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%!PS-Adobe-3.0
%%Creator: Basser Lout Version 3.20 (April 2000)
%%CreationDate: Sat Apr  8 14:53:13 2000
%%DocumentData: Binary
%%DocumentNeededResources: (atend)
%%DocumentSuppliedResources: (atend)
%%DocumentMedia: A4 595 842 0 white ()
%%PageOrder: Ascend
%%Pages: (atend)
%%BoundingBox: 0 0 595 842
%%EndComments

%%BeginProlog
%%BeginResource: procset LoutStartUp
/m  { 3 1 roll moveto show } bind def
/mo { 3 1 roll moveto true charpath stroke } bind def
/s  { exch currentpoint exch pop moveto show } bind def
/so { exch currentpoint exch pop moveto true charpath stroke } bind def
/k  { exch neg 0 rmoveto show } bind def
/ko { exch neg 0 rmoveto true charpath stroke } bind def
/ul { gsave setlinewidth dup 3 1 roll
      moveto lineto stroke grestore } bind def
/in { 1440 mul } def
/cm { 567 mul } def
/pt { 20 mul } def
/em { 120 mul } def
/sp { louts mul } def
/vs { loutv mul } def
/ft { loutf mul } def
/dg {           } def

/LoutGraphic {
  /louts exch def
  /loutv exch def
  /loutf exch def
  /ymark exch def
  /xmark exch def
  /ysize exch def
  /xsize exch def
} def

/LoutGr2 { gsave translate LoutGraphic gsave } def

/LoutFont
{ findfont exch scalefont setfont
} bind def

/LoutRecode {
  { findfont dup length dict begin
    {1 index /FID ne {def} {pop pop} ifelse} forall
    /Encoding exch def
    currentdict end definefont pop
  }
  stopped pop
} bind def

/BeginEPSF {
  /LoutEPSFState save def
  /dict_count countdictstack def
  /op_count count 1 sub def
  userdict begin
  /showpage { } def
  0 setgray 0 setlinecap
  1 setlinewidth 0 setlinejoin
  10 setmiterlimit [] 0 setdash newpath
  /languagelevel where
  { pop languagelevel
    1 ne
    { false setstrokeadjust false setoverprint
    } if
  } if
} bind def

/EndEPSF {
  count op_count sub { pop } repeat
  countdictstack dict_count sub { end } repeat
  LoutEPSFState restore
} bind def
%%EndResource

%%BeginResource: encoding vec2
/vec2 [
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/quotesinglbase /quotedblbase /ellipsis /OE /oe /quotedblleft /quotedblright /fi
/fl /endash /emdash /bullet /dagger /daggerdbl /florin /fraction
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
%%EndResource

%%BeginResource: procset LoutTabPrependGraphic
% @PrependGraphic file /export/home/6monthspace/jeff/lout.lib/include/tabf.lpg
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                  %
%  PostScript @SysPrependGraphic file for @Tab     %
%                                                  %
%  To assist in avoiding name clashes, the names   %
%  of all these symbols begin with "ltab".         %
%                                                  %
%  Jeffrey H. Kingston                             %
%  24 September 1991                               %
%  22 December 1992                                %
%                                                  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% linewidth ltabhs -
% horizontal single line
/ltabhs
{  0 0 moveto xsize 0 lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabhsp -
% horizontal single line with projecting ends
/ltabhsp
{  0 0 moveto xsize 0 lineto
   setlinewidth 2 setlinecap stroke
} def

% linewidth ltabhd -
% horizontal double line
/ltabhd
{  dup dup
   0 0 moveto xsize 0 lineto
   0 exch 3 mul moveto xsize exch 3 mul lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabhdb -
% horizontal double line below mark
/ltabhdb
{  dup dup
   0 0 moveto xsize 0 lineto
   0 exch -3 mul moveto xsize exch -3 mul lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabhdnw -
% horizontal double line with northwest corner
/ltabhdnw
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   xsize exch 3 mul moveto
   -3 mul exch 3 mul lineto
   -3 mul 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabhdne -
% horizontal double line with northeast corner
/ltabhdne
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   0 exch 3 mul moveto
   3 mul xsize add exch 3 mul lineto
   3 mul xsize add 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabhdsw -
% horizontal double line with southwest corner
/ltabhdsw
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   xsize exch -3 mul moveto
   -3 mul exch -3 mul lineto
   -3 mul 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabhdse -
% horizontal double line with southeast corner
/ltabhdse
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   0 exch -3 mul moveto
   3 mul xsize add exch -3 mul lineto
   3 mul xsize add 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabvs -
% vertical single line
/ltabvs
{  0 0 moveto 0 ysize lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabvd -
% vertical double line
/ltabvd
{  dup dup
   0 0 moveto 0 ysize lineto
   -3 mul 0 moveto -3 mul ysize lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabvdr -
% vertical double line to right of mark
/ltabvdr
{  dup dup
   0 0 moveto 0 ysize lineto
   3 mul 0 moveto 3 mul ysize lineto
   setlinewidth 0 setlinecap stroke
} def
%%EndResource

%%BeginResource: procset LoutFigPrependGraphic
% @PrependGraphic file /export/home/6monthspace/jeff/lout.lib/include/figf.lpg
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                    %
%  PostScript @SysPrependGraphic file for @Fig  Jeffrey H. Kingston  %
%  Version 2.0 (includes CIRCUM label)                 January 1992  %
%                                                                    %
%  To assist in avoiding name clashes, the names of all symbols      %
%  defined here begin with "lfig".  However, this is not feasible    %
%  with user-defined labels and some labels used by users.           %
%                                                                    %
%  <point>      is two numbers, a point.                             %
%  <length>     is one number, a length                              %
%  <angle>      is one number, an angle in degrees                   %
%  <dashlength> is one number, the preferred length of a dash        %
%                                                                    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

errordict begin
   /handleerror
   {
      {  /Times-Roman findfont 8 pt scalefont setfont
	 0 setgray 4 pt 4 pt moveto
	 $error /errorname get
	 dup lfigdict exch known
	 { lfigdict exch get }
	 { 30 string cvs } ifelse
	 show
	 (  Command: ) show
	 $error /command get 30 string cvs show
      } stopped {} if
      showpage stop
   } def
end

% concat strings: <string> <string> lfigconcat <string>
% must be defined outside lfigdict since used in lfigpromotelabels
/lfigconcat
{ 2 copy length exch length add string
  dup 0 4 index putinterval
  dup 3 index length 3 index putinterval
  3 1 roll pop pop
} def

% <string> lfigdebugprint -
% must be defined outside lfigdict since used in arbitrary places
% /lfigdebugprint
% { print
%   (;  operand stack:\n) print
%   count copy
%   count 2 idiv
%   { ==
%     (\n) print
%   } repeat
%   (\n) print
% } def

