used action act3 to form a crossed module X3

PackageInfo.g

@@ -8,8 +8,8 @@ SetPackageInfo( rec(
 
 PackageName := "XModAlg",
 Subtitle := "Crossed Modules and Cat1-Algebras",
-Version := "1.25",
-Date := "17/05/2024", # dd/mm/yyyy format
+Version := "1.25dev",
+Date := "14/06/2024", # dd/mm/yyyy format
 License := "GPL-2.0-or-later",
 
 Persons := [

doc/xmod.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  xmod.xml            XModAlg documentation               Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2022, Z. Arvasi & A. Odabas,                    --> 
+<!--  Copyright (C) 2014-2024, Z. Arvasi & A. Odabas,                    --> 
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -238,24 +238,7 @@ Crossed module [<e5>->GF(2^2)[k4]] :-
 ]]>
 </Example>
 
-<ManSection>
-   <Oper Name="XModAlgebraByModule"
-         Arg="M R" />
-<Description> 
-Let <M>M</M> be a <M>R</M>-module.  
-Then <M>\mathcal{X} = (0:M\rightarrow R)</M> is a crossed module. 
-Conversely, given a crossed module 
-<M>\mathcal{X} = (\partial :M\rightarrow R)</M>,
-one can get that <M>\ker\partial</M> is a <M>(R/\partial M)</M>-module.
-<P/>
-</Description>
-</ManSection>
-
-<Example>
-<![CDATA[
-gap> ## example needed 
-]]>
-</Example>
+<#Include Label="XModAlgebraByModule">
 
 <ManSection>
    <Attr Name="Source" Label="for crossed modules of commutative algebras"

examples/module3.g

@@ -0,0 +1,70 @@
+############################################################################
+##
+#W  module3.g            XModAlg example files                 Chris Wensley 
+## 
+
+LoadPackage( "xmodalg" );
+
+## Chapter 2, Section 2.2.3
+m := [ [0,1,0], [0,0,1], [1,0,0] ];
+Print( "m = ", m, "\n" );
+A3 := Algebra( Rationals, [m] );
+SetName( A3, "A3" );;
+V3 := Rationals^3;;
+M3 := LeftAlgebraModule( A3, \*, V3 );
+SetName( M3, "M3" );
+famM3 := ElementsFamily( FamilyObj( M3 ) );;
+v := [3,4,5];;
+v2 := ObjByExtRep( famM3, v );
+Print( "v = ", v, ",  v2 = ", v2, "\n" );
+Print( "m*v2 = ", m*v2, "\n" );
+genM3 := GeneratorsOfLeftModule( M3 );;
+u2 := 6*genM3[1] + 7*genM3[2] + 8*genM3[3];
+u := ExtRepOfObj( u2 );
+Print( "u2 = ", u2, ",  u = ", u, "\n" );
+
+## Chapter 2, Section 2.2.4
+D3 := LeftActingDomain( M3 );;
+T3 := EmptySCTable( Dimension(M3), Zero(D3), "symmetric" );;
+B3a := AlgebraByStructureConstants( D3, T3 );
+Print( "B3a = ", B3a, "\n" );
+Print( "B3a has generators: ", GeneratorsOfAlgebra( B3a ), "\n" );
+B3 := ModuleAsAlgebra( M3 );             
+Print( "B3 has name: ", Name( B3 ), "\n" );
+Print( "B3 has generators: ", GeneratorsOfAlgebra( B3 ), "\n" );
+
+## Chapter 2, Section 2.2.5
+Print( "IsModuleAsAlgebra( B3 )? ", IsModuleAsAlgebra( B3 ), "\n" );
+Print( "IsModuleAsAlgebra( A3 )? ", IsModuleAsAlgebra( A3 ), "\n" );
+
+## Chapter 2, Section 2.2.6
+Print( "the known attributes of B3 are:\n" );
+Print( KnownAttributesOfObject( B3 ), "\n" );
+M2B3 := ModuleToAlgebraIsomorphism( B3 );
+Print( "M2B3 = ", M2B3, "\n" );
+Print( "Source( M2B3 ) = M3? ", Source( M2B3 ) = M3, "\n" );
+Print( "Source( M2B3 ) = V3? ", Source( M2B3 ) = V3, "\n" );
+B2M3 := AlgebraToModuleIsomorphism( B3 );
+Print( "B2M3 = ", B2M3, "\n" );
+Print( "Range( B2M3 ) = M3? ", Range( B2M3 ) = M3, "\n" );
+Print( "Range( B2M3 ) = V3? ", Range( B2M3 ) = V3, "\n" );
+
+## Chapter 2, Section 2.2.7
+act3 := AlgebraActionByModule( A3, M3 );
+Print( "the action act3 of A3 on B3 is:\n", act3, "\n" );
+genA3 := GeneratorsOfAlgebra( A3 );;
+a := 2*m + 3*m^2;
+Print( "a = ", a, ":\n" );
+Print( "the image of a under act3 is:\n", Image( act3, a ), "\n" );
+Print( "the image of the action act3 is:\n", Image( act3 ), "\n" );
+Print( "\n" );
+
+## Chapter 4, Section 4.1.7
+X3 := XModAlgebraByModule( A3, M3 );
+Print( "Name( X3 ) = ", Name( X3 ), "\n" );
+Display( X3 );
+
+
+############################################################################
+##
+#E  module3.g . . . . . . . . . . . . . . . . . . . . . . . . . . ends here

lib/alg2obj.gd

@@ -44,8 +44,6 @@ DeclareOperation( "XModAlgebraByBoundaryAndAction",
 DeclareOperation( "XModAlgebraBySurjection", [ IsAlgebraHomomorphism ] );
 DeclareOperation( "XModAlgebraByMultiplierAlgebra", 
     [ IsAlgebra ] );
-DeclareOperation( "XModAlgebraByModule", 
-    [ IsAlgebra, IsRing ] );
 DeclareOperation( "XModAlgebraByIdeal", 
     [ IsAlgebra, IsAlgebra ] ); 
 DeclareAttribute( "AugmentationXMod", IsGroupAlgebra );