# To unbundle, sh this file
echo mxyzptlk.ps 1>&2
cat >mxyzptlk.ps <<'End of mxyzptlk.ps'
%!PS-Adobe-2.0
%%Creator: dvips 5.518 Copyright 1986, 1993 Radical Eye Software
%%Title: mxyzptlk.dvi
%%CreationDate: Tue Aug 17 09:31:10 1993
%%Pages: 18
%%PageOrder: Ascend
%%BoundingBox: 0 0 612 792
%%EndComments
%DVIPSCommandLine: dvips -o mxyzptlk.ps mxyzptlk
%DVIPSSource:  TeX output 1993.08.17:0930
%%BeginProcSet: tex.pro
/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
/X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get
round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{
statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0
0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn
begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X
array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo
setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx
FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{
pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}
B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup
length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B
/ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type
/stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp
0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2
index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff
ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice
ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{
ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn
/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1
sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D
}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0
moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add
.99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage
userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook
known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
/IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
{}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley
false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley
scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave
transform round exch round exch itransform moveto rulex 0 rlineto 0
ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta
0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}
B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{
3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p
-1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{
3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end
%%EndProcSet
TeXDict begin 40258431 52099146 1000 300 300
(/tmp_mnt/home/calvin/michelotti/cxx/c++_source/mxyzptlk/gnu/mxyzptlk.dvi)
@start /Fa 1 98 df<00200000700000700000700000B80000B80000B800011C00011C
00011C00020E00020E0004070004070007FF000803800803800803801801C03803C0FE0F
F815157F9419>97 D E /Fb 2 34 df<0000180000300000600000E00000C00001800003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>32
D<C000006000003000003800001800000C00000E000007000003000003800001800001C0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>I E /Fc 2 101 df<0F8030C060804000C0
00C000C04061803E000A097E880D>99 D<03C000C000C000C001801D8033806180C300C3
00C300C32047403B800B0E7E8D0F>I E /Fd 1 1 df<FFFFC0FFFFC012027D871A>0
D E /Fe 42 123 df<000FF83F00007FFDFFC001F81FE3E003E03F87E007C03F87E00F80
3F07E00F803F03C00F801F00000F801F00000F801F00000F801F00000F801F00000F801F
0000FFFFFFFC00FFFFFFFC000F801F00000F801F00000F801F00000F801F00000F801F00
