Issue77

CHANGES.md

@@ -1,5 +1,10 @@
 # CHANGES to the 'XModAlg' package
 
+## 1.27 -> 1.28 (31/01/25) 
+ * (31/01/25) removed all operations involving direct sums of crossed modules
+              of algebras because the theoretical basis needs checking;
+              added Nizar Shammu's thesis to the list of references
+
 ## 1.26 -> 1.27 (26/10/24) 
  * (21/10/24) removed references to "Type2" and "XModAlgebraConst"
               tests now use local variables and are mirrored in /examples

PackageInfo.g

@@ -8,8 +8,8 @@ SetPackageInfo( rec(
 
 PackageName := "XModAlg",
 Subtitle := "Crossed Modules and Cat1-Algebras",
-Version := "1.27dev",
-Date := "03/01/2025", # dd/mm/yyyy format
+Version := "1.28",
+Date := "31/01/2025", # dd/mm/yyyy format
 License := "GPL-2.0-or-later",
 
 Persons := [

README.md

@@ -16,7 +16,7 @@ This package allows for computation with crossed modules of commutative algebras
 
 ## Copyright
 
-The 'XModAlg' package is Copyright © Zekeriya Arvasi and Alper Odabas et al, 2014--2022. 
+The 'XModAlg' package is Copyright © Zekeriya Arvasi and Alper Odabas et al, 2014--2025. 
 
 'XModAlg' is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by

doc/algebra.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  algebra.xml           XModAlg documentation             Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2024, Z. Arvasi & A. Odabas,                    -->
+<!--  Copyright (C) 2014-2025, Z. Arvasi & A. Odabas,                    -->
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -353,12 +353,6 @@ gap> [ Image(b2,m2)=m2^3, b2=b1^2 ];
 
 <#Include Label="EmbeddingForDirectSumOfAlgebras">
 
-<#Include Label="DirectSumOfAlgebraHomomorphisms">
-
-<#Include Label="AlgebraActionOnDirectSum">
-
-<#Include Label="DirectSumOfAlgebraActions">
-
 </Section>
 
 <Section>

doc/bib.xml

@@ -185,6 +185,15 @@
   <school>Osmangazi University, Eskisehir</school> 
 </phdthesis></entry>
 
+<entry id="shammu1"><phdthesis> 
+  <author> 
+    <name><first>N. M.</first><last>Shammu</last></name> 
+  </author>
+  <title>Algebraic and categorical structure of categories of crossed modules of algebras</title> 
+  <year>1992</year> 
+  <school>University of Wales, Bangor (U.K.)</school> 
+</phdthesis></entry>
+
 <entry id="porter1"><article>
   <author> 
     <name><first>T.</first><last>Porter</last></name> 

doc/cat1.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  cat1.xml            XModAlg documentation               Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2024, Z. Arvasi & A. Odabas,                    --> 
+<!--  Copyright (C) 2014-2025, Z. Arvasi & A. Odabas,                    --> 
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->

doc/convert.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  convert.xml          XModAlg documentation              Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2024, Z. Arvasi & A. Odabas,                    --> 
+<!--  Copyright (C) 2014-2025, Z. Arvasi & A. Odabas,                    --> 
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->

doc/intro.xml

@@ -18,12 +18,14 @@
 In 1950 S. MacLane and J.H.C. Whitehead, <Cite Key="whitehead"/>
 suggested that crossed modules modeled homotopy <M>2</M>-types. 
 Later crossed modules have been considered as 
-<M>2</M><E>-dimensional groups</E>, <Cite Key="brown1"/>, <Cite Key="brown2"/>. 
+<M>2</M><E>-dimensional groups</E>, <Cite Key="brown1"/>, 
+<Cite Key="brown2"/>. 
 The commutative algebra version of this construction has been adapted by 
 T. Porter, <Cite Key="arvasi2"/>, <Cite Key="porter1"/>. 
 This algebraic version is called <E>combinatorial algebra theory</E>, 
 which contains potentially important new ideas 
-(see <Cite Key="arvasi2"/>, <Cite Key="arvasi3"/>, <Cite Key="arvasi4"/>).
+(see <Cite Key="shammu1"/>, <Cite Key="arvasi2"/>, <Cite Key="arvasi3"/>,
+<Cite Key="arvasi4"/>).
 <P/>
 A share package <Package>XMod</Package>, <Cite Key="alp3"/>, 
 <Cite Key="alp2"/>, was prepared by 