/lfigdict 120 dict def
lfigdict begin

% error messages
/dictfull (dictfull error:  too many labels?) def
/dictstackoverflow (dictstackoverflow error:  labels nested too deeply?) def
/execstackoverflow (execstackoverflow error:  figure nested too deeply?) def
/limitcheck (limitcheck error:  figure nested too deeply or too large?) def
/syntaxerror (syntaxerror error:  syntax error in text of figure?) def
/typecheck (typecheck error:  syntax error in text of figure?) def
/undefined (undefined error:  unknown or misspelt label?) def
/VMError (VMError error:  run out of memory?) def

% push pi onto stack:  - lfigpi <num>
/lfigpi 3.14159 def

% arc directions
/clockwise     false def
/anticlockwise true  def

% maximum of two numbers:  <num> <num> lfigmax <num>
/lfigmax { 2 copy gt { pop } { exch pop } ifelse } def

% minimum of two numbers:  <num> <num> lfigmin <num>
/lfigmin { 2 copy lt { pop } { exch pop } ifelse } def

% add two points:  <point> <point> lfigpadd <point>
/lfigpadd { exch 3 1 roll add 3 1 roll add exch } def

% subtract first point from second:  <point> <point> lfigpsub <point>
/lfigpsub { 3 2 roll sub 3 1 roll exch sub exch } def

% max two points:  <point> <point> lfigpmax <point>
/lfigpmax { exch 3 1 roll lfigmax 3 1 roll lfigmax exch } def

% min two points:  <point> <point> lfigpmin <point>
/lfigpmin { exch 3 1 roll lfigmin 3 1 roll lfigmin exch } def

% scalar multiplication: <point> <num> lfigpmul <point>
/lfigpmul { dup 3 1 roll mul 3 1 roll mul exch } def

% point at angle and distance:  <point> <length> <angle> lfigatangle <point>
/lfigatangle { 2 copy cos mul 3 1 roll sin mul lfigpadd } def

% angle from one point to another:  <point> <point> lfigangle <angle>
/lfigangle { lfigpsub 2 copy 0 eq exch 0 eq and {pop} {exch atan} ifelse } def

% distance between two points:  <point> <point> lfigdistance <length>
/lfigdistance { lfigpsub dup mul exch dup mul add sqrt } def

% difference in x coords: <point> <point> lfigxdistance <length>
/lfigxdistance { pop 3 1 roll pop sub } def

%difference in y coords: <point> <point> lfigydistance <length>
/lfigydistance { 3 1 roll pop sub exch pop } def

% stroke a solid line:  <length> <dashlength> lfigsolid -
/lfigsolid
{  pop pop [] 0 setdash stroke
} def

% stroke a lfigdashed line:   <length> <dashlength> lfigdashed -
/lfigdashed
{  2 copy div 2 le 1 index 0 le or
   {  exch pop 1 pt lfigmax [ exch dup ] 0 setdash }
   {  dup [ exch 4 2 roll 2 copy div
      1 sub 2 div ceiling dup 4 1 roll
      1 add mul sub exch div ] 0 setdash
   } ifelse stroke
} def

% stroke a lfigcdashed line:  <length> <dashlength> lfigcdashed -
/lfigcdashed
{  2 copy le 1 index 0 le or
   { exch pop 1 pt lfigmax [ exch dup ] dup 0 get 2 div setdash }
   { dup [ 4 2 roll exch 2 copy exch div
     2 div ceiling div 1 index sub
     ] exch 2 div setdash
   } ifelse stroke
} def

% stroke a dotted line:  <length> <dashlength> lfigdotted -
/lfigdotted
{  2 copy le 1 index 0 le or
   { exch pop 1 pt lfigmax [ exch 0 exch ] 0 setdash }
   { 1 index exch div ceiling div
     [ 0 3 2 roll ] 0 setdash
   } ifelse stroke
} def

% stroke a noline line:  <length> <dashlength> lfignoline -
/lfignoline
{ pop pop
} def

% painting (i.e. filling): - lfigwhite - (etc.)
/lfignopaint		{			       } def
/lfignochange		{ 			  fill } def
/lfigdarkblue		{ 0.0 0.0 0.5 setrgbcolor fill } def
/lfigblue		{ 0.0 0.0 1.0 setrgbcolor fill } def
/lfiglightblue		{ 0.5 0.5 1.0 setrgbcolor fill } def
/lfigdarkgreen		{ 0.0 0.5 0.0 setrgbcolor fill } def
/lfiggreen		{ 0.0 1.0 0.0 setrgbcolor fill } def
/lfiglightgreen		{ 0.5 1.0 0.5 setrgbcolor fill } def
/lfigdarkred		{ 0.5 0.0 0.0 setrgbcolor fill } def
/lfigred		{ 1.0 0.0 0.0 setrgbcolor fill } def
/lfiglightred		{ 1.0 0.5 0.5 setrgbcolor fill } def
/lfigdarkcyan		{ 0.0 0.5 0.5 setrgbcolor fill } def
/lfigcyan		{ 0.0 1.0 1.0 setrgbcolor fill } def
/lfiglightcyan		{ 0.5 1.0 1.0 setrgbcolor fill } def
/lfigdarkmagenta	{ 0.5 0.0 0.5 setrgbcolor fill } def
/lfigmagenta		{ 1.0 0.0 1.0 setrgbcolor fill } def
/lfiglightmagenta	{ 1.0 0.5 1.0 setrgbcolor fill } def
/lfigdarkyellow		{ 0.5 0.5 0.0 setrgbcolor fill } def
/lfigyellow		{ 1.0 1.0 0.0 setrgbcolor fill } def
/lfiglightyellow	{ 1.0 1.0 0.5 setrgbcolor fill } def
/lfigdarkgray		{ 0.2 0.2 0.2 setrgbcolor fill } def
/lfiggray		{ 0.5 0.5 0.5 setrgbcolor fill } def
/lfiglightgray		{ 0.8 0.8 0.8 setrgbcolor fill } def
/lfigdarkgrey		{ 0.2 0.2 0.2 setrgbcolor fill } def
/lfiggrey		{ 0.5 0.5 0.5 setrgbcolor fill } def
/lfiglightgrey		{ 0.8 0.8 0.8 setrgbcolor fill } def
/lfigblack		{ 0.0 0.0 0.0 setrgbcolor fill } def
/lfigwhite		{ 1.0 1.0 1.0 setrgbcolor fill } def

% line caps (and joins, not currently used)
/lfigbutt       0 def
/lfiground      1 def
/lfigprojecting 2 def
/lfigmiter      0 def
/lfigbevel      2 def

% shape and labels of the @Box symbol
/lfigbox
{
   0     0     /SW  lfigpointdef
   xsize 0     /SE  lfigpointdef
   xsize ysize /NE  lfigpointdef
   0     ysize /NW  lfigpointdef
   SE 0.5 lfigpmul /S   lfigpointdef
   NW 0.5 lfigpmul /W   lfigpointdef
   W SE lfigpadd   /E   lfigpointdef
   S NW lfigpadd   /N   lfigpointdef
   NE 0.5 lfigpmul /CTR lfigpointdef
   [ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef
   SW SE NE NW SW
} def

