Move operations to compile

and compile IsEqualForObjects and PreCompose

Author: Tom Kuhmichel

CompilerForCAP/examples/PrecompileModulePresentationsAsFreydCategoryOfCategoryOfRowsOrColumns.g

@@ -19,52 +19,52 @@ EEE := KoszulDualRing( QQxy * "a,b" );;
 operations_for_arbitrary_ring := [
     "AdditionForMorphisms",
     "AdditiveInverseForMorphisms",
-    #"AssociatorLeftToRightWithGivenTensorProducts",
-    #"AssociatorRightToLeftWithGivenTensorProducts",
-    #"BraidingWithGivenTensorProducts",
-    #"CoevaluationMorphismWithGivenRange",
     "CokernelColiftWithGivenCokernelObject",
     "CokernelProjection",
-    #"Colift",
-    #"ColiftOrFail",
     "DirectSum",
     "EpimorphismFromSomeProjectiveObject",
-    #"EvaluationMorphismWithGivenSource",
     "IdentityMorphism",
     "InjectionOfCofactorOfDirectSumWithGivenDirectSum",
-    #"InternalHomOnMorphismsWithGivenInternalHoms",
-    #"InternalHomOnObjects",
-    #"IsColiftable",
     "IsCongruentForMorphisms",
     "IsEqualForMorphisms",
-    #"IsEqualForObjects",
-    #"IsLiftable",
+    "IsEqualForObjects",
     #"IsWellDefinedForMorphisms",
     #"IsWellDefinedForObjects",
     "IsZeroForMorphisms",
     #"KernelEmbedding",
-    #"LeftUnitorWithGivenTensorProduct",
-    #"Lift",
     #"LiftAlongMonomorphism",
-    #"LiftOrFail",
-    #"MultiplyWithElementOfCommutativeRingForMorphisms",
-    #"PreCompose",
+    "PreCompose",
     "ProjectionInFactorOfDirectSumWithGivenDirectSum",
-    #"RightUnitorWithGivenTensorProduct",
-    #"TensorProductOnMorphismsWithGivenTensorProducts",
-    #"TensorProductOnObjects",
-    #"TensorUnit",
     "UniversalMorphismFromDirectSumWithGivenDirectSum",
     "UniversalMorphismFromZeroObjectWithGivenZeroObject",
     "UniversalMorphismIntoDirectSumWithGivenDirectSum",
     "UniversalMorphismIntoZeroObjectWithGivenZeroObject",
     "ZeroMorphism",
-    "ZeroObject" 
+    "ZeroObject",
 ];;
 
 operations_for_commutative_ring := Concatenation(
     operations_for_arbitrary_ring,
-    [ "MultiplyWithElementOfCommutativeRingForMorphisms" ]
+    [ #"AssociatorLeftToRightWithGivenTensorProducts",
+      #"AssociatorRightToLeftWithGivenTensorProducts",
+      #"BraidingWithGivenTensorProducts",
+      #"CoevaluationMorphismWithGivenRange",
+      #"Colift",
+      #"ColiftOrFail",
+      #"EvaluationMorphismWithGivenSource",
+      #"InternalHomOnMorphismsWithGivenInternalHoms",
+      #"InternalHomOnObjects",
+      #"IsColiftable",
+      #"IsLiftable",
+      #"LeftUnitorWithGivenTensorProduct",
+      #"Lift",
+      #"LiftOrFail",
+      "MultiplyWithElementOfCommutativeRingForMorphisms",
+      #"RightUnitorWithGivenTensorProduct",
+      #"TensorProductOnMorphismsWithGivenTensorProducts",
+      #"TensorProductOnObjects",
+      #"TensorUnit",
+    ]
 );;
 
 precompile_LeftPresentations := function( ring, name, operations )

ModulePresentationsForCAP/gap/ModulePresentationsForCAP.gi

@@ -227,9 +227,6 @@ InstallGlobalFunction( ADD_FUNCTIONS_FOR_LEFT_PRESENTATION,
     # has special cases
     ADD_PRECOMPOSE_LEFT( category );
 
-    # simpler than the compiled version
-    ADD_EQUAL_FOR_OBJECTS( category );
-    
     # IsWellDefined* should not be compiled
     ADD_IS_WELL_DEFINED_FOR_OBJECTS( category );
 
@@ -274,8 +271,6 @@ InstallGlobalFunction( ADD_FUNCTIONS_FOR_RIGHT_PRESENTATION,
 
     ADD_PRECOMPOSE_RIGHT( category );
 