000F801F00000F801F00000F801F00000F801F00000F801F00000F801F00000F801F0000
0F801F00000F801F00000F801F00000F801F00000F801F00000F801F00007FF0FFF0007F
F0FFF00023237FA221>11 D<387CFEFEFE7C3807077C8610>46 D<00180000780001F800
FFF800FFF80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800
01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800
01F80001F80001F8007FFFE07FFFE013207C9F1C>49 D<03FC000FFF003C1FC07007E07C
07F0FE03F0FE03F8FE03F8FE01F87C01F83803F80003F80003F00003F00007E00007C000
0F80001F00003E0000380000700000E01801C0180380180700180E00380FFFF01FFFF03F
FFF07FFFF0FFFFF0FFFFF015207D9F1C>I<00FE0007FFC00F07E01E03F03F03F03F81F8
3F81F83F81F81F03F81F03F00003F00003E00007C0001F8001FE0001FF000007C00001F0
0001F80000FC0000FC3C00FE7E00FEFF00FEFF00FEFF00FEFF00FC7E01FC7801F81E07F0
0FFFC001FE0017207E9F1C>I<0000E00001E00003E00003E00007E0000FE0001FE0001F
E00037E00077E000E7E001C7E00187E00307E00707E00E07E00C07E01807E03807E07007
E0E007E0FFFFFEFFFFFE0007E00007E00007E00007E00007E00007E00007E000FFFE00FF
FE17207E9F1C>I<1000201E01E01FFFC01FFF801FFF001FFE001FF8001BC00018000018
000018000018000019FC001FFF001E0FC01807E01803E00003F00003F00003F80003F838
03F87C03F8FE03F8FE03F8FC03F0FC03F07007E03007C01C1F800FFF0003F80015207D9F
1C>I<001F8000FFE003F07007C0F00F01F81F01F83E01F83E01F87E00F07C00007C0000
FC0800FC7FC0FCFFE0FD80F0FF00F8FE007CFE007CFC007EFC007EFC007EFC007E7C007E
7C007E7C007E3C007C3E007C1E00F80F00F00783E003FFC000FF0017207E9F1C>I<6000
007800007FFFFE7FFFFE7FFFFC7FFFF87FFFF87FFFF0E00060E000C0C00180C00300C003
00000600000C00001C0000180000380000780000780000F00000F00000F00001F00001F0
0001F00003F00003F00003F00003F00003F00003F00003F00001E00017227DA11C>I<00
FE0003FFC00703E00E00F01C00F01C00783C00783E00783F00783F80783FE0F01FF9E01F
FFC00FFF8007FFC003FFE007FFF01E7FF83C1FFC7807FC7801FEF000FEF0003EF0001EF0
001EF0001CF8001C7800383C00381F01F00FFFC001FF0017207E9F1C>I<01FE0007FF80
0F83E01E01F03E00F07C00F87C0078FC007CFC007CFC007CFC007EFC007EFC007EFC007E
7C00FE7C00FE3E01FE1E037E0FFE7E07FC7E00207E00007C00007C1E007C3F00F83F00F8
3F00F03F01E01E03C01C0F800FFE0003F80017207E9F1C>I<387CFEFEFE7C3800000000
00000000387CFEFEFE7C3807167C9510>I<0003FE0080001FFF818000FF01E38001F800
3F8003E0001F8007C0000F800F800007801F800007803F000003803F000003807F000001
807E000001807E00000180FE00000000FE00000000FE00000000FE00000000FE00000000
FE00000000FE00000000FE000000007E000000007E000001807F000001803F000001803F
000003801F800003000F8000030007C000060003F0000C0001F800380000FF00F000001F
FFC0000003FE000021227DA128>67 D<FFFFFF8000FFFFFFF00007F003FC0007F0007E00
07F0003F0007F0001F8007F0000FC007F00007E007F00007E007F00007F007F00003F007
F00003F007F00003F007F00003F807F00003F807F00003F807F00003F807F00003F807F0
0003F807F00003F807F00003F807F00003F807F00003F007F00003F007F00003F007F000
07E007F00007E007F0000FC007F0001F8007F0003F0007F0007E0007F003FC00FFFFFFF0
00FFFFFF800025227EA12B>I<FFFFFFFCFFFFFFFC07F000FC07F0003C07F0001C07F000
0C07F0000E07F0000E07F0000607F0180607F0180607F0180607F0180007F0380007F078
0007FFF80007FFF80007F0780007F0380007F0180007F0180007F0180307F0180307F000
0307F0000607F0000607F0000607F0000E07F0000E07F0001E07F0003E07F001FCFFFFFF
FCFFFFFFFC20227EA125>I<FFFFE0FFFFE003F80003F80003F80003F80003F80003F800
03F80003F80003F80003F80003F80003F80003F80003F80003F80003F80003F80003F800
03F80003F80003F80003F80003F80003F80003F80003F80003F80003F80003F80003F800
FFFFE0FFFFE013227FA115>73 D<FFF000000FFFFFF800001FFF07F800001FE006FC0000
37E006FC000037E006FC000037E0067E000067E0067E000067E0063F0000C7E0063F0000
