Dsum

.gitignore

@@ -21,7 +21,6 @@
 /doc/*.toc
 
 /doc/title.xml
-/doc/xmodalg.xml
 /doc/XModAlg.xml
 /doc/manual.pdf
 /doc/bib.xml.bib

doc/algebra.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  algebra.xml           XModAlg documentation             Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2025, Z. Arvasi & A. Odabas,                    -->
+<!--  Copyright (C) 2014-2026, Z. Arvasi & A. Odabas,                    -->
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -339,6 +339,12 @@ gap> [ Image(b2,m2)=m2^3, b2=b1^2 ];
 
 <#Include Label="EmbeddingForDirectSumOfAlgebras">
 
+<#Include Label="DirectSumOfAlgebraHomomorphisms">
+
+<#Include Label="AlgebraActionOnDirectSum">
+
+<#Include Label="DirectSumOfAlgebraActions">
+
 </Section>
 
 <Section>

doc/xmod.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  xmod.xml            XModAlg documentation               Z. Arvasi  -->
 <!--                                                        & A. Odabas  -->
-<!--  Copyright (C) 2014-2025, Z. Arvasi & A. Odabas,                    --> 
+<!--  Copyright (C) 2014-2026, Z. Arvasi & A. Odabas,                    --> 
 <!--  Osmangazi University, Eskisehir, Turkey                            --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -300,6 +300,8 @@ Crossed module [<e4> -> ..] :-
 [ (Z(5)^0)*<identity> of ...+(Z(5)^0)*f1+(Z(5)^2)*f2+(Z(5)^2)*f1*f2 ]
 ]]></Example>
 
+<#Include Label="DirectSumOfXModAlgebras">
+
 </Section>
 
 

examples/algebra.g

@@ -49,9 +49,9 @@ Print( "BMA1 = BasisVectors( Basis( MA1 ) )\n" );
 Print( "BMA1[3] = ", BMA1[3], "\n" );
 
 ## Section 2.1.5
-hom1 := MultiplierHomomorphism( MA1 );;
-Print( "\nhom1 = MultiplierHomomorphism( MA1 ): ", hom1, "\n" );
-Print( "ImageElm( hom1, BA1[2] ) = ", ImageElm( hom1, BA1[2] ), "\n" ); 
+mhom1 := MultiplierHomomorphism( MA1 );;
+Print( "\nmhom1 = MultiplierHomomorphism( MA1 ): ", mhom1, "\n" );
+Print( "ImageElm( mhom1, BA1[2] ) = ", ImageElm( mhom1, BA1[2] ), "\n" ); 
 
 ## Section 2.2.2
 A1 := GroupRing( GF(5), Group( (1,2,3,4,5,6) ) );;

examples/module.g

@@ -19,16 +19,11 @@ Amg3 := AlgebraByGenerators( Rationals, [ mg3 ] );;
 homg3 := AlgebraHomomorphismByImages( A3, Amg3, [ m3 ], [ mg3 ] );;
 actg3 := AlgebraActionByHomomorphism( homg3, Rc3 );
 Print ( "action actg3 of A3 on Rc3:\n", actg3, "\n" );
-
-## Section 4.1.7
 homg3 := AlgebraHomomorphismByImages( A3, Amg3, [ m3 ], [ mg3 ] );
 bdy3 := AlgebraHomomorphismByImages( Rc3, A3, [g3 ], [m3 ] );
 X3 := XModAlgebraByBoundaryAndAction( bdy3, actg3 );
 
 ## Section 2.3
-m3 := [ [0,1,0], [0,0,1], [1,0,0] ];;
-A3 := Algebra( Rationals, [m3] );;
-SetName( A3, "A3" );;
 V3 := Rationals^3;;
 M3 := LeftAlgebraModule( A3, \*, V3 );;
 SetName( M3, "M3" );

lib/dsum-xmod.gd

@@ -1,8 +1,8 @@
- #############################################################################
+#############################################################################
 ##
 #W  dsum-xmod.gd               The XMODALG package            Zekeriya Arvasi
 #W                                                             & Alper Odabas
-#Y  Copyright (C) 2014-2025, Zekeriya Arvasi & Alper Odabas,  
+#Y  Copyright (C) 2014-2026, Zekeriya Arvasi & Alper Odabas,  
 ##
 