% shape and labels of the @CurveBox symbol
/lfigcurvebox
{

   xsize 0.5 mul	ysize 0.5 mul	/CTR lfigpointdef
   xsize 0.5 mul	0		/S   lfigpointdef
   xsize		ysize 0.5 mul	/E   lfigpointdef
   xsize 0.5 mul	ysize		/N   lfigpointdef
   0			ysize 0.5 mul	/W   lfigpointdef

   xmark 0.293 mul		xmark 0.293 mul		  /SW  lfigpointdef
   xsize xmark 0.293 mul sub	xmark 0.293 mul		  /SE  lfigpointdef
   xsize xmark 0.293 mul sub	ysize xmark 0.293 mul sub /NE  lfigpointdef
   xmark 0.293 mul		ysize xmark 0.293 mul sub /NW  lfigpointdef

   [ xsize ysize 0.5 lfigpmul xmark /lfigcurveboxcircum cvx ] lfigcircumdef

   xmark		0
   xsize xmark sub	0
   [ xsize xmark sub	xmark		]
   xsize		xmark
   xsize		ysize xmark sub
   [ xsize xmark sub	ysize xmark sub	]
   xsize xmark sub	ysize
   xmark		ysize
   [ xmark		ysize xmark sub	]
   0			ysize xmark sub
   0			xmark
   [ xmark		xmark		]
   xmark		0
} def

% shadow of the @ShadowBox symbol
% its shape and labels are done, somewhat inaccurately, with lfigbox
/lfigshadow
{ xmark 2 mul 0 moveto xsize 0 lineto
  xsize ysize xmark 2 mul sub lineto
  xsize xmark sub ysize xmark 2 mul sub lineto
  xsize xmark sub xmark lineto
  xmark 2 mul xmark lineto closepath fill
} def

% shape and labels of the @Square symbol
/lfigsquare
{
   xsize ysize 0.5 lfigpmul /CTR lfigpointdef
   CTR xsize xsize ysize ysize lfigpmax 0.5 lfigpmul lfigpadd /NE lfigpointdef
   CTR 0 0 CTR NE lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef
   CTR 0 0 CTR NE lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef
   CTR 0 0 CTR NE lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef
   SW 0.5 lfigpmul SE 0.5 lfigpmul lfigpadd /S lfigpointdef
   NW 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /N lfigpointdef
   SW 0.5 lfigpmul NW 0.5 lfigpmul lfigpadd /W lfigpointdef
   SE 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /E lfigpointdef
   [ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef
   SW SE NE NW SW
} def

% shape and labels of the @Diamond symbol
/lfigdiamond
{
   xsize 0 0.5 lfigpmul /S   lfigpointdef
   0 ysize 0.5 lfigpmul /W   lfigpointdef
   S W         lfigpadd /CTR lfigpointdef
   CTR W       lfigpadd /N   lfigpointdef
   CTR S       lfigpadd /E   lfigpointdef
   [ xsize ysize 0.5 lfigpmul /lfigdiamondcircum cvx ] lfigcircumdef
   S E N W S
} def

% shape and labels of the @Ellipse symbol
/lfigellipse
{
   xsize 0 0.5 lfigpmul /S   lfigpointdef
   0 ysize 0.5 lfigpmul /W   lfigpointdef
   S W         lfigpadd /CTR lfigpointdef
   CTR W       lfigpadd /N   lfigpointdef
   CTR S       lfigpadd /E   lfigpointdef
   CTR xsize 0 0.3536 lfigpmul lfigpadd 0 ysize 0.3536 lfigpmul lfigpadd /NE lfigpointdef
   0 ysize 0.3536 lfigpmul CTR xsize 0 0.3536 lfigpmul lfigpadd lfigpsub /SE lfigpointdef
   xsize 0 0.3536 lfigpmul CTR lfigpsub 0 ysize 0.3536 lfigpmul lfigpadd /NW lfigpointdef
   0 ysize 0.3536 lfigpmul xsize 0 0.3536 lfigpmul CTR lfigpsub lfigpsub /SW lfigpointdef
   [ xsize ysize 0.5 lfigpmul /lfigellipsecircum cvx ] lfigcircumdef
   S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S
} def

% shape and labels of the @Circle symbol
/lfigcircle
{
   xsize ysize 0.5 lfigpmul /CTR lfigpointdef
   CTR xsize 0 ysize 0 lfigpmax 0.5 lfigpmul lfigpadd /E lfigpointdef
   CTR 0 0 CTR E lfigdistance 45 lfigatangle lfigpadd /NE lfigpointdef
   CTR 0 0 CTR E lfigdistance 90 lfigatangle lfigpadd /N lfigpointdef
   CTR 0 0 CTR E lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef
   CTR 0 0 CTR E lfigdistance 180 lfigatangle lfigpadd /W lfigpointdef
   CTR 0 0 CTR E lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef
   CTR 0 0 CTR E lfigdistance 270 lfigatangle lfigpadd /S lfigpointdef
   CTR 0 0 CTR E lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef
   [ S E lfigpsub /lfigellipsecircum cvx ] lfigcircumdef
   S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S
} def

% shape and labels of the @HLine and @HArrow symbols
/lfighline
{
   0 ymark lfigprevious /FROM lfigpointdef
   xsize ymark lfigprevious /TO lfigpointdef
} def

% shape and labels of the @VLine and @VArrow symbols
/lfigvline
{
   xmark ysize lfigprevious /FROM lfigpointdef
   xmark 0 lfigprevious /TO lfigpointdef
} def

% points of a polygon around base with given no of sides, vert init angle:
% <sides> <angle> figpolygon <point> ... <point>
/lfigpolygon
{  xsize ysize 0.5 lfigpmul /CTR lfigpointdef
   90 sub CTR 2 copy lfigmax 5 3 roll
   [ 4 copy pop /lfigpolycircum cvx ] lfigcircumdef
   exch dup 360 exch div exch
   1 1  3 2 roll
   {  4 string cvs (P) exch lfigconcat cvn
      6 copy pop pop lfigatangle 2 copy 10 2 roll
      3 2 roll lfigpointdef
      dup 3 1 roll add exch
   }  for
   pop lfigatangle
} def

% next array element:  <array> <index> lfiggetnext <array> <index> <any> true
%                                               or <array> <index> false
/lfiggetnext
{  2 copy exch length ge
   { false }
   { 2 copy get exch 1 add exch true } ifelse
} def

% check whether thing is number:  <any> lfigisnumbertype <any> <bool>
/lfigisnumbertype
{  dup type dup
   /integertype eq exch /realtype eq or
} def

% check whether thing is an array:  <any> lfigisarraytype <any> <bool>
/lfigisarraytype { dup type /arraytype eq } def