C7E0061F800187E0061F800187E0060FC00307E0060FC00307E0060FC00307E00607E006
07E00607E00607E00603F00C07E00603F00C07E00601F81807E00601F81807E00601F818
07E00600FC3007E00600FC3007E006007E6007E006007E6007E006003FC007E006003FC0
07E006001F8007E006001F8007E006001F8007E006000F0007E0FFF00F00FFFFFFF00600
FFFF30227EA135>77 D<0007FC0000003FFF800000FC07E00003F001F80007E000FC000F
C0007E001F80003F001F80003F003F00001F803F00001F807F00001FC07E00000FC07E00
000FC0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE0000
0FE0FE00000FE0FE00000FE07E00000FC07F00001FC07F00001FC03F00001F803F80003F
801F80003F000FC0007E0007E000FC0003F001F80000FC07E000003FFF80000007FC0000
23227DA12A>79 D<FFFFFF00FFFFFFE007F007F007F001FC07F000FC07F0007E07F0007E
07F0007F07F0007F07F0007F07F0007F07F0007F07F0007E07F0007E07F000FC07F001FC
07F007F007FFFFE007FFFF0007F0000007F0000007F0000007F0000007F0000007F00000
07F0000007F0000007F0000007F0000007F0000007F0000007F00000FFFF8000FFFF8000
20227EA126>I<01FC0407FF8C1F03FC3C007C7C003C78001C78001CF8000CF8000CFC00
0CFC0000FF0000FFE0007FFF007FFFC03FFFF01FFFF80FFFFC03FFFE003FFE0003FF0000
7F00003F00003FC0001FC0001FC0001FE0001EE0001EF0003CFC003CFF00F8C7FFE080FF
8018227DA11F>83 D<7FFFFFFF807FFFFFFF807E03F80F807803F807807003F803806003
F80180E003F801C0E003F801C0C003F800C0C003F800C0C003F800C0C003F800C00003F8
00000003F800000003F800000003F800000003F800000003F800000003F800000003F800
000003F800000003F800000003F800000003F800000003F800000003F800000003F80000
0003F800000003F800000003F800000003F800000003F8000003FFFFF80003FFFFF80022
227EA127>I<07FC001FFF803F07C03F03E03F01E03F01F01E01F00001F00001F0003FF0
03FDF01FC1F03F01F07E01F0FC01F0FC01F0FC01F0FC01F07E02F07E0CF81FF87F07E03F
18167E951B>97 D<FF000000FF0000001F0000001F0000001F0000001F0000001F000000
1F0000001F0000001F0000001F0000001F0000001F0000001F0FE0001F3FF8001FF07C00
1F801E001F001F001F000F801F000F801F000FC01F000FC01F000FC01F000FC01F000FC0
1F000FC01F000FC01F000FC01F000F801F001F801F801F001FC03E001EE07C001C3FF800
180FC0001A237EA21F>I<00FF8007FFE00F83F01F03F03E03F07E03F07C01E07C0000FC
0000FC0000FC0000FC0000FC0000FC00007C00007E00007E00003E00301F00600FC0E007
FF8000FE0014167E9519>I<0001FE000001FE0000003E0000003E0000003E0000003E00
00003E0000003E0000003E0000003E0000003E0000003E0000003E0001FC3E0007FFBE00
0F81FE001F007E003E003E007E003E007C003E00FC003E00FC003E00FC003E00FC003E00
FC003E00FC003E00FC003E00FC003E007C003E007C003E003E007E001E00FE000F83BE00
07FF3FC001FC3FC01A237EA21F>I<00FE0007FF800F87C01E01E03E01F07C00F07C00F8
FC00F8FC00F8FFFFF8FFFFF8FC0000FC0000FC00007C00007C00007E00003E00181F0030
0FC07003FFC000FF0015167E951A>I<003F8000FFC001E3E003C7E007C7E00F87E00F83
C00F80000F80000F80000F80000F80000F8000FFFC00FFFC000F80000F80000F80000F80
000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80
000F80000F80007FF8007FF80013237FA211>I<03FC1E0FFF7F1F0F8F3E07CF3C03C07C
03E07C03E07C03E07C03E07C03E03C03C03E07C01F0F801FFF0013FC0030000030000038
00003FFF801FFFF00FFFF81FFFFC3800FC70003EF0001EF0001EF0001EF0001E78003C7C
007C3F01F80FFFE001FF0018217E951C>I<FF000000FF0000001F0000001F0000001F00
00001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F07
E0001F1FF8001F307C001F403C001F803E001F803E001F003E001F003E001F003E001F00
3E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F00
3E001F003E00FFE1FFC0FFE1FFC01A237EA21F>I<1C003E007F007F007F003E001C0000
00000000000000000000000000FF00FF001F001F001F001F001F001F001F001F001F001F
001F001F001F001F001F001F001F001F00FFE0FFE00B247EA310>I<FF000000FF000000
