3 The colors in the IntPic package
  
  The idea in what concerns the colors is the following: the reader is free to
  choose  his  colors  (taking  into  account that the latex xcolor package is
  used),  but  we  try  to  make  users life reasonably easy. He is allowed to
  choose tones. The default colors used by IntPic are not many, although (from
  our experience) sufficient for most examples.
  
  
  3.1 Colors by tones
  
  The colors are divided by tones.
  
    red  
    gap> IP_ColorsRedTones; #red
    [ "red", "red!50", "red!20", "red!80!green!50", "red!80!blue!60" ]
  
  
    green  
    gap> IP_ColorsGreenTones; #green
    [ "green", "green!50", "green!20", "green!80!red!50", "green!80!blue!60" ]
  
  
    blue  
    gap> IP_ColorsBlueTones; #blue
    [ "blue", "blue!50", "blue!20", "blue!80!red!50", "blue!80!green!60" ]
  
  
    cyan  
    gap> IP_ColorsCompRedTones; # cyan (complement of red)
    [ "-red", "-red!50", "-red!20", "-red!80!green!50", "-red!80!blue!60" ]
  
  
    magenta  
    gap> IP_ColorsCompGreenTones; # magenta (complement of green)
    [ "-green", "-green!50", "-green!20", "-green!80!red!50", "-green!80!blue!60" 
     ]
  
  
    yellow  
    gap> IP_ColorsCompBlueTones; # yellow (complement of blue)
    [ "-blue", "-blue!50", "-blue!20", "-blue!80!red!50", "-blue!80!green!60" ]
  
  
    dark gray  
    gap> IP_ColorsDGrayTones; # dark gray
    [ "black!80", "black!70", "black!60", "black!50", "black!40" ]
  
  
    light gray  
    gap> IP_ColorsLGrayTones; # light gray
    [ "black!30", "black!25", "black!20", "black!15", "black!10" ]
  
  
  
  3.2 Lists of colors
  
    array of colors by tones  
    gap> ListsOfIP_Colors;
    [ [ "red", "red!50", "red!20", "red!80!green!50", "red!80!blue!60" ], 
      [ "green", "green!50", "green!20", "green!80!red!50", "green!80!blue!60" ], 
      [ "blue", "blue!50", "blue!20", "blue!80!red!50", "blue!80!green!60" ], 
      [ "-red", "-red!50", "-red!20", "-red!80!green!50", "-red!80!blue!60" ], 
      [ "-green", "-green!50", "-green!20", "-green!80!red!50", 
          "-green!80!blue!60" ], 
      [ "-blue", "-blue!50", "-blue!20", "-blue!80!red!50", "-blue!80!green!60" ],
      [ "black!80", "black!70", "black!60", "black!50", "black!40" ], 
      [ "black!30", "black!25", "black!20", "black!15", "black!10" ] ]
  
  
    list of colors by tones  
    gap> IP_Colors;
    [ "red", "red!50", "red!20", "red!80!green!50", "red!80!blue!60", "green", 
      "green!50", "green!20", "green!80!red!50", "green!80!blue!60", "blue", 
      "blue!50", "blue!20", "blue!80!red!50", "blue!80!green!60", "-red", 
      "-red!50", "-red!20", "-red!80!green!50", "-red!80!blue!60", "-green", 
      "-green!50", "-green!20", "-green!80!red!50", "-green!80!blue!60", "-blue", 
      "-blue!50", "-blue!20", "-blue!80!red!50", "-blue!80!green!60", "black!80", 
      "black!70", "black!60", "black!50", "black!40", "black!30", "black!25", 
      "black!20", "black!15", "black!10" ]
  
  
  
  3.3 The IntPic default list of colors
  
  The  colors  are  shuffled  by  concatenating  the  transposed of the matrix
  ListsOfIP_Colors. The list obtained is taken as the default list of colors.
  
    default list of colors  
    gap> ShuffledIP_colors;
    [ "red", "green", "blue", "-red", "-green", "-blue", "black!80", "black!30", 
      "red!50", "green!50", "blue!50", "-red!50", "-green!50", "-blue!50", 
      "black!70", "black!25", "red!20", "green!20", "blue!20", "-red!20", 
      "-green!20", "-blue!20", "black!60", "black!20", "red!80!green!50", 
      "green!80!red!50", "blue!80!red!50", "-red!80!green!50", "-green!80!red!50",
      "-blue!80!red!50", "black!50", "black!15", "red!80!blue!60", 
      "green!80!blue!60", "blue!80!green!60", "-red!80!blue!60", 
      "-green!80!blue!60", "-blue!80!green!60", "black!40", "black!10" ]
  
  
  These  are the IntPic default colors. Although the user is free to use other
  colors,  we  warn that there is a need of compatibility with the colors used
  in  other  packages  (the  LaTeX  xcolor,  for  instance).  To emphasize the
  integers  of  some  sets  by using some of the colors in some list of colors
  (for  instance  the default colors) one may use empty lists to force the non
  usage  of the colors whose order in the list of colors is the order of these
  empty lists in the array of integers to be emphasized.
  
    Example  
    gap> m3 := Filtered([1..40],i->i mod 3=0);
    [ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 ]
    gap> m5 := Filtered([1..40],i->i mod 5=0);
    [ 5, 10, 15, 20, 25, 30, 35, 40 ]
    gap> m7 := Filtered([1..40],i->i mod 7=0);
    [ 7, 14, 21, 28, 35 ]
    gap> 
    gap> arr := [[],[],m3,[],m5,[],m7];;
    gap> tkz:=IP_TikzArrayOfIntegers([1..40],10,rec(highlights:=arr));;
  
  
  
  3.4 Functions to deal with colors
  
  For  the  moment  we  only  provide one function, which shuffles colors from
  lists of colors.
  
  
  3.4-1 Shuffle colors from lists of colors
  
  ShuffleIP_Colors( mat )  function
  
  The argument mat is a list of lists of colors of the same length. The output
  is obtained by concatenating the transposed of mat.
  
    Example  
    gap> ShuffleIP_Colors([IP_ColorsRedTones,IP_ColorsCompBlueTones]);
    [ "red", "-blue", "red!50", "-blue!50", "red!20", "-blue!20", 
      "red!80!green!50", "-blue!80!red!50", "red!80!blue!60", "-blue!80!green!60" 
     ]