep" Arg='obj' Type="representation"/>
+ ##
+ ##  <Description>
+ ##  An object <A>obj</A> in <Ref Filt="IsUpperTriangularMatrixRep"/> describes
+ ##  a matrix object that stores the matrix entries as a flat list of an
+ ##  upper triangular matrix, i.e. obj[i,j] = 0 for j < i. 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. IsUpperTriangularMatrixRep e.g. are positional objects and so on.
+ DeclareRepresentation( "IsUpperTriangularMatrixRep",
+         IsMatrixObj and IsMatrixOrMatrixObj and IsPositionalObjectRep
+     and IsNoImmediateMethodsObject
+     and HasNumberRows and HasNumberColumns
+     and HasBaseDomain and HasOneOfBaseDomain and HasZeroOfBaseDomain,
+     [] );
+
+ # If we implement our object as 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
+ BindConstant( "UPPERTRIANGULARMATREP_BDPOS", 1 );
+ # Position in the positional object of the number of rows and columns
+ BindConstant( "UPPERTRIANGULARMATREP_NRPOS", 2 );
+ # Position in the positional object of the list of entries
+ BindConstant( "UPPERTRIANGULARMATREP_ELSPOS", 3 );