made ProjectionInFactorOfDirectProductWithGivenDirectProduct 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 := "2021.12-04",
+Version := "2021.12-05",
 
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),
 License := "GPL-2.0-or-later",

examples/PrecompileCategoryOfSkeletalFinSets.g

@@ -25,7 +25,6 @@ CapJitPrecompileCategoryAndCompareResult(
             uncompiled_SkeletalFinSets
         ),
         [
-            "ProjectionInFactorOfDirectProduct", # uses CAP prepare functions
             "UniversalMorphismIntoDirectProduct", # uses CAP prepare functions
         ]
     )

gap/SkeletalFinSetsForCAP.gi

@@ -528,32 +528,19 @@ AddDirectProduct( SkeletalFinSets,
 end );
 
 ##
-AddProjectionInFactorOfDirectProduct( SkeletalFinSets, CAPOperationPrepareFunction( "ProjectionInFactorOfBinaryDirectProductToProjectionInFactorOfDirectProduct", SkeletalFinSets, function ( cat, M, N, pos )
-    local S, T, n, imgs, i;
+AddProjectionInFactorOfDirectProductWithGivenDirectProduct( SkeletalFinSets,
+  function ( cat, D, k, P )
+    local T, l, a;
 
-    S := DirectProduct( [ M, N ] );
-    if pos = 1 then
-        T := M;
-    else
-        T := N;
-    fi;
+    T := D[k];
 
-    n := Length( N );
+    l := Length( T );
 
-    imgs := [ ];
-
-    for i in AsList( S ) do
-        if pos = 2 then
-            Add( imgs, (i - 1) mod n );
-        else
-            Add( imgs, Int( (i - 1) / n ) );
-        fi;
-    od;
+    a := Product( D{[ k + 1 .. Length( D ) ]}, M -> Length( M ) );
 
-    imgs := List( imgs, img -> img + 1 );
-
-    return MapOfFinSets( S, imgs, T );
-end ) );
+    return MapOfFinSets( P, List( [ 0 .. Length( P ) - 1 ], i -> 1 + RemInt( QuoInt( i, a ), l ) ), T );
+    
+end );
 
 ##
 AddUniversalMorphismIntoDirectProduct( SkeletalFinSets, CAPOperationPrepareFunction( "UniversalMorphismIntoBinaryDirectProductToUniversalMorphismIntoDirectProduct", SkeletalFinSets, function ( cat, tau1, tau2 )

gap/precompiled_categories/CategoryOfSkeletalFinSetsPrecompiled.gi

@@ -634,6 +634,25 @@ end
 
     , 100 );
 
+    ##
+    AddProjectionInFactorOfDirectProductWithGivenDirectProduct( cat,
+        
+########
+function ( cat_1, objects_1, k_1, P_1 )
+    local hoisted_1_1, hoisted_2_1, deduped_3_1;
+    deduped_3_1 := objects_1[k_1];
+    hoisted_2_1 := Length( deduped_3_1 );
+    hoisted_1_1 := Product( objects_1{[ k_1 + 1 .. Length( objects_1 ) ]}, function ( M_2 )
+            return Length( M_2 );
+        end );
+    return MapOfFinSets( P_1, List( [ 0 .. Length( P_1 ) - 1 ], function ( i_2 )
+              return 1 + REM_INT( QUO_INT( i_2, hoisted_1_1 ), hoisted_2_1 );
+          end ), deduped_3_1 );
+end
+########
+        
+    , 100 );
+    
     ##
     AddProjectionOntoCoequalizerWithGivenCoequalizer( cat,