made CartesianEvaluationMorphismWithGivenSource 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 := "2021.12-03",
+Version := "2021.12-04",
 
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),
 License := "GPL-2.0-or-later",

gap/SkeletalFinSetsForCAP.gi

@@ -847,13 +847,12 @@ end );
 ##
 AddCartesianEvaluationMorphismWithGivenSource( SkeletalFinSets,
   function ( cat, M, N, HM_NxM )
-    local HM_N, m;
+    local m, n;
 
     m := Length( M );
+    n := Length( N );
 
-    HM_N := List( Tuples( AsList( N ), m ), x -> MapOfFinSets( M, x, N ) );
-    
-    return MapOfFinSets( HM_NxM, List( Cartesian( HM_N, AsList( M ) ), fx -> fx[1](fx[2]) ), N );
+    return MapOfFinSets( HM_NxM, List( [ 0 .. Length( HM_NxM ) - 1 ], i -> 1 + RemInt( QuoInt( QuoInt( i, m ), n^(m - RemInt( i, m ) - 1 ) ), n ) ), N );
 
 end );
 

gap/precompiled_categories/CategoryOfSkeletalFinSetsPrecompiled.gi

@@ -27,10 +27,11 @@ end
 
 ########
 function ( cat_1, a_1, b_1, s_1 )
-    return MapOfFinSets( s_1, List( Cartesian( List( Tuples( AsList( b_1 ), Length( a_1 ) ), function ( x_2 )
-                  return MapOfFinSets( a_1, x_2, b_1 );
-              end ), AsList( a_1 ) ), function ( fx_2 )
-              return fx_2[1]( fx_2[2] );
+    local hoisted_1_1, hoisted_2_1;
+    hoisted_2_1 := Length( b_1 );
+    hoisted_1_1 := Length( a_1 );
+    return MapOfFinSets( s_1, List( [ 0 .. Length( s_1 ) - 1 ], function ( i_2 )
+              return 1 + REM_INT( QUO_INT( QUO_INT( i_2, hoisted_1_1 ), hoisted_2_1 ^ (hoisted_1_1 - REM_INT( i_2, hoisted_1_1 ) - 1) ), hoisted_2_1 );
           end ), b_1 );
 end
 ########