doc/xmod.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  xmod.xml            XModAlg documentation               Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2024, Z. Arvasi & A. Odabas,                    --> 
+<!--  Copyright (C) 2014-2025, Z. Arvasi & A. Odabas,                    --> 
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -262,8 +262,6 @@ Crossed module [A2->Q2] :-
 
 <#Include Label="XModAlgebraByModule">
 
-<#Include Label="DirectSumOfXModAlgebras">
-
 
 <ManSection>
    <Oper Name="SubXModAlgebra"

examples/convert.g

@@ -45,6 +45,8 @@ Cn := Cat1AlgebraOfXModAlgebra( Xn );
 Print( "Cn = Cat1AlgebraOfXModAlgebra( Xn ): ", Cn, "\n" );
 Display( Cn );
 
+bdy3 := AlgebraHomomorphismByImages( Rc3, A3, [ g3 ], [ m3 ] );;
+X3 := XModAlgebraByBoundaryAndAction( bdy3, actg3 );;
 C3 := Cat1AlgebraOfXModAlgebra( X3 );
 Print( "\nC3 = Cat1AlgebraOfXModAlgebra( X3 ): ", C3, "\n" );
 Display( C3 );                 

examples/module.g

@@ -20,12 +20,10 @@ homg3 := AlgebraHomomorphismByImages( A3, Amg3, [ m3 ], [ mg3 ] );;
 actg3 := AlgebraActionByHomomorphism( homg3, Rc3 );
 Print ( "action actg3 of A3 on Rc3:\n", actg3, "\n" );
 
-## Section 4.1.6
-bdy3 := AlgebraHomomorphismByImages( Rc3, A3, [ g3 ], [ m3 ] );
-Print( "bdy3 = ", bdy3, "\n" );
+## Section 4.1.7
+homg3 := AlgebraHomomorphismByImages( A3, Amg3, [ m3 ], [ mg3 ] );
+bdy3 := AlgebraHomomorphismByImages( Rc3, A3, [g3 ], [m3 ] );
 X3 := XModAlgebraByBoundaryAndAction( bdy3, actg3 );
-Print( "crossed module X3:\n" );
-Display( X3 );
 
 ## Section 2.3
 m3 := [ [0,1,0], [0,0,1], [1,0,0] ];;
@@ -81,49 +79,14 @@ Print( "the image of a3 under act3 is:\n", Image( act3, a3 ), "\n" );
 Print( "the image of the action act3 is:\n", Image( act3 ), "\n" );
 Print( "\n" );
 
-## Section 4.1.7
-X4 := XModAlgebraByModule( A3, M3 );
-Print( "Name( X4 ) = ", Name( X4 ), "\n" );
-Display( X4 );
-
-## Section 5.1.1
-C4 := Cat1AlgebraOfXModAlgebra( X4 );
-Print( "Name( C4 ) = ", Name( C4 ), "\n" );
-Display( C4 );
-
 ## Section 2.4.1
-A3Rc3 := DirectSumOfAlgebras( A3, Rc3 );;
-SetName( A3Rc3, Concatenation( Name(A3), "(+)", Name(Rc3) ) );
-SetDirectSumOfAlgebrasInfo( A3Rc3, 
-  rec( algebras := [A3,Rc3], first := [1,Dimension(A3)+1],
-       embeddings := [ ], projections := [ ] ) );;
+A3Rc3 := DirectSumOfAlgebrasWithInfo( A3, Rc3 );
+Print( "A3Rc3 has name: ", Name( A3Rc3 ), "\n" );
 
