Merge pull request gap-packages#78 from cdwensley/oct21

preparing to release v1.27

CHANGES.md

@@ -1,5 +1,11 @@
 # CHANGES to the 'XModAlg' package
 
+## 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
+              xmod.tst now agrees with sections 4.1.7-4.1.10 in the manual
+              changed names of variables in tests to avoid duplications
+
 ## 1.25 -> 1.26 (09/07/24) 
  * (08/07/24) renamed the actions and algebras in the tests/examples as 
               act1, act2, ,,, act6  and added direct sum operations
@@ -17,16 +23,16 @@
               and prior to the function being moved to the main GAP library 
 
 ## 1.18 -> 1.22 (29/04/22) 
- * (27/04/22) required version 2.87 of XMod which uses Size2d in place of Size, 
-              and so replaced Size by Size2d for 2d-algebras 
+ * (27/04/22) required version 2.87 of XMod which uses Size2d in place of
+              Size, and so replaced Size by Size2d for 2d-algebras 
  * (15/07/21) revised PreXModAlgebraOfPreCat1Algebra 
  * (14/07/21) revised IsPreXModAlgebra and IsXModAlgebra 
-              renamed AlgebraAction4 AlgebraActionByModule 
+              renamed AlgebraAction4 as AlgebraActionByModule 
  * (09/07/21) added section on Multipliers and MultiplierAlgebras 
- * (09/06/21) renamed AlgebraAction3 AlgebraActionBySurjection 
+ * (09/06/21) renamed AlgebraAction3 as AlgebraActionBySurjection 
               renamed XModAlgebraByCentralExtension XModAlgebraBySurjection 
               revised these operations and added examples
- * (25/05/21) renamed AlgebraAction1 AlgebraActionByMultipliers 
+ * (25/05/21) renamed AlgebraAction1 as AlgebraActionByMultipliers 
               added operation SemidirectProductofAlgebras 
               added chapter Commutative algebras and their actions to manual
  * (12/05/21) added algebra attribute AugmentationXMod 

doc/algebra.xml

@@ -88,8 +88,8 @@ for all <M>a,b</M> in the basis for <M>A</M>.
 <![CDATA[
 gap> IsAlgebraMultiplier( m1 ); 
 true
-gap> one := One( A1 );; 
-gap> L1 := List( BA1, v -> one );; 
+gap> id1 := One( A1 );; 
+gap> L1 := List( BA1, v -> id1 );; 
 gap> h1 := LeftModuleHomomorphismByImages( A1, A1, BA1, L1 ); 
 [ (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) 
@@ -314,9 +314,9 @@ LeftModuleHomomorphismByMatrix( Basis( A2,
   [ [ 0, 0, 1, 4 ], [ 0, 0, 0, 1 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ] ] ), 
 [ [ 0, 0 ], [ 1, 0 ], [ 0, 1 ] ], CanonicalBasis( Q2 ) )
 gap> act2 := AlgebraActionBySurjection( nat2 );; 
-gap> C2 := Image( act2 );;
-gap> BC2 := BasisVectors( Basis( C2 ) );;
-gap> b1 := BC2[1];;  b2 := BC2[2];;
+gap> I2 := Image( act2 );;
+gap> BI2 := BasisVectors( Basis( I2 ) );;
+gap> b1 := BI2[1];;  b2 := BI2[2];;
 gap> [ Image(b1,m2)=m2^2, Image(b1,m2^2)=m2^3, Image(b1,m2^3)=Zero(A2) ];
 [ true, true, true ]
 gap> [ Image(b2,m2)=m2^3, b2=b1^2 ];

doc/cat1.xml

@@ -322,26 +322,26 @@ subcat<M>^{1}</M>-algebras of a given cat<M>^{1}</M>-algebra.
 
 <Example>
 <![CDATA[
-gap> C3 := Cat1AlgebraSelect( 2, 6, 2, 4 );; 
-gap> A3 := Source( C3 );
+gap> C6 := Cat1AlgebraSelect( 2, 6, 2, 4 );;
+gap> A6 := Source( C6 );
 GF(2)_c6
-gap> B3 := Range( C3 ); 
-GF(2)_c3
-gap> eA3 := Elements( A3 );;
-gap> eB3 := Elements( B3 );;
-gap> AA3 := Subalgebra( A3, [ eA3[1], eA3[2], eA3[3] ] );
+gap> B6 := Range( C6 );
+<algebra of dimension 3 over GF(2)>
+gap> eA6 := Elements( A6 );;
+gap> eB6 := Elements( B6 );;
+gap> SA6 := Subalgebra( A6, [ eA6[1], eA6[2], eA6[3] ] );
 <algebra over GF(2), with 3 generators>
-gap> [ Size(A3), Size(AA3) ]; 
+gap> [ Size(A6), Size(SA6) ]; 
 [ 64, 4 ]
-gap> BB3 := Subalgebra( B3, [ eB3[1], eB3[2] ] ); 
+gap> SB6 := Subalgebra( B6, [ eB6[1], eB6[2] ] ); 
 <algebra over GF(2), with 2 generators>
-gap> [ Size(B3), Size(BB3) ]; 
+gap> [ Size(B6), Size(SB6) ]; 
 [ 8, 2 ]
-gap> CC3 := SubCat1Algebra( C3, AA3, BB3 );
+gap> SC6 := SubCat1Algebra( C6, SA6, SB6 );
 [Algebra( GF(2), [ <zero> of ..., (Z(2)^0)*(), (Z(2)^0)*()+(Z(2)^0)*(4,5) 
  ] ) -> Algebra( GF(2), [ <zero> of ..., (Z(2)^0)*() ] )]
-gap> Display( CC3 );
-Cat1-algebra [..=>..] :-
+gap> Display( SC6 );
+Cat1-algebra [..=>..] :- 
 : source algebra has generators:
   [ <zero> of ..., (Z(2)^0)*(), (Z(2)^0)*()+(Z(2)^0)*(4,5) ]
 :  range algebra has generators:
@@ -358,6 +358,8 @@ Cat1-algebra [..=>..] :-
   [ <zero> of ..., <zero> of ... ]
 : kernel embedding maps generators of kernel to:
   [ <zero> of ..., (Z(2)^0)*()+(Z(2)^0)*(4,5) ]
+gap> IsSubCat1Algebra( C6, SC6 );
+true
 ]]>
 </Example>
 