% get next item:  <array> <index> lfiggetnextitem <array> <index> 0
%                                              or <array> <index> <array> 1
%                                              or <array> <index> <point> 2
/lfiggetnextitem
{   lfiggetnext
    {	lfigisarraytype
	{   1
	}
	{   lfigisnumbertype
	    {	3 1 roll
		lfiggetnext
		{   lfigisnumbertype
		    {	4 3 roll exch  2
		    }
		    {	pop 3 2 roll pop  0
		    } ifelse
		}
		{   3 2 roll pop  0
		} ifelse
	    }
	    {	pop 0
	    } ifelse
	} ifelse
    }
    {	0
    } ifelse
} def

% set arc path:  bool x1 y1  x2 y2  x0 y0  lfigsetarc  <angle> <angle> <dist>
% the path goes from x1 y1 to x2 y2 about centre x0 y0,
% anticlockwise if bool is true else clockwise.
% The orientations of backwards pointing and forwards pointing
% arrowheads are returned in the two angles, and
% the length of the arc is returned in <dist>.
/lfigsetarc
{
  20 dict begin
     matrix currentmatrix 8 1 roll
     2 copy translate 2 copy 8 2 roll
     4 2 roll lfigpsub 6 2 roll lfigpsub
     dup /y1 exch def dup mul /y1s exch def
     dup /x1 exch def dup mul /x1s exch def
     dup /y2 exch def dup mul /y2s exch def
     dup /x2 exch def dup mul /x2s exch def

     y1s y2s eq
     {	-1
     }
     {	y1s x2s mul y2s x1s mul sub y1s y2s sub div
     } ifelse
     /da exch def

     x1s x2s eq
     {	-1
     }
     {	x1s y2s mul x2s y1s mul sub x1s x2s sub div
     } ifelse
     /db exch def

     da 0 gt db 0 gt and
     {	/LMax da sqrt db sqrt lfigmax def
	/scalex da sqrt LMax div def
	/scaley db sqrt LMax div def
	scalex scaley scale
	0 0 LMax
	0 0 x1 scalex mul y1 scaley mul lfigangle
	0 0 x2 scalex mul y2 scaley mul lfigangle
	2 copy eq { 360 add } if
	2 copy 8 2 roll
	5 index { arc } { arcn } ifelse
	2 index 1 index
	{ 90 sub } { 90 add } ifelse
	dup sin scaley mul exch cos scalex mul atan
	2 index 2 index
	{ 90 add } { 90 sub } ifelse
	dup sin scaley mul exch cos scalex mul atan
	5 2 roll  % res1 res2 ang1 ang2 anticlockwise
	{ exch sub } { sub } ifelse
	dup 0 le { 360 add } if  lfigpi mul LMax mul 180 div
     }
     {	0 0 x1 y1 lfigdistance 0 0 x2 y2 lfigdistance eq
	0 0 x1 y1 lfigdistance 0 gt and
	{	0 0
		0 0 x1 y1 lfigdistance
		0 0 x1 y1 lfigangle
		0 0 x2 y2 lfigangle
		2 copy eq { 360 add } if
		2 copy 8 2 roll
		5 index { arc } { arcn } ifelse
		2 index 1 index
		{ 90 sub } { 90 add } ifelse
		2 index 2 index
		{ 90 add } { 90 sub } ifelse
		5 2 roll % res1 res2 ang1 ang2 clockwise
		{ exch sub } { sub } ifelse
		dup 0 le { 360 add } if lfigpi mul 0 0 x1 y1 lfigdistance mul 180 div
	}
	{	x2 y2 lineto pop
		x2 y2 x1 y1 lfigangle
		x1 y1 x2 y2 lfigangle
		x1 y1 x2 y2 lfigdistance
	} ifelse
     } ifelse
     4 -1 roll setmatrix
   end
} def

% lfigsetcurve: set up a Bezier curve from x0 y0 to x3 y3
% and return arrowhead angles and length of curve (actually 0)
% x0 y0 x1 y1 x2 y2 x3 y3 lfigsetcurve <angle> <angle> <length>
/lfigsetcurve
{ 8 copy curveto pop pop
  lfigangle
  5 1 roll
  4 2 roll lfigangle
  exch
  0
} def

% lfigpaintpath: paint a path of the given shape
% /paint [ shape ] lfigpaintpath -
/lfigpaintpath
{
  10 dict begin
    0 newpath
    /prevseen false def
    /curveseen false def
    { lfiggetnextitem
      dup 0 eq { pop exit }
      { 1 eq
        { /curveseen true def
	  /curve exch def
	  curve length 0 eq { /curveseen false def } if
        }
        { /ycurr exch def
	  /xcurr exch def
	  prevseen
	  { curveseen
	    { curve length 4 eq
	      { xprev yprev
		curve 0 get curve 1 get
		curve 2 get curve 3 get
		xcurr ycurr
		lfigsetcurve pop pop pop
	      }
	      { xprev yprev xcurr ycurr
	        curve length 1 ge { curve 0 get } { 0 } ifelse
	        curve length 2 ge { curve 1 get } { 0 } ifelse
	        curve length 3 ge { curve 2 get } { true } ifelse
	        7 1 roll
	        lfigsetarc pop pop pop
	      } ifelse
	    }
	    { xcurr ycurr lineto
	    } ifelse
	  }
	  { xcurr ycurr moveto
	  } ifelse
	  /xprev xcurr def
	  /yprev ycurr def
	  /prevseen true def
	  /curveseen false def
        } ifelse
      } ifelse
    } loop pop pop cvx exec
  end
} def

% stroke a path of the given shape in the given linestyle and dash length.
% Return the origin and angle of the backward and forward arrow heads.
% dashlength /linestyle [shape] lfigdopath  [<point> <angle>] [<point> <angle>] 
/lfigdopath
{
  10 dict begin
    0
    /prevseen  false def
    /curveseen false def
    /backarrow []    def
    /fwdarrow  []    def
    {
	lfiggetnextitem
	dup 0 eq { pop exit }
	{
	    1 eq
	    {	/curveseen true def
		/curve exch def
		curve length 0 eq { /prevseen false def } if
	    }
	    {	/ycurr exch def
		/xcurr exch def
		prevseen
		{   newpath xprev yprev moveto
		    curveseen
		    {	curve length 4 eq
			{   xprev yprev
			    curve 0 get curve 1 get
			    curve 2 get curve 3 get
			    xcurr ycurr lfigsetcurve
			}
			{   xprev yprev xcurr ycurr
			    curve length 1 ge { curve 0 get } { 0 } ifelse
			    curve length 2 ge { curve 1 get } { 0 } ifelse
			    curve length 3 ge { curve 2 get } { true } ifelse
			    7 1 roll
			    lfigsetarc
			} ifelse
		    }
		    {	xcurr ycurr lineto
			xcurr ycurr xprev yprev lfigangle dup 180 sub
			xprev yprev xcurr ycurr lfigdistance
		    } ifelse
		    6 index 6 index cvx exec
		    [ xprev yprev 5 -1 roll ]
		    backarrow length 0 eq
		    { /backarrow exch def }
		    { pop } ifelse
		    [ xcurr ycurr 4 -1 roll ] /fwdarrow exch def
		} if
		/xprev xcurr def
		/yprev ycurr def
		/prevseen true def
		/curveseen false def
	    } ifelse
	} ifelse
    } loop
    pop pop pop pop
    backarrow length 0 eq { [ 0 0 0 ] } { backarrow } ifelse
    fwdarrow  length 0 eq { [ 0 0 0 ] } { fwdarrow  } ifelse
  end
} def