 ############################################################################
@@ -36,7 +36,6 @@ DeclareOperation( "AlgebraActionByDirectSum",
 ############################################################################
 ##
 #O DirectSumOfAlgebraHomomorphisms( <hom> <hom> )
-#O AlgebraHomomorphismFromDirectSum( <hom> <hom> )
 ##
 ## <#GAPDoc Label="DirectSumOfAlgebraHomomorphisms"> 
 ## <ManSection>
@@ -46,15 +45,11 @@ DeclareOperation( "AlgebraActionByDirectSum",
 ## <Description>
 ## Let <M>\theta_1 : B_1 \to A_1</M> and <M>\theta_2 : B_2 \to A_2</M>
 ## be algebra homomorphisms. 
-## The first operation uses embeddings into <M>A = A_1 \oplus A_2</M> 
+## This operation uses embeddings into <M>A = A_1 \oplus A_2</M> 
 ## and <M>B = B_1 \oplus B_2</M> to construct
 ## <M>\theta = \theta_1 \oplus \theta_2 : B \to A</M>
 ## where <M>\theta(b_1,b_2) = (\theta_1b_1,\theta_2b_2)</M>.
 ## <P/>
-## When <M>A_1=A_2</M> the second operation constructs
-## <M>\theta = \theta_1 \oplus \theta_2 : B \to A_1</M>
-## where <M>\theta(b_1,b_2) = \theta_1b_1 + \theta_2b_2</M>.
-## <P/>
 ## The example uses the homomorphism <C>homg3</C> used in 
 ## Section <Ref Sect="AlgebraActionByHomomorphism" />
 ## <P/>
@@ -77,8 +72,6 @@ DeclareOperation( "AlgebraActionByDirectSum",
 ##
 DeclareOperation( "DirectSumOfAlgebraHomomorphisms", 
     [ IsAlgebraHomomorphism, IsAlgebraHomomorphism ] );
-DeclareOperation( "AlgebraHomomorphismFromDirectSum", 
-    [ IsAlgebraHomomorphism, IsAlgebraHomomorphism ] );
 
 ## section 2.4.4
 ############################################################################

lib/dsum-xmod.gi

@@ -2,7 +2,7 @@
 ##
 #W  dsum-xmod.gi               The XMODALG package           Zekeriya Arvasi
 #W                                                            & Alper Odabas
-#Y  Copyright (C) 2014-2025, Zekeriya Arvasi & Alper Odabas,  
+#Y  Copyright (C) 2014-2026, Zekeriya Arvasi & Alper Odabas,  
 ##
 
 #############################################################################
@@ -212,43 +212,6 @@ InstallMethod( DirectSumOfAlgebraHomomorphisms,
     return hom;
 end);
 