@@ -429,10 +431,10 @@ These are the six main attributes of a cat<M>^{1}</M>-algebra morphism.
 
 <Example>
 <![CDATA[
-gap> C1 := Cat1Algebra( 2, 1, 1, 1 );
+gap> C1 := Cat1AlgebraSelect( 2, 1, 1, 1 );
 [GF(2)_triv -> GF(2)_triv]
 gap> Display( C1 );
-Cat1-algebra [GF(2)_triv=>GF(2)_triv] :-
+Cat1-algebra [GF(2)_triv=>GF(2)_triv] :- 
 : source algebra has generators:
   [ (Z(2)^0)*(), (Z(2)^0)*() ]
 :  range algebra has generators:
@@ -444,11 +446,10 @@ Cat1-algebra [GF(2)_triv=>GF(2)_triv] :-
 : range embedding maps range generators to:
   [ (Z(2)^0)*(), (Z(2)^0)*() ]
 : the kernel is trivial.
-
-gap> C2 := Cat1Algebra( 2, 2, 1, 2 );
+gap> C2 := Cat1AlgebraSelect( 2, 2, 1, 2 );
 [GF(2)_c2 -> GF(2)_triv]
-gap> Display( C2 );
-Cat1-algebra [GF(2)_c2=>GF(2)_triv] :-
+gap> Display( C2 );                        
+Cat1-algebra [GF(2)_c2=>GF(2)_triv] :- 
 : source algebra has generators:
   [ (Z(2)^0)*(), (Z(2)^0)*(1,2) ]
 :  range algebra has generators:
@@ -467,30 +468,32 @@ Cat1-algebra [GF(2)_c2=>GF(2)_triv] :-
   [ (Z(2)^0)*()+(Z(2)^0)*(1,2) ]
 gap> C1 = C2;
 false
-gap> R1 := Source( C1 );;
-gap> R2 := Source( C2 );;
-gap> S1 := Range( C1 );;
-gap> S2 := Range( C2 );;
-gap> gR1 := GeneratorsOfAlgebra( R1 );
+gap> SC1 := Source( C1 );;
+gap> SC2 := Source( C2 );
+GF(2)_c2
+gap> RC1 := Range( C1 );;
+gap> RC2 := Range( C2 );;
+gap> gSC1 := GeneratorsOfAlgebra( SC1 );
 [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> gR2 := GeneratorsOfAlgebra( R2 );
+gap> gSC2 := GeneratorsOfAlgebra( SC2 );
 [ (Z(2)^0)*(), (Z(2)^0)*(1,2) ]
-gap> gS1 := GeneratorsOfAlgebra( S1 );
+gap> gRC1 := GeneratorsOfAlgebra( RC1 );
 [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> gS2 := GeneratorsOfAlgebra( S2 );
+gap> gRC2 := GeneratorsOfAlgebra( RC2 );
 [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> im1 := [ gR2[1], gR2[1] ];
+gap> imS := [ gSC2[1], gSC2[1] ];
 [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> f1 := AlgebraHomomorphismByImages( R1, R2, gR1, im1 );
+gap> homS := AlgebraHomomorphismByImages( SC1, SC2, gSC1, imS );
 [ (Z(2)^0)*(), (Z(2)^0)*() ] -> [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> im2 := [ gS2[1], gS2[1] ];
+gap> imR := [ gRC2[1], gRC2[1] ];
 [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> f2 := AlgebraHomomorphismByImages( S1, S2, gS1, im2 );
+gap> homR := AlgebraHomomorphismByImages( RC1, RC2, gRC1, imR );
 [ (Z(2)^0)*(), (Z(2)^0)*() ] -> [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> m := Cat1AlgebraMorphism( C1, C2, f1, f2 );
+gap> m12 := Cat1AlgebraMorphism( C1, C2, homS, homR );
 [[GF(2)_triv=>GF(2)_triv] => [GF(2)_c2=>GF(2)_triv]]
-gap> Display( m );
-Morphism of cat1-algebras :-
+gap> Display( m12 );
+
+Morphism of cat1-algebras :- 
 : Source = [GF(2)_triv=>GF(2)_triv] with generating sets:
   [ (Z(2)^0)*(), (Z(2)^0)*() ]
   [ (Z(2)^0)*(), (Z(2)^0)*() ]
@@ -501,13 +504,15 @@ Morphism of cat1-algebras :-
   [ (Z(2)^0)*(), (Z(2)^0)*() ]
 : Range Homomorphism maps range generators to:
   [ (Z(2)^0)*(), (Z(2)^0)*() ]
-gap> IsSurjective( m );
+
+## gap> Image2dAlgMapping( m12 );
+## [GF(3)_c2^3=>GF(3)_c2^3]
+gap> IsSurjective( m12 );
 false
-gap> IsInjective( m );
+gap> IsInjective( m12 );
 true
-gap> IsBijective( m );
+gap> IsBijective( m12 );
 false
-
 ]]>
 </Example>
 