% lfigdoarrow: draw an arrow head of given form
% dashlength /lstyle /pstyle hfrac height width [ <point> <angle> ] lfigdoarrow -
/lfigdoarrow
{  matrix currentmatrix 8 1 roll
   dup 0 get 1 index 1 get translate
   2 get rotate
   [ 2 index neg 2 index 0 0
     3 index 3 index neg
     1 index 10 index mul 0
     7 index 7 index ]
   4 1 roll pop pop pop
   dup 3 1 roll
   gsave lfigpaintpath grestore lfigdopath pop pop
   setmatrix
} def

% arrow head styles
/lfigopen     0.0 def
/lfighalfopen 0.5 def
/lfigclosed   1.0 def

% stroke no arrows, forward, back, and both
/lfignoarrow { pop pop pop pop pop pop pop pop                        } def
/lfigforward { 7 -1 roll lfigdoarrow pop                              } def
/lfigback    { 8 -2 roll pop lfigdoarrow                              } def
/lfigboth    { 8 -1 roll 7 copy lfigdoarrow pop 7 -1 roll lfigdoarrow } def

% lfigprevious: return previous point on path
/lfigprevious
{ lfigisnumbertype
  { 2 copy }
  { lfigisarraytype
    { 2 index 2 index }
    { 0 0 }
    ifelse
  } ifelse
} def

% label a point in 2nd top dictionary:  <point> /name lfigpointdef -
/lfigpointdef
{
  % (Entering lfigpointdef) lfigdebugprint
  [ 4 2 roll transform
    /itransform cvx ] cvx
    currentdict end
    3 1 roll
    % currentdict length currentdict maxlength lt
    % { def }
    % { exec moveto (too many labels) show stop }
    % ifelse
    def
    begin
  % (Leaving lfigpointdef) lfigdebugprint
} def

% promote labels from second top to third top dictionary
% <string> lfigpromotelabels -
/lfigpromotelabels
{
  % (Entering lfigpromotelabels) lfigdebugprint
  currentdict end exch currentdict end
  { exch 20 string cvs 2 index
    (@) lfigconcat exch lfigconcat cvn exch def
  } forall pop begin
  % (Leaving lfigpromotelabels) lfigdebugprint
} def

% show labels (except CIRCUM): - lfigshowlabels -
/lfigshowlabels
{
  % (Entering lfigshowlabels) lfigdebugprint
  currentdict end
    currentdict
    { 1 index 20 string cvs (CIRCUM) search % if CIRCUM in key
      { pop pop pop pop pop }
      { pop cvx exec 2 copy
        newpath 1.5 pt 0 360 arc
        0 setgray fill
        /Times-Roman findfont 8 pt scalefont setfont
        moveto 0.2 cm 0.1 cm rmoveto 20 string cvs show
      }
      ifelse
    } forall
  begin
  % (Leaving lfigshowlabels) lfigdebugprint
} def

% fix an angle to 0 <= res < 360:  <angle> lfigfixangle <angle>
/lfigfixangle
{
  % (Entering lfigfixangle) lfigdebugprint
  { dup 0 ge { exit } if
    360 add
  } loop
  { dup 360 lt { exit } if
    360 sub
  } loop
  % (Leaving lfigfixangle) lfigdebugprint
} def

% find point on circumference of box:  alpha a b lfigboxcircum x y
/lfigboxcircum
{
  % (Entering lfigboxcircum) lfigdebugprint
  4 dict begin
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def
    0 0 a b lfigangle /theta exch def

    % if alpha <= theta, return (a, a*tan(alpha))
    alpha theta le
    { a  a alpha sin mul alpha cos div }
    {
      % else if alpha <= 180 - theta, return (b*cot(alpha), b)
      alpha 180 theta sub le
      { b alpha cos mul alpha sin div  b }
      {
        % else if alpha <= 180 + theta, return (-a, -a*tan(alpha))
        alpha 180 theta add le
        { a neg  a neg alpha sin mul alpha cos div }
        {
	  % else if alpha <= 360 - theta, return (-b*cot(alpha), -b)
	  alpha 360 theta sub le
          { b neg alpha cos mul alpha sin div  b neg }
	  {
	    % else 360 - theta <= alpha, return (a, a*tan(alpha))
	    a  a alpha sin mul alpha cos div
	  } ifelse
        } ifelse
      } ifelse
    } ifelse
  end
  % (Leaving lfigboxcircum) lfigdebugprint
} def

% find quadratic roots (assume a != 0): a b c lfigqroots x1 x2 2
%                                                     or    x2 1
%                                                     or       0
/lfigqroots
{
  4 dict begin
    /c exch def
    /b exch def
    /a exch def
    /disc b b mul 4 a c mul mul sub def
    disc 0 lt
    { 0
    }
    { disc 0 eq
      { b neg 2 a mul div
	1
      }
      { b neg disc sqrt add 2 a mul div
        b neg disc sqrt sub 2 a mul div
	2
      }
      ifelse
    }
    ifelse
  end
} def

% work our which quadrant: <angle> lfigquadrant <0-3>
/lfigquadrant
{ dup 90 lt
  { pop 0
  }
  { dup 180 lt
    { pop 1
    }
    { 270 lt
      { 2
      }
      { 3
      } ifelse
    } ifelse
  } ifelse
} def

% find curvebox circum, assuming upper right quadrant: alpha a b xmk lfigcb x y
/lfigcb
{
  6 dict begin
    /xmk exch def
    /b exch def
    /a exch def
    /alpha exch def
    /theta1 0 0 a b xmk sub lfigangle def
    /theta2 0 0 a xmk sub b lfigangle def
    alpha theta1 le
    { % if alpha <= theta1, return (a, a*tan(alpha))
      a  a alpha sin mul alpha cos div
    }
    { alpha theta2 ge
      { % else if alpha > theta2, return (b*cot(alpha), b)
	b alpha cos mul alpha sin div  b
      }
      {
	% else, return the intersection of line and circle
	a xmk sub b xmk sub xmk  0 0 alpha lfigcircleintersect
	dup 0 eq
	{ % should never happen, just return any reasonable point
	  pop
	  a b 0.5 lfigpmul
	}
	{ 1 eq
	  { % should never happen, just return the point on top of stack
	  }
	  { % the usual case, two points on stack, return the larger
	    lfigpmax
	  } ifelse
	} ifelse
      } ifelse
    } ifelse
  end
} def