-    ADD_EQUAL_FOR_OBJECTS( category );
-    
     ADD_IS_WELL_DEFINED_FOR_OBJECTS( category );
 
     ADD_IS_WELL_DEFINED_FOR_MORPHISM_RIGHT( category );
@@ -394,21 +389,6 @@ InstallGlobalFunction( ADD_IS_WELL_DEFINED_FOR_MORPHISM_RIGHT,
 
 end );
 
-##
-InstallGlobalFunction( ADD_EQUAL_FOR_OBJECTS,
-                       
-  function( category )
-    
-    AddIsEqualForObjects( category,
-                   
-      function( cat, object1, object2 )
-        
-        return UnderlyingMatrix( object1 ) = UnderlyingMatrix( object2 );
-        
-    end );
-    
-end );
-
 ##
 InstallGlobalFunction( ADD_KERNEL_LEFT,
 
@@ -510,12 +490,6 @@ InstallGlobalFunction( ADD_PRECOMPOSE_LEFT,
     AddPreCompose( category,
 
       [ 
-        [ function( cat, left_morphism, right_morphism )
-            
-            return PresentationMorphism( Source( left_morphism ), UnderlyingMatrix( left_morphism ) * UnderlyingMatrix( right_morphism ), Range( right_morphism ) );
-            
-          end, [ ] ],
-        
         [ function( cat, left_morphism, identity_morphism )
 
             return left_morphism;
@@ -560,13 +534,6 @@ InstallGlobalFunction( ADD_PRECOMPOSE_RIGHT,
     AddPreCompose( category,
 
       [ 
-        
-        [ function( cat, left_morphism, right_morphism )
-          
-          return PresentationMorphism( Source( left_morphism ), UnderlyingMatrix( right_morphism ) * UnderlyingMatrix( left_morphism ), Range( right_morphism ) );
-          
-          end, [ ] ],
-        
         [ function( cat, left_morphism, identity_morphism )
 
             return left_morphism;

ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfArbitraryRingPrecompiled.gi

@@ -129,6 +129,25 @@ end
 
     , 100 );
 
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) and NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
 
@@ -140,6 +159,17 @@ end
 
     , 100 );
 
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( alpha_1 ) * UnderlyingMatrix( beta_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
 

ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfCommutativeRingPrecompiled.gi

@@ -129,6 +129,25 @@ end
 
     , 100 );
 
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) and NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
 
@@ -140,6 +159,17 @@ end
 
     , 100 );
 
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( alpha_1 ) * UnderlyingMatrix( beta_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
 

ModulePresentationsForCAP/gap/precompiled_categories/LeftPresentationsAsFreydCategoryOfCategoryOfRowsOfFieldPrecompiled.gi

@@ -129,6 +129,25 @@ end
 
     , 100 );
 
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) and NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
 
@@ -140,6 +159,17 @@ end
 
     , 100 );
 
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( alpha_1 ) * UnderlyingMatrix( beta_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
 

ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfArbitraryRingPrecompiled.gi

@@ -129,6 +129,25 @@ end
 
     , 100 );
 
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) and NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
 
@@ -140,6 +159,17 @@ end
 
     , 100 );
 
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( beta_1 ) * UnderlyingMatrix( alpha_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,
 

ModulePresentationsForCAP/gap/precompiled_categories/RightPresentationsAsFreydCategoryOfCategoryOfColumnsOfCommutativeRingPrecompiled.gi

@@ -129,6 +129,25 @@ end
 
     , 100 );
 
+    ##
+    AddIsEqualForObjects( cat,
+        
+########
+function ( cat_1, arg2_1, arg3_1 )
+    local deduped_1_1, deduped_2_1;
+    deduped_2_1 := UnderlyingMatrix( arg3_1 );
+    deduped_1_1 := UnderlyingMatrix( arg2_1 );
+    if NumberColumns( deduped_1_1 ) = NumberColumns( deduped_2_1 ) and NumberRows( deduped_1_1 ) = NumberRows( deduped_2_1 ) then
+        return deduped_1_1 = deduped_2_1;
+    else
+        return false;
+    fi;
+    return;
+end
+########
+        
+    , 100 );
+    
     ##
     AddIsZeroForMorphisms( cat,
 
@@ -140,6 +159,17 @@ end
 
     , 100 );
 
+    ##
+    AddPreCompose( cat,
+        
+########
+function ( cat_1, alpha_1, beta_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, Source( alpha_1 ), Range( beta_1 ), UnderlyingMatrix, UnderlyingMatrix( beta_1 ) * UnderlyingMatrix( alpha_1 ) );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionInFactorOfDirectSumWithGivenDirectSum( cat,