From 4ab1868e0ac7dd9d085ed02cbcefc1e505fcb56a Mon Sep 17 00:00:00 2001
From: cdwensley <cdwensley.maths@btinternet.com>
Date: Sat, 26 Oct 2024 18:46:55 +0100
Subject: [PATCH] update chapter 5 in the manual

---
 doc/convert.xml | 19 +++++++++----------
 lib/module.gd   | 20 +++++++++++++-------
 tst/convert.tst |  4 ++--
 3 files changed, 24 insertions(+), 19 deletions(-)

diff --git a/doc/convert.xml b/doc/convert.xml
index 52eaea8..0617744 100644
--- a/doc/convert.xml
+++ b/doc/convert.xml
@@ -71,10 +71,10 @@ As an example we use the crossed module <C>XAB</C> constructed in section
 
 <Example>
 <![CDATA[
-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)] :- 
+gap> Cn := Cat1AlgebraOfXModAlgebra( Xn );
+[An |X Bn -> An]
+gap> Display( Cn );
+Cat1-algebra [An |X Bn => An] :- 
 :  range algebra has generators:
 [ 
   [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], 
@@ -93,7 +93,7 @@ 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), 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:
+: 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 ] ], 
@@ -105,9 +105,8 @@ 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 ]
-: kernel has generators:
-  [ v.4, v.5 ]
+: range embedding maps range generators to:    [ v.1, v.2 ]
+: kernel has generators:  [ v.4, v.5 ]
 ]]>
 </Example>
 
@@ -128,9 +127,9 @@ constructed in section <Ref Sect="SubCat1Algebra"/>.
 
 <Example>
 <![CDATA[
-gap> X3 := XModAlgebraOfCat1Algebra( C3 );
+gap> X6 := XModAlgebraOfCat1Algebra( C6 );
 [ <algebra of dimension 3 over GF(2)> -> <algebra of dimension 3 over GF(2)> ]
-gap> Display( X3 ); 
+gap> Display( X6 ); 
 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), 
diff --git a/lib/module.gd b/lib/module.gd
index b18cf34..2a24e72 100644
--- a/lib/module.gd
+++ b/lib/module.gd
@@ -339,19 +339,25 @@ DeclareOperation( "XModAlgebraByModule", [ IsAlgebra, IsLeftModule ] );
 ##
 ## <Example>
 ## <![CDATA[
-## gap> C4 := Cat1AlgebraOfXModAlgebra( X4 );
-## [A4 |X A(M4)=>A4]
-## gap> Display( C4 );           
-## Cat1-algebra [A4 |X A(M4) => A4] :- 
-## :  range algebra has generators:[ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ]
-## : tail homomorphism = head homomorphism
-##   they map the source generators to:  
+## gap> C3 := Cat1AlgebraOfXModAlgebra( X3 );
+## [A3 |X GR(c3) -> A3]
+## gap> Display( C3 );                 
+## Cat1-algebra [A3 |X GR(c3) => A3] :- 
+## : range algebra has generators:[ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ]
+## : tail homomorphism maps source generators to:  
 ## [ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], 
 ##   [ [ 0, 0, 1 ], [ 1, 0, 0 ], [ 0, 1, 0 ] ], 
 ##   [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], 
 ##   [ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], 
 ##   [ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], 
 ##   [ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ] ]
+## : head homomorphism maps source generators to:  
+## [ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], 
+##   [ [ 0, 0, 1 ], [ 1, 0, 0 ], [ 0, 1, 0 ] ], 
+##   [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], 
+##   [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], 
+##   [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], 
+##   [ [ 0, 0, 1 ], [ 1, 0, 0 ], [ 0, 1, 0 ] ] ]
 ## : range embedding maps range generators to:    [ v.1 ]
 ## : kernel has generators:  [ v.4, v.5, v.6 ]
 ## ]]>
diff --git a/tst/convert.tst b/tst/convert.tst
index 93ccde4..baf7af1 100644
--- a/tst/convert.tst
+++ b/tst/convert.tst
@@ -41,8 +41,8 @@ gap> Xn := XModAlgebraByIdeal( An, Bn );
 [ Bn -> An ]
 gap> SetName( Xn, "Xn" ); 
 
-gap> ############################ 
-gap> ## Chapter 5,  Section 5.1.1
+############################ 
+## Chapter 5,  Section 5.1.1
 gap> Cn := Cat1AlgebraOfXModAlgebra( Xn );
 [An |X Bn -> An]
 gap> Display( Cn );