-#############################################################################
-##
-#M  AlgebraHomomorphismFromDirectSum
-##
-InstallMethod( AlgebraHomomorphismFromDirectSum, 
-    "for two algebra homomorphisms",
-    [ IsAlgebraHomomorphism, IsAlgebraHomomorphism ],
-    function( hom1, hom2 )
-    local B1, A, gen1, im1, B2, gen2, im2,
-          dom, B, eB1, eB2, genB, imhom, hom;
-    B1 := Source( hom1 );
-    A := Range( hom1 );
-    gen1 := GeneratorsOfAlgebra( B1 );
-    im1 := List( gen1, g -> ImageElm( hom1, g ) );
-    B2 := Source( hom2 );
-    if not ( A = Range( hom2 ) ) then
-        Error( "hom1 and hom2 should have the same range" );
-    fi;
-    gen2 := GeneratorsOfAlgebra( B2 );
-    im2 := List( gen2, g -> ImageElm( hom2, g ) );
-    dom := LeftActingDomain( B1 );
-    if not ( dom = LeftActingDomain( B2 ) ) then
-        Error( "homomorphisms are over different domains" );
-    fi;
-    B := DirectSumOfAlgebrasWithInfo( B1, B2 );
-    eB1 := Embedding( B, 1 );
-    eB2 := Embedding( B, 2 );
-    genB := Concatenation( List( gen1, b -> ImageElm( eB1, b ) ),
-                           List( gen2, b -> ImageElm( eB2, b ) ) );
-Print( "genB = ", genB, "\n" );
-    imhom := Concatenation( im1, im2 );
-Print( "imhom = ", imhom, "\n" );
-Error("here");
-    hom := AlgebraHomomorphismByImages( B, A, genB, imhom );
-    return hom;
-end);
-
 #############################################################################
 ##
 #M  AlgebraActionOnDirectSum
@@ -303,8 +266,8 @@ InstallMethod( DirectSumOfAlgebraActions, "for two algebra actions", true,
     [ IsAlgebraAction, IsAlgebraAction ], 0,
 function( act1, act2 )
     local domA, A1, basA1, nA1, A2, basA2, nA2, A, basA, firstA,
-          B1, basB1, nB1, B2, basB2, nB2, B, basB, firstB, zB, zB1, zB2,
-          C1, basC1, nC1, C2, basC2, nC2, C, basC, c, imc, hom,
+          B1, basB1, nB1, B2, basB2, nB2, B, basB, firstB,
+          C1, basC1, nC1, C2, basC2, nC2, C, basC, c, imc1, imc2, imc, hom,
           eA1, imA1, eA2, imA2, eB1, imB1, eB2, imB2, i, act;
     A1 := Source( act1 );
     domA := LeftActingDomain( A1 );
@@ -360,18 +323,12 @@ function( act1, act2 )
     imB2 := List( [1..nB2], j -> ImageElm( eB2, basB2[j] ) );
     basB := Concatenation( imB1, imB2 );
     basC := ListWithIdenticalEntries( nC1+nC2, 0 );
-    zB := Zero( B );
-    zB1 := List( [1..nB1], i -> zB );
-    zB2 := List( [1..nB2], i -> zB );
-##    zB1 := imB1;
-##    zB2 := imB2;
-## Print( "zB1 = ", zB1, "\n" );
-## Print( "zB2 = ", zB2, "\n" );
     for i in [1..nC1] do
         ## c := ImageElm( act1, basA1[i] );
         c := basC1[i];
-        imc := List( basB1, b -> ImageElm( eB1, ImageElm( c, b ) ) );
-        imc := Concatenation( imc, zB2 );
+        imc1 := List( basB1, b -> ImageElm( eB1, ImageElm( c, b ) ) );
+        imc2 := List( basB2, b -> ImageElm( eB2, b ) );
+        imc := Concatenation( imc1, imc2 );
 ## Print( "\nimc1 = ", imc,  "\n\n" );
         hom := LeftModuleHomomorphismByImages( B, B, basB, imc );
 ## Error("here");
@@ -383,8 +340,9 @@ function( act1, act2 )
     for i in [1..nC2] do
         ## c := ImageElm( act2, basA2[i] );
         c := basC2[i];
-        imc := List( basB2, b -> ImageElm( eB2, ImageElm( c, b ) ) );
-        imc := Concatenation( zB1, imc );
+        imc1 := List( basB1, b -> ImageElm( eB1, b ) );
+        imc2 := List( basB2, b -> ImageElm( eB2, ImageElm( c, b ) ) );
+        imc := Concatenation( imc1, imc2 );
 ## Print( "\nimc2 = ", imc, "\n\n" );
         hom := LeftModuleHomomorphismByImages( B, B, basB, imc );
         basC[nC1+i] := hom;
@@ -433,7 +391,7 @@ function( X1, X2 )
     act2 := XModAlgebraAction( X2 );
     ## now construct the combined boundary
     bdy12 := DirectSumOfAlgebraHomomorphisms( bdy1, bdy2 );
-    act12 := AlgebraActionOnDirectSum( act1, act2 );
+    act12 := DirectSumOfAlgebraActions( act1, act2 );
     X12 := PreXModAlgebraByBoundaryAndAction( bdy12, act12 );
     ok := IsPreXModAlgebra( X12 );
     Print( "X12 is a pre-crossed module of algebras? ", ok, "\n" );

tst/algebra.tst

@@ -2,7 +2,7 @@
 ##
 #W  algebra.tst             XModAlg test files          Z. Arvasi - A. Odabas 
 ## 
-#@local level,A1,BA1,v,I1,v1,m1,id1,L1,h1,u1,S1,MS1,BMS1,MA1,BMA1,hom1,act1,act12,theta1,m2,A2,S2,nat2,Q2,act2,I2,BI2,b1,b2,P1,P2,A2c6,R2c3,homAR,homRA,bijAA,ideAA
+#@local level,A1,BA1,v,I1,v1,m1,id1,L1,h1,u1,S1,MS1,BMS1,MA1,BMA1,mhom1,act1,act12,theta1,m2,A2,S2,nat2,Q2,act2,I2,BI2,b1,b2,P1,P2,A2c6,R2c3,homAR,homRA,bijAA,ideAA
 
 gap> START_TEST( "XModAlg package: algebra.tst" );
 gap> level := InfoLevel( InfoXModAlg );; 
@@ -57,8 +57,8 @@ gap> BMA1[3];
 <linear mapping by matrix, A1 -> A1>
 
