Merge pull request #122 from gap-packages/my-dev

introduced Size2d and Size3d

CHANGES.md

@@ -1,8 +1,9 @@
 # CHANGES to the 'XMod' package
 
-## 2.86 -> 2.86dev (14/03/2022) 
+## 2.86 -> 2.87 (27/04/2022) 
 
- * (
+ * (27/04/22) introduced Size2d for 2d-objects and Size3d for 3d-objects 
+              added the Arvasi/Odabas/Wensley paper to the list of references
 
 ## 2.85 -> 2.86 (14/03/2022) 
 

PackageInfo.g

@@ -7,8 +7,8 @@ SetPackageInfo( rec(
 
 PackageName := "XMod",
 Subtitle := "Crossed Modules and Cat1-Groups",
-Version := "2.86dev",
-Date := "14/03/2022", # dd/mm/yyyy format
+Version := "2.87",
+Date := "27/04/2022", # dd/mm/yyyy format
 License := "GPL-2.0-or-later",
 
 Persons := [

doc/apps.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  apps.xml              XMod documentation            Chris Wensley  -->
 <!--                                                        & Murat Alp  -->
-<!--  Copyright (C) 2001-2020, Chris Wensley et al,                      --> 
+<!--  Copyright (C) 2001-2022, Chris Wensley et al,                      --> 
 <!--  School of Computer Science, Bangor University, U.K.                --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -112,7 +112,7 @@ gap> classes := LoopClasses( X8 );;
 gap> List( classes, c -> Length(c) );
 [ 1, 21, 56, 42, 24, 24 ]
 gap> LX := LoopsXMod( X8, (1,2)(5,6) );;
-gap> Size( LX ); 
+gap> Size2d( LX ); 
 [ 8, 64 ]
 gap> IdGroup( LX );
 [ [ 8, 5 ], [ 64, 138 ] ]

doc/bib.xml

@@ -73,6 +73,20 @@
   <pages>473-495</pages>
 </article></entry>
 
+<entry id="AOW"><article>
+  <author>
+    <name><first>Z.</first><last>Arvasi</last></name>
+    <name><first>A.</first><last>Odabas</last></name>
+    <name><first>C. D.</first><last>Wensley</last></name>
+  </author>  
+  <title>Computing 3-Dimensional Groups : 
+         Crossed Squares and Cat2-groups</title>
+  <journal>J. Symbolic Computation</journal>
+  <year>(to appear)</year>
+  <volume></volume>
+  <pages></pages>
+</article></entry>
+
 <entry id="B82"><inproceedings>
   <author>
     <name><first>R.</first><last>Brown</last></name>

doc/gp2ind.xml

@@ -216,7 +216,7 @@ gap> inc45 := InclusionMappingGroups( s5, s4 );;
 gap> iota45 := iso4 * inc45;; 
 gap> indX8 := InducedXMod( X8, iota45 );
 i*(X8)
-gap> Size( indX8 );
+gap> Size2d( indX8 );
 [ 120, 120 ]
 gap> StructureDescription( indX8 );          
 [ "SL(2,5)", "S5" ]

doc/gp2obj.xml

@@ -341,19 +341,41 @@ gap> ImageElmXModAction( X12, (1,2,3,4,5,6), (8,9) );
 </Example>
 
 <ManSection>
-   <Attr Name="Size"
+   <Attr Name="Size2d"
          Arg="X0" Label="for crossed modules" />
+<Description>
+The standard operation <C>Size</C> cannot be used for crossed modules 
+because the size of a collection is required to be a number, 
+and we wish to return a list. 
+<C>Size2d( X0 )</C> returns the two-element list, 
+<C>[ Size( Source(X0) ), Size( Range(X0) ) ]</C>. 
+<P/> 
+</Description>
+</ManSection>
+
+In the simple example below, <Code>X5</Code> is the automorphism crossed module 
+constructed in subsection <Ref Oper="XModByAutomorphismGroup"/>. 
+<P/>
+<Example>
+<![CDATA[
+gap> Size2d( X5 ); 
+[ 5, 4 ]
+]]>
+</Example>
+
+<ManSection>
    <Attr Name="Name"
          Arg="X0" Label="for crossed modules" />
    <Attr Name="IdGroup"
          Arg="X0" Label="for crossed modules" />
    <Attr Name="ExternalSetXMod"
          Arg="X0" />
 <Description>
-More familiar attributes are <C>Name</C>, <C>Size</C> and <C>IdGroup</C>. 
+More familiar attributes are <C>Name</C> and <C>IdGroup</C>. 
 The name is formed by concatenating the names of the source and range 
 (if these exist). 
-<C>Size</C> and <C>IdGroup</C> return two-element lists. 
+<C>IdGroup( X0 )</C> returns a two-element list 
+<C>[ IdGroup( Source(X0) ), IdGroup( Range(X0) ) ]</C>. 
 <P/> 
 The <Ref Attr="ExternalSetXMod"/> for a crossed module is the source group considered as a G-set of the range group using the crossed module action. 
 <P/> 
@@ -362,15 +384,12 @@ The <C>Display</C> function is used to print details of 2d-groups.
 </Description>
 </ManSection>
 