1F0000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F000000
1F0000001F0000001F00FF801F00FF801F0038001F0060001F01C0001F0380001F070000
1F0E00001F1C00001F7E00001FFF00001FCF00001F0F80001F07C0001F03E0001F01E000
1F01F0001F00F8001F007C001F003C00FFE0FFC0FFE0FFC01A237EA21E>107
D<FF00FF001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F
001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F00FFE0FFE00B
237EA210>I<FF07F007F000FF1FFC1FFC001F303E303E001F403E403E001F801F801F00
1F801F801F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F00
1F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F00
1F001F001F001F001F001F001F001F001F00FFE0FFE0FFE0FFE0FFE0FFE02B167E9530>
I<FF07E000FF1FF8001F307C001F403C001F803E001F803E001F003E001F003E001F003E
001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E
001F003E001F003E00FFE1FFC0FFE1FFC01A167E951F>I<00FE0007FFC00F83E01E00F0
3E00F87C007C7C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007EFC007E7C007C
7C007C3E00F81F01F00F83E007FFC000FE0017167E951C>I<FF0FE000FF3FF8001FF07C
001F803E001F001F001F001F801F001F801F000FC01F000FC01F000FC01F000FC01F000F
C01F000FC01F000FC01F000FC01F001F801F001F801F803F001FC03E001FE0FC001F3FF8
001F0FC0001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F0000
00FFE00000FFE000001A207E951F>I<FE1F00FE3FC01E67E01EC7E01E87E01E87E01F83
C01F00001F00001F00001F00001F00001F00001F00001F00001F00001F00001F00001F00
001F0000FFF000FFF00013167E9517>114 D<0FF3003FFF00781F00600700E00300E003
00F00300FC00007FE0007FF8003FFE000FFF0001FF00000F80C00780C00380E00380E003
80F00700FC0E00EFFC00C7F00011167E9516>I<01800001800001800001800003800003
80000780000780000F80003F8000FFFF00FFFF000F80000F80000F80000F80000F80000F
80000F80000F80000F80000F80000F80000F81800F81800F81800F81800F81800F830007
C30003FE0000F80011207F9F16>I<FF01FE00FF01FE001F003E001F003E001F003E001F
003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F003E001F
003E001F003E001F003E001F007E001F00FE000F81BE0007FF3FC001FC3FC01A167E951F
>I<FFE01FE0FFE01FE00F8006000F8006000FC00E0007C00C0007E01C0003E0180003E0
180001F0300001F0300000F8600000F86000007CC000007CC000007FC000003F8000003F
8000001F0000001F0000000E0000000E00001B167F951E>I<7FFFF07FFFF07C03E07007
C0600FC0E01F80C01F00C03E00C07E0000FC0000F80001F00003F03007E03007C0300F80
701F80703F00603E00E07C03E0FFFFE0FFFFE014167E9519>122
D E /Ff 8 123 df<40E06020202040408003097D820A>59 D<07E01FC000E006000170
0400017004000138040001380400021C0800021C0800020E0800020E0800040710000407
100004039000040390000801E0000801E0000800E0000800E00018004000FE0040001A14
7F931A>78 D<07800C4010E031C0600060006000C000C0004020404021801E000B0D7E8C
0F>99 D<007C000C0018001800180018003007B00C7010703060606060606060C0C0C0C8
C0C841C862D03C700E147E9311>I<3818204C18604C18208C3020983020183020183020
30604030604030608030608018B1000F1E00130D7F8C18>119 D<0E3C13CE238E430C43
000300030006000608C608E610CA2071C00F0D7F8C13>I<38184C184C188C3098301830
183030603060306030E011C00EC000C00080E180E30046003C000D137F8C11>I<07100F
2010E000400080010002000C00102020203840478083000C0D7F8C10>I
E /Fg 13 115 df<FFFFFF80FFFFFF8019027D8A20>0 D<03C00FF01C38300C60066006
C003C003C003C00360066006300C1C380FF003C010107E9115>14
D<03C00FF01FF83FFC7FFE7FFEFFFFFFFFFFFFFFFF7FFE7FFE3FFC1FF80FF003C010107E
9115>I<FFFFFFE07FFFFFE0000000000000000000000000000000000000000000000000
00000000FFFFFFE0FFFFFFE0000000000000000000000000000000000000000000000000
000000007FFFFFE0FFFFFFE01B147E9320>17 D<007FFF8001FFFF80078000000E000000
1800000030000000300000006000000060000000C0000000C0000000C0000000C0000000
