Merge pull request #233 from mohamed-barakat/devel

d&i CategoryFromNerveData/DataTables using IndicesOfGeneratingMorphisms

Author: mohamed-barakat

PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "Algebroids",
 Subtitle := "Algebroids and bialgebroids as preadditive categories generated by enhanced quivers",
-Version := "2022.12-26",
+Version := "2022.12-29",
 
 Date := ~.Version{[ 1 .. 10 ]},
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),

examples/CategoryFromDataTables.g

@@ -6,17 +6,16 @@ LoadPackage( "Algebroids" );
 Delta1 := SimplicialCategoryTruncatedInDegree( 1 );
 #! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
 #! / [ s*id = C0, t*id = C0 ]
-C := CategoryFromDataTables( Name( Delta1 ),
-             RangeCategoryOfHomomorphismStructure( Delta1 ),
-             DataTablesOfCategory( Delta1 ),
-             [ 1, 2, 3 ],
-             [ [ "C0", "C1" ],
-               [ "id", "s", "t" ] ] );
+C := CategoryFromDataTables( Delta1 );
 #! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
 #! / [ s*id = C0, t*id = C0 ]
 NerveTruncatedInDegree2Data( Delta1 ) = NerveTruncatedInDegree2Data( C );
 #! true
-InfoOfInstalledOperationsOfCategory( C );
+Display( C );
+#! A CAP category with name
+#! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
+#! / [ s*id = C0, t*id = C0 ]:
+#! 
 #! 16 primitive operations were used to derive 50 operations for this category
 #! which algorithmically
 #! * IsEquippedWithHomomorphismStructure

examples/CategoryFromNerveData.g

@@ -9,13 +9,16 @@ Delta1 := SimplicialCategoryTruncatedInDegree( 1 );
 N1 := NerveTruncatedInDegree2Data( Delta1 );;
 N1[1];
 #! [ |2|, |7|, |26| ]
-C := CategoryFromNerveData( Name( Delta1 ), N1,
-             [ 1, 2, 3 ], [ [ "C0", "C1" ], [ "id", "s", "t" ] ] );
+C := CategoryFromNerveData( Delta1 );
 #! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
 #! / [ s*id = C0, t*id = C0 ]
 NerveTruncatedInDegree2Data( C ) = N1;
 #! true
-InfoOfInstalledOperationsOfCategory( C );
+Display( C );
+#! A CAP category with name
+#! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
+#! / [ s*id = C0, t*id = C0 ]:
+#! 
 #! 16 primitive operations were used to derive 50 operations for this category
 #! which algorithmically
 #! * IsEquippedWithHomomorphismStructure

gap/CategoryFromDataTables.gd

@@ -182,13 +182,17 @@ DeclareAttribute( "OppositeCategoryFromDataTables",
 ####################################
 
 #! @Description
-#!  Construct a <A>V</A>-enriched category with name <A>str</A> from the given <A>data_tables</A>.
+#!  Construct a <A>V</A>-enriched category with name <A>str</A> from the given <A>data_tables</A> (of a f.p. category <A>C</A>).
 #! @Arguments str, V, data_tables, indices_of_generating_morphisms, labels
 #! @Returns a &CAP; category
 DeclareOperation( "CategoryFromDataTables",
         [ IsString, IsCapCategory, IsList, IsList, IsList ] );
 #! @InsertChunk CategoryFromDataTables
 
+#! @Arguments C
+DeclareAttribute( "CategoryFromDataTables",
+        IsFpCategory );
+
 #! @Description
 #!  Construct the <A>o</A>-th object in the category <A>C</A> created from data tables.
 #! @Arguments C, o

gap/CategoryFromDataTables.gi

@@ -258,6 +258,22 @@ InstallMethod( CategoryFromDataTables,
 
 end );
 
+##
+InstallMethod( CategoryFromDataTables,
+        "for a f.p. category",
+        [ IsFpCategory ],
+        
+  function( C )
+    
+    return CategoryFromDataTables( Name( C ),
+                   RangeCategoryOfHomomorphismStructure( C ),
+                   DataTablesOfCategory( C ),
+                   IndicesOfGeneratingMorphisms( C ),
+                   [ List( SetOfObjects( C ), Label ),
+                     List( SetOfGeneratingMorphisms( C ), Label ) ] );
+    
+end );
+
 ##
 InstallMethodForCompilerForCAP( CreateObject,
         "for a category from data tables and an integer",

gap/CategoryFromNerveData.gd

@@ -167,13 +167,17 @@ DeclareAttribute( "OppositeCategoryFromNerveData",
 ####################################
 
 #! @Description
-#!  Construct a category with name <A>str</A> from the given <A>nerve_data</A>.
+#!  Construct a category with name <A>str</A> from the given <A>nerve_data</A> (of a f.p. category <A>C</A>).
 #! @Arguments str, nerve_data, indices_of_generating_morphisms, labels
 #! @Returns a &CAP; category
 DeclareOperation( "CategoryFromNerveData",
         [ IsString, IsList, IsList, IsList ] );
 #! @InsertChunk CategoryFromNerveData
 
+#! @Arguments C
+DeclareAttribute( "CategoryFromNerveData",
+        IsFpCategory );
+
 #! @Description
 #!  Construct the <A>o</A>-th object in the category <A>C</A> created from nerve data.
 #! @Arguments C, o

gap/CategoryFromNerveData.gi

@@ -476,6 +476,21 @@ InstallMethod( CategoryFromNerveData,
 
 end );
 