@@ -523,8 +528,8 @@ this operation returns the image crossed module.
 
 <Example>
 <![CDATA[
-gap> imm := ImagesSource2DimensionalMapping( m );;
-gap> Display( imm ); 
+gap> im12 := ImagesSource2DimensionalMapping( m12 );;
+gap> Display( im12 ); 
 Cat1-algebra [..=>..] :- 
 : source algebra has generators:
   [ (Z(2)^0)*(), (Z(2)^0)*() ]

doc/convert.xml

@@ -64,8 +64,8 @@ instead of the operation <Ref Oper="Cat1AlgebraSelect"/>.
 <Description> 
 These operations are used for constructing a cat<M>^{1}</M>-algebra 
 from a given crossed module of algebras. 
-As an example we use the crossed module <C>XAB</C> constructed in 
-<Ref Oper="XModAlgebraByIdeal"/>. 
+As an example we use the crossed module <C>XAB</C> constructed in section
+<Ref Sect="XModAlgebraByIdeal"/>. 
 </Description>
 </ManSection> 
 
@@ -74,16 +74,14 @@ As an example we use the crossed module <C>XAB</C> constructed in
 gap> CAB := Cat1AlgebraOfXModAlgebra( XAB );
 [A(l,m) |X A(m)=>A(l,m)]
 gap> Display( CAB );
-Cat1-algebra [A(l,m) |X A(m)=>A(l,m)] :- 
+Cat1-algebra [A(l,m) |X A(m) => A(l,m)] :- 
 :  range algebra has generators:
-  
 [ 
   [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], 
       [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
   [ [ 0*Z(5), Z(5)^0, Z(5)^3 ], [ 0*Z(5), 0*Z(5), Z(5)^0 ], 
       [ 0*Z(5), 0*Z(5), 0*Z(5) ] ] ]
-: tail homomorphism maps source generators to:
-  
+: tail homomorphism maps source generators to:  
 [ 
   [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], 
       [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
@@ -96,7 +94,6 @@ Cat1-algebra [A(l,m) |X A(m)=>A(l,m)] :-
   [ [ 0*Z(5), 0*Z(5), 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5) ], 
       [ 0*Z(5), 0*Z(5), 0*Z(5) ] ] ]
 : head homomorphism maps source generators to:
-  
 [ 
   [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], 
       [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
@@ -108,8 +105,7 @@ Cat1-algebra [A(l,m) |X A(m)=>A(l,m)] :-
       [ 0*Z(5), 0*Z(5), 0*Z(5) ] ], 
   [ [ 0*Z(5), 0*Z(5), Z(5)^0 ], [ 0*Z(5), 0*Z(5), 0*Z(5) ], 
       [ 0*Z(5), 0*Z(5), 0*Z(5) ] ] ]
-: range embedding maps range generators to:
-  [ v.1, v.2 ]
+: range embedding maps range generators to:  [ v.1, v.2 ]
 : kernel has generators:
   [ v.4, v.5 ]
 ]]>
@@ -125,6 +121,8 @@ Cat1-algebra [A(l,m) |X A(m)=>A(l,m)] :-
 <Description> 
 These operations are used for constructing a crossed module of algebras 
 from a given cat<M>^{1}</M>-algebra.
+The example uses the cat<M>^1</M>-algebra <C>C3</C> 
+constructed in section <Ref Sect="SubCat1Algebra"/>.
 </Description>
 </ManSection> 
 
@@ -133,7 +131,6 @@ from a given cat<M>^{1}</M>-algebra.
 gap> X3 := XModAlgebraOfCat1Algebra( C3 );
 [ <algebra of dimension 3 over GF(2)> -> <algebra of dimension 3 over GF(2)> ]
 gap> Display( X3 ); 
-
 Crossed module [..->..] :- 
 : Source algebra has generators:
   [ (Z(2)^0)*()+(Z(2)^0)*(4,5), (Z(2)^0)*(1,2,3)+(Z(2)^0)*(1,2,3)(4,5),