% find point on circumference of curvebox: alpha a b xmk lfigcurveboxcircum x y
/lfigcurveboxcircum
{
  % (Entering lfigcurveboxcircum) lfigdebugprint
  5 dict begin
    /xmk exch def
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def

    % work out which quadrant we are in, and reflect accordingly
    /quad alpha lfigquadrant def
    quad 0 eq
    { alpha a b xmk lfigcb
    }
    { quad 1 eq
      { 180 alpha sub a b xmk lfigcb exch neg exch
      }
      { quad 2 eq
	{ alpha 180 sub a b xmk lfigcb neg exch neg exch
	}
	{ 360 alpha sub a b xmk lfigcb neg
	} ifelse
      } ifelse
    } ifelse
  end
  % (Leaving lfigcurveboxcircum) lfigdebugprint
} def

% find point on circumference of diamond:  alpha a b lfigdiamondcircum x y
/lfigdiamondcircum
{
  % (Entering lfigdiamondcircum) lfigdebugprint
  4 dict begin
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def
    b alpha cos abs mul  a alpha sin abs mul  add  /denom exch def
    a b mul alpha cos mul denom div
    a b mul alpha sin mul denom div
  end
  % (Leaving lfigdiamondcircum) lfigdebugprint
} def

% find point on circumference of ellipse:  alpha a b lfigellipsecircum x y
/lfigellipsecircum
{
  % (Entering lfigellipsecircum) lfigdebugprint
  4 dict begin
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def
    b alpha cos mul dup mul  a alpha sin mul dup mul  add sqrt /denom exch def
    a b mul alpha cos mul denom div
    a b mul alpha sin mul denom div
  end
  % (Leaving lfigellipsecircum) lfigdebugprint
} def

% find point of intersection of two lines each defined by two points
% x1 y1 x2 y2  x3 y3 x4 y4  lfiglineintersect x y
/lfiglineintersect
{
  % (Entering lfiglineintersect) lfigdebugprint
  13 dict begin
    /y4 exch def
    /x4 exch def
    /y3 exch def
    /x3 exch def
    /y2 exch def
    /x2 exch def
    /y1 exch def
    /x1 exch def
    x2 x1 sub /x21 exch def
    x4 x3 sub /x43 exch def
    y2 y1 sub /y21 exch def
    y4 y3 sub /y43 exch def
    y21 x43 mul y43 x21 mul sub /det exch def
  
    % calculate x 
    y21 x43 mul x1 mul
    y43 x21 mul x3 mul sub
    y3 y1 sub x21 mul x43 mul add
    det div

    % calculate y
    x21 y43 mul y1 mul
    x43 y21 mul y3 mul sub
    x3 x1 sub y21 mul y43 mul add
    det neg div

  end
  % (Leaving lfiglineintersect) lfigdebugprint
} def

% find point on circumference of polygon
% alpha radius num theta lfigpolycircum x y
/lfigpolycircum
{
  % (Entering lfigpolycircum) lfigdebugprint
  13 dict begin
    /theta exch def
    /num exch def
    /radius exch def
    /alpha exch def

    % calculate delta, the angle from theta to alpha
    alpha theta sub lfigfixangle

    % calculate the angle which is the multiple of 360/num closest to delta
    360 num div div truncate 360 num div mul theta add /anglea exch def

    % calculate the next multiple of 360/num after anglea
    anglea 360 num div add /angleb exch def

    % intersect the line through these two points with the alpha line
    anglea cos anglea sin  angleb cos angleb sin
    0 0  alpha cos 2 mul alpha sin 2 mul
    lfiglineintersect radius lfigpmul

  end
  % (Leaving lfigpolycircum) lfigdebugprint
} def

% find point of intersection of a point and a circle
% x0 y0 r  x1 y1 theta  lfigcircleintersect xa ya xb yb 2
%                                        or       xb yb 1
%                                        or             0
/lfigcircleintersect
{
  % (Entering lfigcircleintersect) lfigdebugprint
  15 dict begin
    /theta exch def
    /y1    exch def
    /x1    exch def
    /r     exch def
    /y0    exch def
    /x0    exch def

    % if sin(theta) = 0 then line is horizontal and y must be y1
    theta sin abs 0.00001 lt
    { 
      /a 1 def
      /b -2 x0 mul def
      /c x0 dup mul y1 y0 sub dup mul add r dup mul sub def
      a b c lfigqroots dup
      0 eq
      { pop
	0
      }
      { 1 eq
	{ y1 1
	}
	{ y1 exch y1 2
	} ifelse
      } ifelse
    }
    {
      /ct theta cos theta sin div def
      /a ct ct mul 1 add def
      /b ct x1 x0 sub mul y1 add y0 sub 2 mul def
      /c x1 x0 sub dup mul y1 y0 sub dup mul add r dup mul sub def
      a b c lfigqroots dup
      0 eq
      { pop
	0
      }
      { 1 eq
	{ y1 add /yb exch def
	  yb y1 sub ct mul x1 add /xb exch def
	  xb yb 1
	}
	{ y1 add /ya exch def
	  ya y1 sub ct mul x1 add /xa exch def
	  y1 add /yb exch def
	  yb y1 sub ct mul x1 add /xb exch def
	  xa ya xb yb 2
	} ifelse
      } ifelse
    } ifelse
  end
  % (Leaving lfigcircleintersect) lfigdebugprint
} def

% add CIRCUM operator with this body:  <array> lfigcircumdef -
/lfigcircumdef
{   % (Entering lfigcircumdef) lfigdebugprint
    /CIRCUM exch cvx
    currentdict end
    3 1 roll
    % currentdict length currentdict maxlength lt
    % { def }
    % { exec moveto (too many labels) show stop }
    % ifelse
    def
    begin
    % (Leaving lfigcircumdef) lfigdebugprint
} def

end
%%EndResource

%%BeginResource: procset LoutBasicSetup
% @PrependGraphic file /export/home/6monthspace/jeff/lout.lib/include/bsf.lpg

% width height linethickness louteuro -
% draw a Euro symbol of this width and height with this line thickness
/louteuro {
  20 dict begin
    /eurothick exch def
    /euroheight exch def
    /eurowidth exch def
    /eurostrokewidth euroheight 0.8 mul def
    /eurostep eurothick 60 cos mul 60 sin div def
    /eurotheta 40 def

    % llx lly width thickness louteurobox -
    % draw angled box starting at (llx, lly) with given width and thickness
    /louteurobox
    {
      /euroboxthick exch def
      /euroboxwidth exch def
      newpath moveto euroboxwidth 0 rlineto
      eurostep euroboxthick rlineto
      euroboxwidth neg 0 rlineto closepath fill
    } def

    % lower cross stroke
    0 euroheight 2 div eurothick 1.5 mul sub
    eurostrokewidth eurothick louteurobox