+##
+InstallMethod( CategoryFromNerveData,
+        "for a f.p. category",
+        [ IsFpCategory ],
+        
+  function( C )
+    
+    return CategoryFromNerveData( Name( C ),
+                   NerveTruncatedInDegree2Data( C ),
+                   IndicesOfGeneratingMorphisms( C ),
+                   [ List( SetOfObjects( C ), Label ),
+                     List( SetOfGeneratingMorphisms( C ), Label ) ] );
+    
+end );
+
 ##
 InstallMethod( CreateObject,
         "for a category from nerve data and an integer",

gap/FpCategories.gd

@@ -210,6 +210,9 @@ DeclareOperation( "SetOfGeneratingMorphisms",
 DeclareOperation( "SetOfGeneratingMorphisms",
         [ IsFpCategory, IsInt, IsInt ] );
 
+DeclareAttribute( "IndicesOfGeneratingMorphisms",
+        IsFpCategory );
+
 #! @Description
 #!  Assigns the generating morphisms of the finitely presented category <A>C</A> to global variables.
 #!  Names of the variables are the concatenation of <A>label</A> with the names of the defining arrows.
@@ -226,6 +229,9 @@ DeclareOperation( "AssignSetOfGeneratingMorphisms",
 DeclareAttribute( "RelationsOfFpCategory",
         IsFpCategory );
 
+DeclareAttribute( "RelationsOfFpCategoryData",
+        IsFpCategory );
+
 #! @Description
 #!  The finitely presented category defined by the opposite of the underlying quiver with relations.
 #! @Arguments C

gap/FpCategories.gi

@@ -159,6 +159,80 @@ InstallOtherMethod( AssignSetOfGeneratingMorphisms,
 
 end );
 
+##
+InstallMethod( RelationsOfFpCategoryData,
+        "for a f.p. category",
+        [ IsFpCategory ],
+        
+  function( C )
+    local relations, objs, mors, func;
+    
+    relations := RelationsOfFpCategory( C );
+    
+    if IsEmpty( relations ) then
+        return [ ];
+    fi;
+    
+    Assert( 0, IsQuotientOfPathAlgebra( UnderlyingQuiverAlgebra( C ) ) );
+    
+    objs := List( SetOfObjects( C ), UnderlyingVertex );
+    
+    mors := List( SetOfGeneratingMorphisms( C ), p -> BasisPathOfPathAlgebraBasisElement( UnderlyingQuiverAlgebraElement( p ) ) );
+    
+    func :=
+      function( path )
+        if IsQuiverVertex( path ) then
+            return [ ];
+        fi;
+        
+        return List( ArrowList( path ), g -> 1 + SafePosition( mors, g ) );
+    end;
+    
+    return List( relations, pair -> Pair( func( pair[1] ), func( pair[2] ) ) );
+    
+end );
+
+##
+InstallMethod( IndicesOfGeneratingMorphisms,
+        "for a f.p. category",
+        [ IsFpCategory ],
+        
+  function( C )
+    local V, C0, N0, D00, N0N0, p21, p22, C1, T, st, mors;
+    
+    V := RangeCategoryOfHomomorphismStructure( C );
+    
+    C0 := SetOfObjects( C );
+    N0 := FinSet( V, Length( C0 ) );
+    
+    D00 := [ N0, N0 ];
+    
+    ## N0 × N0 -> N0
+    p21 := ProjectionInFactorOfDirectProduct( V, D00, 1 );
+    p22 := ProjectionInFactorOfDirectProduct( V, D00, 2 );
+    
+    C1 := List( DirectProduct( V, D00 ), i ->
+                HomomorphismStructureOnObjects( C,
+                        C0[1 + AsList( p21 )[1 + i]],
+                        C0[1 + AsList( p22 )[1 + i]] ) );
+    
+    T := DistinguishedObjectOfHomomorphismStructure( C );
+    
+    st := List( DefiningPairOfUnderlyingQuiver( C )[2], pair ->
+                UniversalMorphismIntoDirectProduct( V,
+                        D00,
+                        T,
+                        [ MapOfFinSets( V, T, [ pair[1] ], N0 ),
+                          MapOfFinSets( V, T, [ pair[2] ], N0 ) ] ) );
+
+    mors := SetOfGeneratingMorphisms( C );
+    
+    return List( [ 1 .. Length( st ) ], i ->
+                 Sum( C1{[ 1 .. AsList( st[i] )[1 + 0] ]}, Length ) +
+                 AsList( InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure( C, mors[i] ) )[1 + 0] );
+    
+end );
+
 ##
 InstallMethod( DataTablesOfCategory,
         "for a f.p. category",
@@ -391,15 +465,8 @@ InstallMethod( BasisPathOfPathAlgebraBasisElement,
         [ IsQuotientOfPathAlgebraElement ],
 
   function( basis_element )
-    local representative, paths;
-    
-    representative := Representative( basis_element );
-    
-    paths := Paths( representative );
 
-    Assert( 0, Length( paths ) = 1 and Coefficients( representative ) = [ 1 ] );
-    
-    return paths[1];
+    return BasisPathOfPathAlgebraBasisElement( Representative( basis_element ) );
 
 end );