-In the simple example below, <Code>X5</Code> is the automorphism crossed module 
-constructed in subsection <Ref Oper="XModByAutomorphismGroup"/>. 
 The <C>Print</C> statements at the end of the example list the &GAP; 
 representations and attributes of <Code>X5</Code>. 
 <P/>
 <Example>
 <![CDATA[
-gap> Size( X5 );  IdGroup( X5 ); 
-[ 5, 4 ]
+gap> IdGroup( X5 ); 
 [ [ 5, 1 ], [ 4, 1 ] ]
 gap> ext := ExternalSetXMod( X5 ); 
 <xset:[ (), (5,6,7,8,9), (5,7,9,6,8), (5,8,6,9,7), (5,9,8,7,6) ]>
@@ -380,10 +399,10 @@ gap> a := GeneratorsOfGroup( Range( X5 ) )[1]^2;
 [ (5,6,7,8,9) ] -> [ (5,9,8,7,6) ]
 gap> ImageElmXModAction( X5, (5,7,9,6,8), a );
 (5,8,6,9,7)
-gap> RepresentationsOfObject( X5 );
+gap> Print( RepresentationsOfObject(X5), "\n" );
 [ "IsComponentObjectRep", "IsAttributeStoringRep", "IsPreXModObj" ]
-gap> KnownAttributesOfObject( X5);
-[ "Name", "Size", "Range", "Source", "IdGroup", "Boundary", "XModAction", 
+gap> Print( KnownAttributesOfObject(X5), "\n" );
+[ "Name", "Range", "Source", "IdGroup", "Boundary", "Size2d", "XModAction", 
   "ExternalSetXMod", "HigherDimension" ]
 ]]>
 </Example>
@@ -444,11 +463,15 @@ listed in section <Ref Sect="sect-constructions" />:
 
 <Example>
 <![CDATA[
-gap> KnownPropertiesOfObject( X5 );
-[ "IsEmpty", "IsTrivial", "IsNonTrivial", "IsFinite", 
-  "CanEasilyCompareElements", "CanEasilySortElements", "IsDuplicateFree", 
-  "IsGeneratorsOfSemigroup", "IsPreXModDomain", "IsPreXMod", "IsXMod", 
-  "IsAutomorphismGroup2DimensionalGroup" ]
+gap> [ IsTrivial( X5 ),  IsNonTrivial( X5 ),  IsFinite( X5 ) ];
+[ false, true, true ]
+gap> kpoX5 := KnownPropertiesOfObject(X5);;
+gap> ForAll( [ "IsTrivial", "IsNonTrivial", "IsFinite", 
+>  "CanEasilyCompareElements", "CanEasilySortElements", "IsDuplicateFree", 
+>  "IsGeneratorsOfSemigroup", "IsPreXModDomain", "IsPreXMod", "IsXMod", 
+>  "IsAutomorphismGroup2DimensionalGroup" ], 
+>  s -> s in kpoX5 ); 
+true
 ]]>
 </Example>
 
@@ -532,9 +555,11 @@ and the action of <M>C</M> on <M>K</M> is given by <M>k^{Jr} = k^r</M>.
 <![CDATA[
 gap> d8d8 := Group( (1,2,3,4), (1,3), (5,6,7,8), (5,7) );;
 gap> X88 := XModByAutomorphismGroup( d8d8 );;
-gap> Size( X88 );
+gap> Size2d( X88 );
 [ 64, 2048 ]
 gap> Y88 := KernelCokernelXMod( X88 );;
+gap> IdGroup(Y88);
+[ [ 4, 2 ], [ 128, 928 ] ]
 gap> StructureDescription( Y88 );
 [ "C2 x C2", "(D8 x D8) : C2" ] 
 ]]>
@@ -720,7 +745,7 @@ gap> C18 := Cat1Group( t1, h1, e1 );
          Arg="C" Label="for cat1-groups" />
    <Attr Name="Name"
          Arg="C" Label="for cat1-groups" />
-   <Attr Name="Size"
+   <Attr Name="Size2d"
          Arg="C" Label="for cat1-groups" />
 <Description> 
 These are the attributes of a cat<M>^1</M>-group <M>\calC</M> 
@@ -756,7 +781,7 @@ gap> KernelEmbedding( C18 );
 [ (4,5,6) ] -> [ (4,5,6) ]
 gap> Name( C18 );
 "[g18=>s3a]"
-gap> Size( C18 );
+gap> Size2d( C18 );
 [ 18, 6 ]
 gap> StructureDescription( C18 );
 [ "(C3 x C3) : C2", "S3" ]

