made UniversalMorphismIntoDirectProductWithGivenDirectProduct purely functional

for SkeletalFinSets

Author: mohamed-barakat

PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "FinSetsForCAP",
 Subtitle := "The elementary topos of (skeletal) finite sets",
-Version := "2021.12-05",
+Version := "2021.12-06",
 
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),
 License := "GPL-2.0-or-later",

examples/PrecompileCategoryOfSkeletalFinSets.g

@@ -12,22 +12,12 @@ given_arguments := [ ];;
 compiled_category_name := "CategoryOfSkeletalFinSetsPrecompiled";;
 package_name := "FinSetsForCAP";;
 
-uncompiled_SkeletalFinSets :=
-    CategoryOfSkeletalFinSets( : no_precompiled_code := true );;
-
 CapJitPrecompileCategoryAndCompareResult(
     category_constructor,
     given_arguments,
     package_name,
     compiled_category_name
-    : operations := Difference(
-        ListPrimitivelyInstalledOperationsOfCategory(
-            uncompiled_SkeletalFinSets
-        ),
-        [
-            "UniversalMorphismIntoDirectProduct", # uses CAP prepare functions
-        ]
-    )
+    : operations := "primitive"
 );;
 
 CategoryOfSkeletalFinSetsPrecompiled( );

gap/SkeletalFinSetsForCAP.gi

@@ -543,23 +543,21 @@ AddProjectionInFactorOfDirectProductWithGivenDirectProduct( SkeletalFinSets,
 end );
 
 ##
-AddUniversalMorphismIntoDirectProduct( SkeletalFinSets, CAPOperationPrepareFunction( "UniversalMorphismIntoBinaryDirectProductToUniversalMorphismIntoDirectProduct", SkeletalFinSets, function ( cat, tau1, tau2 )
-    local S, T, n, imgs, i;
+AddUniversalMorphismIntoDirectProductWithGivenDirectProduct( SkeletalFinSets,
+  function ( cat, D, T, tau, P )
+    local l, d, dd, taus;
 
-    S := Source( tau1 );
-    T := DirectProduct( [ Range( tau1 ), Range( tau2 ) ] );
+    l := Length( D );
 
-    n := Length( Range( tau2 ) );
+    d := List( D, x -> Length( x ) );
 
-    imgs := [ ];
+    dd := List( [ 1 .. l ], i -> Product( d{[ i + 1 .. l ]} ) );
 
-    for i in AsList( S ) do
-        Add( imgs, (AsList( tau1 )[i] - 1) * n + AsList( tau2 )[i] );
-    od;
+    taus := List( tau, x -> AsList( x ) );
 
-    return MapOfFinSets( S, imgs, T );
+    return MapOfFinSets( T, List( AsList( T ), i -> 1 + Sum( [ 1 .. l ], j -> ( taus[j][i] - 1 ) * dd[j] ) ), P );
 
-end ) );
+end );
 
 ##
 AddEqualizer( SkeletalFinSets,

gap/precompiled_categories/CategoryOfSkeletalFinSetsPrecompiled.gi

@@ -746,6 +746,35 @@ end
 
     , 100 );
 
+    ##
+    AddUniversalMorphismIntoDirectProductWithGivenDirectProduct( cat,
+        
+########
+function ( cat_1, objects_1, T_1, tau_1, P_1 )
+    local hoisted_1_1, hoisted_2_1, hoisted_3_1, hoisted_4_1, hoisted_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := Length( objects_1 );
+    deduped_6_1 := [ 1 .. deduped_7_1 ];
+    hoisted_5_1 := deduped_6_1;
+    hoisted_3_1 := List( objects_1, function ( x_2 )
+            return Length( x_2 );
+        end );
+    hoisted_2_1 := deduped_7_1;
+    hoisted_4_1 := List( deduped_6_1, function ( i_2 )
+            return Product( hoisted_3_1{[ i_2 + 1 .. hoisted_2_1 ]} );
+        end );
+    hoisted_1_1 := List( tau_1, function ( x_2 )
+            return AsList( x_2 );
+        end );
+    return MapOfFinSets( T_1, List( AsList( T_1 ), function ( i_2 )
+              return 1 + Sum( hoisted_5_1, function ( j_3 )
+                        return (hoisted_1_1[j_3][i_2] - 1) * hoisted_4_1[j_3];
+                    end );
+          end ), P_1 );
+end
+########
+        
+    , 100 );
+    
     ##
     AddUniversalMorphismIntoEqualizerWithGivenEqualizer( cat,