 ## Section 2.4.2
-Print( "\n first embedding into A3Rc3:\n", Embedding( A3Rc3, 1 ), "\n" );
-Print( "second projection from A3Rc3:\n", Projection( A3Rc3, 2 ), "\n" );
-
-## Section 2.4.3
-hom33 := DirectSumOfAlgebraHomomorphisms( homg3, homg3 );
-Print( "\nthe direct sum of homg3 with itself is:\n", hom33, "\n" );
-
-## Section 2.4.4
-actMA3 := AlgebraActionByMultipliers( A3, A3, A3 );;
-act4 := AlgebraActionOnDirectSum( actMA3, actg3 );;
-Print( "\naction of A on the direct sum of A3 and Rc3\n", act4, "\n" );
-
-## Section 2.4.5
-act5 := DirectSumOfAlgebraActions( actg3, act3 );;
-A5 := Source( act5 );
-B5 := AlgebraActedOn( act5 );
-Print( "\nact5 is the direct sum action of ", A5, " on ", B5, "\n" );
-em3 := ImageElm( Embedding( A5, 1 ), m3 ); 
-Print( "matrix m3 embeds in A5 as: ", em3, "\n" );
-iem3 := ImageElm( act5, em3 );                     
-Print( "the action act5 maps em3 to:\n", iem3, "\n" );
-ea3 := ImageElm( Embedding( A5, 2 ), a3 );
-Print( "element a3 embeds in A5 as: ", ea3, "\n" );
-iea3 := ImageElm( act5, ea3 );
-Print( "the action act5 maps ea3 to:\n", iea3, "\n" );
+info := DirectSumOfAlgebrasInfo( A3Rc3 );;
+Print( "first embedding into A3Rc3:\n", info.embeddings[1], "\n" );
+Print( "second projection from A3Rc3:\n", info.projections[2], "\n" );
 
 ############################################################################
 ##

examples/readall.g

@@ -1,16 +1,21 @@
 #############################################################################
 ##
-#W  readall.g                 The XMODALG package           Zekeriya Arvasi
-#W                                                             & Alper Odabas
-##  version 1.12, 10/11/2015 
+#W  readall.g                 The XMODALG package            Zekeriya Arvasi
+#W                                                            & Alper Odabas
 ##
-#Y  Copyright (C) 2014-2015, Zekeriya Arvasi & Alper Odabas,  
+#Y  Copyright (C) 2014-2025, Zekeriya Arvasi & Alper Odabas,  
 ##
 
 LoadPackage( "xmodalg", false ); 
+
 xmodalg_examples_dir := DirectoriesPackageLibrary( "xmodalg", "examples" ); 
 
+Read( Filename( xmodalg_examples_dir, "algebra.g" ) ); 
+Read( Filename( xmodalg_examples_dir, "module.g" ) ); 
 Read( Filename( xmodalg_examples_dir, "xmod.g" ) ); 
+Read( Filename( xmodalg_examples_dir, "xmod-more.g" ) ); 
 Read( Filename( xmodalg_examples_dir, "cat1.g" ) ); 
+Read( Filename( xmodalg_examples_dir, "cat1-more.g" ) ); 
+Read( Filename( xmodalg_examples_dir, "convert.g" ) ); 
 
 

examples/xmod.g

@@ -103,11 +103,6 @@ Print( "XModAlgebraAction( Y3 ) = act3? ",
        Image( XModAlgebraAction( Y3 ), m3 ) = Image( act3, m3 ), "\n" );
 Display( Y3 );
 
-############################
-## Section 4.1.9
-XY3 := DirectSumOfXModAlgebras( X3, Y3 );
-Print( "XY3 = DirectSumOfXModAlgebras( X3, Y3 ): ", XY3, "\n" );
-
 ############################
 ## Section 4.1.10
 e4 := Elements( IAk4 )[4];