doc/gp3cat2.xml

@@ -119,6 +119,11 @@ subject to the following conditions:
 </Display>
 where <M>\ker t = (\ker \ddot{t},\ \ker \dot{t})</M>, 
 and similarly for <M>\ker h</M>. 
+<P/> 
+A recent paper 
+<E>Computing 3-Dimensional Groups :L Crossed Squares and Cat2-Groups</E>, 
+by Arvasi, Odabas and Wensley <Cite Key="AOW"/>, 
+contains tables listing the numbers of isomorphism classes of cat2-groups on groups of order at most 30 – a total of 1007 cat2-groups.
 
 <ManSection Label="cat2-group">
    <Func Name="Cat2Group"
@@ -349,7 +354,7 @@ gap> C2act := Cat2GroupOfCrossedSquare( XSact );
 (pre-)cat2-group with generating (pre-)cat1-groups:
 1 : [((c5:c4 |X c5:c4) |X (d20 |X d10a))=>(c5:c4 |X c5:c4)]
 2 : [((c5:c4 |X c5:c4) |X (d20 |X d10a))=>(c5:c4 |X d20)]
-gap> Size( C2act );
+gap> Size3d( C2act );
 [ 80000, 400, 400, 20 ]
 ]]>
 </Example>

doc/gp3xsq.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  gp3xsq.xml            XMod documentation            Chris Wensley  -->
 <!--                                                                     -->
-<!--  Copyright (C) 1996-2021, Chris Wensley et al,                      --> 
+<!--  Copyright (C) 1996-2022, Chris Wensley et al,                      --> 
 <!--  School of Computer Science, Bangor University, U.K.                --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -251,6 +251,24 @@ false
 ]]>
 </Example>
 
+<ManSection>
+   <Attr Name="Size3d"
+         Arg="XS" Label="for 3d-objects" />
+<Description>
+Just as <C>Size2d</C> was used in place of <C>Size</C> for crossed modules, so <C>Size3d</C> is used for crossed squares:
+<C>Size3d( XS )</C> returns a four-element list containing the sizes
+of the four groups at the corners of the square.
+<P/> 
+</Description>
+</ManSection>
+
+<Example>
+<![CDATA[
+gap> Size3d( PXS ); 
+[ 2, 2, 2, 1 ]
+]]>
+</Example>
+
 <ManSection>
    <Oper Name="CrossedSquareByNormalSubgroups"
          Arg="L M N P" />

doc/history.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  history.xml           XMod documentation            Chris Wensley  -->
 <!--                                                                     -->
-<!--  Copyright (C) 1996-2021, Murat Alp and Chris Wensley,              --> 
+<!--  Copyright (C) 1996-2022, Murat Alp and Chris Wensley,              --> 
 <!--  School of Computer Science, Bangor University, U.K.                --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
@@ -215,6 +215,16 @@ Added functions for quasi-isomorphisms.
 </Item>
 </List> 
 </Subsection>
+
+<Subsection><Heading>Version 2.86 - 2.87</Heading>
+<List>
+<Item>
+Added attributes <C>Size2d</C> for 2d-objects and <C>Size3d</C> for 3d-objects 
+since lists are inappropriate values for the standard function <C>Size</C>.  
+</Item>
+</List> 
+</Subsection>
+
 </Section> 
 
 

doc/isoclinic.xml

@@ -2,7 +2,7 @@
 <!--                                                                     -->
 <!--  isoclinic.xml          XMod documentation            Alper Odabas  -->
 <!--                                                       & Enver Uslu  -->
-<!--  Copyright (C) 2015-2020, Chris Wensley et al                       --> 
+<!--  Copyright (C) 2015-2022, Chris Wensley et al                       --> 
 <!--                                                                     -->
 <!-- ------------------------------------------------------------------- -->
 