 ## Section 2.1.5
-gap> hom1 := MultiplierHomomorphism( MA1 );;
-gap> ImageElm( hom1, BA1[2] ); 
+gap> mhom1 := MultiplierHomomorphism( MA1 );;
+gap> ImageElm( mhom1, BA1[2] ); 
 Basis( A1, [ (Z(5)^0)*(), (Z(5)^0)*(1,2,3,4,5,6), (Z(5)^0)*(1,3,5)(2\
 ,4,6), 
   (Z(5)^0)*(1,4)(2,5)(3,6), (Z(5)^0)*(1,5,3)(2,6,4), (Z(5)^0)*(1,6,5,4,3,2) 
@@ -84,7 +84,9 @@ gap> theta1 := NaturalHomomorphismByIdeal( A1, I1 );
 gap> List( BA1, v -> ImageElm( theta1, v ) ); 
 [ v.1, v.2, v.3, v.4, (Z(5)^2)*v.1+(Z(5)^2)*v.3, (Z(5)^2)*v.2+(Z(5)^2)*v.4 ]
 gap> AlgebraActionBySurjection( theta1 );
+!!!
 kernel of hom is not in the annihilator of A
+!!!
 fail
 gap> ## an example which does not fail: 
 gap> m2 := [ [0,1,2,3], [0,0,1,2], [0,0,0,1], [0,0,0,0] ];; 

tst/cat1.tst

@@ -2,7 +2,7 @@
 ##
 #W  cat1.tst                XModAlg test files          Z. Arvasi - A. Odabas 
 ## 
-#@local level,Ak4,IAk4,XIAk4,m,A1,A3,nat13,X13,G,F,R,e5,S,act,bdy,XM,A2c6,R2c3,homAR,homRA,t4,e4,C4,C,C0,C6,A6,B6,eA6,eB6,SA6,SB6,SC6,C1,C2,SC1,SC2,RC1,RC2,gSC1,gSC2,gRC1,gRC2,imS,homS,imR,homR,m12,im12
+#@local level,Ak4,IAk4,XIAk4,m2,A2,S2,nat2,X2,G,F,R,e5,S,act,bdy,XM,A2c6,R2c3,homAR,homRA,t4,e4,C4,C,C0,C6,A6,B6,eA6,eB6,SA6,SB6,SC6,C1,C2,SC1,SC2,RC1,RC2,gSC1,gSC2,gRC1,gRC2,imS,homS,imR,homR,m12,im12
 
 gap> START_TEST( "XModAlg package: cat1.tst" );
 gap> level := InfoLevel( InfoXModAlg );; 
@@ -15,11 +15,11 @@ gap> IAk4 := AugmentationIdeal( Ak4 );;
 gap> SetName( IAk4, "I(GF5[k4])" );
 gap> XIAk4 := XModAlgebraByIdeal( Ak4, IAk4 );;
 
-gap> m := [ [0,1,2,3], [0,0,1,2], [0,0,0,1], [0,0,0,0] ];; 
-gap> A1 := Algebra( Rationals, [m] );;
-gap> A3 := Subalgebra( A1, [m^3] );; 
-gap> nat13 := NaturalHomomorphismByIdeal( A1, A3 );; 
-gap> X13 := XModAlgebraBySurjection( nat13 );; 
+gap> m2 := [ [0,1,2,3], [0,0,1,2], [0,0,0,1], [0,0,0,0] ];; 
+gap> A2 := Algebra( Rationals, [m2] );;
+gap> S2 := Subalgebra( A2, [m2^3] );; 
+gap> nat2 := NaturalHomomorphismByIdeal( A2, S2 );; 
+gap> X2 := XModAlgebraBySurjection( nat2 );; 
 
 gap> G := SmallGroup( 4, 2 );;
 gap> F := GaloisField( 4 );;