    % upper cross stroke
    0 euroheight 2 div eurothick 0.5 mul add
    eurostrokewidth eurostep 2 mul add eurothick louteurobox

    % circular part
    /eurohctr eurowidth euroheight 2 div eurotheta cos mul sub def
    /eurovctr euroheight 2 div def
    newpath
    eurohctr eurovctr eurovctr eurotheta 350 eurotheta sub arc
    eurohctr eurovctr eurovctr eurothick sub 365 eurotheta sub eurotheta arcn
    closepath fill
  end
} def

% path for @FullWidthRule symbol
/LoutRule
{ 0 0 moveto xsize 0 lineto
} def

% path for @Box symbol
/LoutBox
{ 0 0 moveto xsize 0 lineto
  xsize ysize lineto 0 ysize lineto
  closepath
} def

% path for @CurveBox symbol
/LoutCurveBox
{ xmark 0 moveto
  xsize xmark sub xmark xmark 270 360 arc
  xsize xmark sub ysize xmark sub xmark 0 90 arc
  xmark ysize xmark sub xmark 90 180 arc
  xmark xmark xmark 180 270 arc
  closepath
} def

% path for @ShadowBox symbol
/LoutShadowBox
{ xmark 2 mul 0 moveto xsize 0 lineto
  xsize ysize xmark 2 mul sub lineto
  xsize xmark sub ysize xmark 2 mul sub lineto
  xsize xmark sub xmark lineto
  xmark 2 mul xmark lineto
  closepath
} def

% set up dictionary containing margin note data: parity LoutMargSet -
/LoutMargSet
{ /LoutMargDict 12 dict def
  LoutMargDict begin
    /parity exch def
    /matr matrix currentmatrix def
    /rightx xsize def
    /lefty ysize def   % highest allowable point for top of next left note
    /righty ysize def  % highest allowable point for top of next right note
    /max { 2 copy gt { pop } { exch pop } ifelse } def
    /min { 2 copy lt { pop } { exch pop } ifelse } def
  end
} def

%translate coordinate system for marginal notes:  type LoutMargShift -
% where type 0 is left margin, 1 is right margin, 2 is outer, 3 is inner
/LoutMargShift
{ LoutMargDict begin

    % y coordinate of top of note, in margin coords, before vertical adjust
    0 ysize transform matr itransform exch pop

    % decide whether left or right margin based on type and parity
    exch [ 0 1 parity 1 parity sub ] exch get 0 eq
    {
      % left margin: adjust top of note downwards if overlaps previous note
      lefty min

      % bottom of note is new lefty position and also translate position
      ysize sub dup /lefty exch def

      % want right edge of note at coordinate zero
      xsize neg exch
    }
    {
      % right margin: adjust top of note downwards if overlaps previous note
      righty min

      % bottom of note is new righty position and also translate position
      ysize sub dup /righty exch def

      % want left edge of note at coordinate rightx
      rightx exch
    } ifelse

    % stack now contains coord of bottom left corner in margin coordinates
    matr setmatrix translate
  end
} def

% create LoutPageDict with left, right, foot, top for @Place symbol users
/LoutPageSet
{
  /LoutPageDict 5 dict def
  LoutPageDict begin
    /matr matrix currentmatrix def
    /left 0 def
    /right xsize def
    /foot 0 def
    /top ysize def
  end

} def

%%EndResource

%%EndProlog

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/Times-Boldfnt84 vec2 /Times-Bold LoutRecode
/fnt84 { /Times-Boldfnt84 LoutFont } def
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/Times-Italicfnt83 vec2 /Times-Italic LoutRecode
/fnt83 { /Times-Italicfnt83 LoutFont } def
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grestore
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gsave
grestore save gsave 200 dict begin lfigdict begin
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480 1544 translate
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grestore
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grestore
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grestore
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grestore
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grestore

grestore
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grestore
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grestore
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338 338 56 282 240 288 12 0 0 LoutGr2
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338 338 56 282 240 288 12 0 0 LoutGr2

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192 fnt83 123 128(a)m 
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0 0 0 0 240 288 12 338 282 LoutGr2

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grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
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338 338 56 282 240 288 12 0 0 LoutGr2

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192 fnt83 123 105(b)m 
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0 0 0 0 240 288 12 732 282 LoutGr2

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0 0 0 0 240 288 12 1520 790 LoutGr2

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0 0 0 0 240 288 12 3096 1298 LoutGr2

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0 0 0 0 240 288 12 3096 1806 LoutGr2

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grestore
3096 1862 0 1806 240 288 12 3152 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1717 338 56 282 240 288 12 1379 1524 LoutGr2
currentdict end 70 dict begin begin
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338 338 56 282 240 288 12 0 0 LoutGr2

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192 fnt78
156 121(|)m 
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1520 1354 0 1298 240 288 12 0 0 LoutGr2
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1067 338 56 282 240 288 12 453 1016 LoutGr2
currentdict end 70 dict begin begin
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614 338 56 282 240 288 12 0 0 LoutGr2

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192 fnt83 56 107(SPLIT)m 
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732 846 0 790 240 288 12 0 0 LoutGr2
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grestore
608 338 56 282 240 288 12 124 508 LoutGr2
currentdict end 70 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83 56 107(COL)m

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338 338 56 282 240 288 12 0 0 LoutGr2
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grestore
338 338 56 282 240 288 12 0 0 LoutGr2
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338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83 123 128(a)m 
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0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83 128 128(c)m 
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0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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0 0 0 0 240 288 12 732 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
732 846 0 790 240 288 12 788 0 LoutGr2
currentdict end 70 dict begin begin
grestore
628 338 56 282 240 288 12 104 508 LoutGr2
currentdict end 70 dict begin begin
grestore
524 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83
56 107(R)m 7(O)k 9(W)k 
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(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83 128 128(c)m

grestore
(T) lfigpromotelabels
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0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
192 fnt83 118 105(d)m 
grestore
(T) lfigpromotelabels
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0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore
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0 0 0 0 240 288 12 1520 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore
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0 0 0 0 240 288 12 1520 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore

grestore
1520 1354 0 1298 240 288 12 1576 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1067 338 56 282 240 288 12 453 1016 LoutGr2
currentdict end 70 dict begin begin
grestore
614 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
192 fnt83 56 107(SPLIT)m 
grestore
(T) lfigpromotelabels
grestore
732 846 0 790 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
608 338 56 282 240 288 12 124 508 LoutGr2
currentdict end 70 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
192 fnt83
56 107(COL)m 
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grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83 123 105(b)m 
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0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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192 fnt83 118 105(d)m

grestore
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0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore
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0 0 0 0 240 288 12 732 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore

grestore
732 846 0 790 240 288 12 788 0 LoutGr2
currentdict end 70 dict begin begin
grestore
628 338 56 282 240 288 12 104 508 LoutGr2
currentdict end 70 dict begin begin
grestore
524 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
192 fnt83 56 107(R)m 7(O)k 9(W)k 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
192 fnt83
128 128(c)m 
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(T) lfigpromotelabels
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0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
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grestore
192 fnt83 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
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grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
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grestore

grestore
(S) lfigpromotelabels
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0 0 0 0 240 288 12 1520 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
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grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3096 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 6248 1806 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 10598(In)m 244(f)s 2(act,)k
693(common)s 1576(sube)s 3(xpressions)k 3060(are)s 3395(identi\207ed)s
4343(\(tri)s 6(vially\))k 5286(and)s 5678(the)s 6013(result)s
6591(is)s 6788(a)s 6942(directed)s 7756(ac)s 3(yclic)k
8469(graph;)s 0 10310(each)m 486(af)s 6(fected)k 1296(leaf)s
1716(has)s 2076(tw)s 2(o)k 2477(parents,)s 3264(one)s
3657(for)s 3985(width)s 4578(and)s 4972(one)s 5365(for)s
5693(height;)s 6394(and)s 6788(each)s 240 fnt83 7274 10312(COL)m
240 fnt82 7790 10310(or)m 240 fnt83 8040 10312(R)m 9(O)k 12(W)k
240 fnt82 8604 10310(node)m 0 10022(has)m 360(one)s 752(parent)s
1398(and)s 1792(one)s 2184(child)s 2709(for)s 3037(each)s
3521(object)s 4155(lying)s 4690(on)s 4976(the)s 5314(corresponding)s
6726(mark.)s 7370(The)s 7788(data)s 8235(structure)s 0 9734(roughly)m
799(doubles)s 1595(in)s 1838(size,)s 2316(and)s 2720(this)s
3116(occurs)s 3791(only)s 4271(rarely)s 4881(in)s 5124(practice.)s
480 9360(This)m 956(method)s 1732(can)s 2121(cope)s 2629(with)s
3111(an)s 3(y)k 3508(le)s 3(g)k 1(al)k
4023(input,)s 4622(including)s 220 fnt35 480 8859({  a  //  c  |  d  }  |  {  b  /  e  })m 480 8571(/  {  f  /  i  }  |  {  g  |  h  //  j  })m
240 fnt82 0 8072(which)m 642(produces)s 1557(o)s 3(v)k 3(erlapping)k
2747(spanning)s 3665(columns:)s gsave
480 5924 translate
240 fnt83 1699 1808 0 1695 240 288 60 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1133 452 113 339 240 288 60 0 1356 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 511 178(a)m 
grestore
566 452 113 339 240 288 60 1133 1356 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83
228 150(b)m 
grestore
566 452 113 339 240 288 60 0 904 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 234 178(c)m 
grestore
566 452 113 339 240 288 60 566 904 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 222 150(d)m

grestore
566 452 113 339 240 288 60 1132 904 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 235 178(e)m 
grestore
566 452 113 339 240 288 60 0 452 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 235 173(f)m 
grestore
566 452 113 339 240 288 60 566 452 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83
228 200(g)m 
grestore
566 452 113 339 240 288 60 1132 452 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 228 149(h)m 
grestore
566 452 113 339 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 253 153(i)m

grestore
1133 452 113 339 240 288 60 566 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt83 535 176(j)m 
grestore
end end restore
grestore
0 5473(The)m 428(box)s 3(es)k
1035(ha)s 4(v)k 3(e)k 1536(been)s 2045(added)s
2675(to)s 2914(clarify)s 3590(the)s 3938(structure.)s 4937(The)s
5365(width)s 5967(of)s 6238(this)s 6634(object)s 7278(is)s
7488(formally)s 240 fnt78 480 4915(\()m 564(\()s 240 fnt83
648 4923(width)m 240 fnt78 1187 4915(\()m 240 fnt83 1271 4923(a)m
240 fnt78 1398 4915(\))m 1548(\255)s 1769(\()s 240 fnt83
1853 4923(x)m 240 fnt78 2031 4915(+)m 240 fnt83 2232 4923(y)m
240 fnt78 2346 4915(\))m 2424(\))s 2562(+)s 240 fnt83
2763 4923(z)m 240 fnt78 2866 4915(\))m 3016(\255)s 3237(\()s
240 fnt83 3321 4923(x)m 240 fnt78 3499 4915(+)m 3700(\()s
3784(\()s 240 fnt83 3868 4923(y)m 240 fnt78 4042 4915(+)m
240 fnt83 4243 4923(z)m 240 fnt78 4346 4915(\))m 4496(\255)s
240 fnt83 4717 4923(width)m 240 fnt78 5256 4915(\()m 240 fnt83
5340 4923(j)m 240 fnt78 5418 4915(\))m 5496(\))s 5574(\))s
240 fnt82 0 4419(where)m 240 fnt83 480 3918(x)m 240 fnt78
670 3910(=)m 240 fnt83 883 3918(width)m 240 fnt78 1422 3910(\()m
240 fnt83 1506 3918(c)m 240 fnt78 1620 3910(\))m 1770(\255)s
240 fnt83 1991 3918(width)m 240 fnt78 2530 3910(\()m 240 fnt83
2662 3918(f)m 240 fnt78 2823 3910(\))m 2973(\255)s 240 fnt83
3194 3918(width)m 240 fnt78 3733 3910(\()m 240 fnt83 3817 3918(i)m
240 fnt78 3892 3910(\))m 240 fnt83 480 3367(y)m 240 fnt78
666 3359(=)m 240 fnt83 879 3367(width)m 240 fnt78 1418 3359(\()m
240 fnt83 1502 3367(d)m 240 fnt78 1688 3359(\))m 1838(\255)s
240 fnt83 2059 3367(width)m 240 fnt78 2598 3359(\()m 240 fnt83
2682 3367(g)m 240 fnt78 2808 3359(\))m 240 fnt83 480 2816(z)m
240 fnt78 655 2808(=)m 240 fnt83 868 2816(width)m 240 fnt78
1407 2808(\()m 240 fnt83 1491 2816(b)m 240 fnt78 1617 2808(\))m
1767(\255)s 240 fnt83 1988 2816(width)m 240 fnt78 2527 2808(\()m
240 fnt83 2611 2816(e)m 240 fnt78 2722 2808(\))m 2872(\255)s
240 fnt83 3093 2816(width)m 240 fnt78 3632 2808(\()m 240 fnt83
3716 2816(h)m 240 fnt78 3843 2808(\))m 240 fnt82 0 2312(It)m
224(seems)s 878(clear)s 1420(that)s 240 fnt83 1857 2314(y)m
240 fnt82 2038 2312(at)m 2289(least)s 2805(must)s 3349(appear)s
4065(twice)s 4657(in)s 4919(an)s 3(y)k 5335(e)s 3(xpression)k
6431(for)s 6788(the)s 7155(width)s 7776(of)s 8066(this)s
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