@@ -53,7 +53,7 @@ is a special case of this construction.
 gap> d24 := DihedralGroup( IsPermGroup, 24 );; 
 gap> SetName( d24, "d24" );
 gap> Y24 := XModByAutomorphismGroup( d24 );; 
-gap> Size( Y24 );
+gap> Size2d( Y24 );
 [ 24, 48 ]
 gap> X24 := Image( IsomorphismPerm2DimensionalGroup( Y24 ) );
 [d24->Group([ (2,4), (1,2,3,4), (6,7), (5,6,7) ])]
@@ -66,7 +66,7 @@ gap> Xn1 := nsx[pos1];
 [Group( [ f2*f4^2, f3*f4 ] )->Group( [ f3, f4, f5 ] )]
 gap> nat1 := NaturalMorphismByNormalSubPreXMod( X24, Xn1 );; 
 gap> Qn1 := FactorPreXMod( X24, Xn1 );; 
-gap> [ Size( Xn1 ), Size( Qn1 ) ];
+gap> [ Size2d( Xn1 ), Size2d( Qn1 ) ];
 [ [ 4, 8 ], [ 6, 6 ] ]
 ]]>
 </Example>
@@ -509,7 +509,7 @@ gap> Length( IA66 );
 gap> x36 := AllXMods( 36 );; 
 gap> Length( x36 ); 
 205
-gap> size36 := List( x36, x -> [ Size(Source(x)), Size(Range(x)) ] );;
+gap> size36 := List( x36, x -> Size2d( x ) );;
 gap> Collected( size36 );
 [ [ [ 1, 36 ], 14 ], [ [ 2, 18 ], 7 ], [ [ 3, 12 ], 21 ], [ [ 4, 9 ], 14 ], 
   [ [ 6, 6 ], 17 ], [ [ 9, 4 ], 102 ], [ [ 12, 3 ], 8 ], [ [ 18, 2 ], 18 ], 

lib/gp2ind.gi

@@ -2,7 +2,7 @@
 ##
 #W  gp2ind.gi                      XMOD Package                  Chris Wensley
 ##
-#Y  Copyright (C) 2001-2020, Chris Wensley et al,  
+#Y  Copyright (C) 2001-2022, Chris Wensley et al,  
 #Y  School of Computer Science, Bangor University, U.K. 
 ##  
 ##  This file implements functions for induced crossed modules. 

lib/gp2map.gi

@@ -5,7 +5,7 @@
 ##  This file installs methods for 2DimensionalMappings 
 ##  for crossed modules and cat1-groups. 
 ##
-#Y  Copyright (C) 2001-2021, Chris Wensley et al, 
+#Y  Copyright (C) 2001-2022, Chris Wensley et al, 
 #Y  School of Computer Science, Bangor University, U.K. 
 
 ##############################################################################
@@ -1117,7 +1117,7 @@ function( C1G1, C1G2 )
           t1, h1, t2, h2, t3, h3, C3, phi, autG2, iterG2, 
           salpha, ralpha, mgira, isalpha, R4, t4, h4, C4, smor, rmor;
 
-    if not ( Size( C1G1 ) = Size( C1G2 ) ) then 
+    if not ( Size2d( C1G1 ) = Size2d( C1G2 ) ) then 
         return fail; 
     fi; 
     ok1 := IsPreCat1GroupWithIdentityEmbedding( C1G1 ); 
@@ -1951,7 +1951,7 @@ function( C, id, show )
     ## deal with trivial cases first 
     ids := [ id ]; 
     K := KernelCokernelXMod( C ); 
-    if Product( Size(K) ) = ids[1][1] then 
+    if Product( Size2d(K) ) = ids[1][1] then 
         return [ IdentityMapping( C ) ]; 
     fi; 
     qmor := QuotientQuasiIsomorphism( C, show ); 

lib/gp2obj.gd

@@ -17,6 +17,12 @@ DeclareProperty( "IsPreCat1Domain", Is2DimensionalDomain );
 InstallTrueMethod( Is2DimensionalDomain, IsPreXModDomain );
 InstallTrueMethod( Is2DimensionalDomain, IsPreCat1Domain );
 
+#############################################################################
+## 
+#A  Size2d( <obj> ) 
+##
+DeclareAttribute( "Size2d", Is2DimensionalDomain ); 
+
 #############################################################################
 ##
 #R  IsPreXModObj( <obj> )