# Search for a Hadamard difference set
# Read("ShiftProcedures_2007.txt");
# Ken Smith
# June 23, 2007

############################################################
# Shift Procedures
############################################################

 ShiftLeft := function( list, shift )
 local length, list2, i, x;
   length := Size(list);
   list2 := ShallowCopy(list);
   for i in [1..length] do
     x := (shift+i-1) mod length; 
     list2[i] := list[x+1];
   od;
   return list2;
 end;

 ShiftLeft_2D := function( list, shift )
 local length, list2, x;
    # We shift b2, which requires shifting all the entries in b2.
     list2 := [ ];  
     for x in list do
       Add( list2, ShiftLeft(x, shift ) );
     od;
   return list2;
 end;


 ShiftLeft_3D := function( list, shift )
 local length, list2, x;
    # We shift b2, which requires shifting all the entries in b2.
     list2 := [ ];  
     for x in list do
       Add( list2, ShiftLeft_2D(x, shift ) );
     od;
   return list2;
 end;

 # I tried to create a faster subroutine, but this is 
 # about the same timing as ShiftLeft_3D...
 ShiftLeft_3D_new := function( list, shift )
 local length, list2, list3, x;
    # We shift b2, which requires shifting all the entries in b2.
     list2 := [ ];  
     for x in list do  # x is a list of lists
       list3 := [ ];
       for y in x do  # y  is a list
         Add( list3, ShiftLeft(y, shift ) );
       od;
       Add( list2, list3 );
     od;
   return list2;
 end;

DemoFlag := 0; # Don't demo.  Change this to 1 if you want to see the demos.
if DemoFlag = 1 then

# Demo
list := [1,2,3,4,5,6,7,8,9,10,11];
Print("\nWe demo ShiftLeft: \n");
Print("Here is a list \n", list,"\nand here is ShiftLeft( list, 2 ):\n", ShiftLeft(list,2),"\n");
Sleep(3);

# Demo
 listlist := [[1,2,3,4,5,6,7,8,9,10,11],[1,2,3,2,1,2,1,2,1,2,1],[1,2,3,4,5,6,7,8,9,10,11]];
 Print("\nWe demo ShiftLeft_2D: \n");
 Print("Here is a list of lists \n", listlist,"\nand here is ShiftLeft_2D( listlist, 2 ):\n", ShiftLeft_2D(listlist,2),"\n");
 Sleep(3);

# Demo
 listlistlist := [
[[1,2,3,4,5,6,7,8,9,10,11],[1,2,3,2,1,2,1,2,1,2,1],[1,2,3,4,5,6,7,8,9,10,11]],
[[1,2,3,4,5,6,7,8,9,10,11],[9,8,7,6,5,4,3,2,1,0,-1],[1,2,3,4,5,6,7,8,9,10,11]],
[[1,2,3,4,5,6,7,8,9,10,11],[1,2,3,2,1,2,1,2,1,2,1],[1,2,3,4,5,6,7,8,9,10,11]]
];
 Print("\nWe demo ShiftLeft_3D: \n");
 Print("Here is a list of lists of lists \n", listlistlist,"\nand here is ShiftLeft_3D( listlistlist, 2 ):\n", ShiftLeft_3D(listlistlist,2),"\n");
  Sleep(3);

fi;