C0000000C0000000C000000060000000600000003000000030000000180000000E000000
0780000001FFFF80007FFF80000000000000000000000000000000000000000000000000
000000007FFFFF807FFFFF8019227D9920>I<000001800000078000001E000000780000
01E00000078000001E00000078000001E00000078000001E00000078000000E000000078
0000001E0000000780000001E0000000780000001E0000000780000001E0000000780000
001E00000007800000018000000000000000000000000000000000000000000000000000
0000007FFFFF00FFFFFF8019227D9920>20 D<0000000400000000020000000002000000
00010000000000800000000040FFFFFFFFF8FFFFFFFFF800000000400000000080000000
0100000000020000000002000000000400250E7E902A>33 D<C0C0C0C0C0C0E0E0C0C0C0
C0C0C0030E7E9000>55 D<008001800300030003000600060006000C000C000C00180018
001800300030003000600060006000C000C0006000600060003000300030001800180018
000C000C000C0006000600060003000300030001800080092A7C9E10>104
D<C000C0006000600060003000300030001800180018000C000C000C0006000600060003
0003000300018001800300030003000600060006000C000C000C00180018001800300030
003000600060006000C000C000092A7E9E10>I<C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C002297B9E0C>I<00000000
4000000000C0000000018000000001800000000300000000030000000006000000000600
0000000C000000000C000000001800000000180000000030000000003000000000600000
00006000000000C000000000C0000000018000000001800000000300000C000300003C00
0600004E000600008E000C000007000C0000070018000003801800000380300000038030
000001C060000001C060000000E0C0000000E0C0000000718000000071800000003B0000
00003B000000001E000000001E000000000C000000000C000000222A7E8123>112
D<FFFFFFFCFFFFFFFC7FFFFFF838000010380000101C0000201C0000200E0000400E0000
400700008007000080038001000380010001C0020001C0020000E0040000E00400007008
00007008000038100000381000001C2000001E2000000E4000000F400000078000000780
0000030000000300001E1D7E9B23>114 D E /Fh 24 123 df<0FFFF81FFFF83FFFF060
8400408400808C00010C00010C00030C00030C00020C00061C00061C000E1C000C1C001C
0E001C0E00180C0015127E9118>25 D<60F0F06004047C830C>58
D<60F0F0701010101020204080040C7C830C>I<00010003000600060006000C000C000C
0018001800180030003000300060006000C000C000C00180018001800300030003000600
06000C000C000C00180018001800300030003000600060006000C000C00010297E9E15>
61 D<003E0000C3000100800200C0030060078060078070030030000030000030000030
00FC700382700601700C01701800F03800E03000E07000E07001C0E001C0E001C0E00180
E00380E00300E00600E00600600C003018001860000F8000141F7E9D16>64
D<01FC00FF80001C001C00002E001800002E001000002E00100000270010000047002000
0043002000004380200000438020000081C040000081C040000081C040000080E0400001
00E080000100708000010070800001007080000200390000020039000002003900000200
1D000004001E000004000E000004000E00000C000E00001C00040000FF80040000211C7E
9B21>78 D<01FFFE00003C03C0003800E0003800F00038007000380070007000F0007000
F0007000F0007001E000E001C000E0078000E01E0000FFF00001C0300001C0180001C01C
0001C01C0003801C0003801C0003801C0003801C0007003C0007003C0807003C0807003C
100F001E10FFE00E20000007C01D1D7E9B20>82 D<7FF03FE00F0007000E0006000E0004
000E0004000E0004001C0008001C0008001C0008001C0008003800100038001000380010
003800100070002000700020007000200070002000E0004000E0004000E0004000E00080
00E0008000E00100006002000060040000300800001830000007C000001B1D7D9B1C>85
D<01E3000717000C0F00180F00380E00300E00700E00700E00E01C00E01C00E01C00E01C
00E03880E03880E038806078803199001E0E0011127E9116>97 D<3F00070007000E000E
000E000E001C001C001C001C0039E03A303C1838187018701C701C701CE038E038E038E0
30E070E060E0C061C023001E000E1D7E9C12>I<01F0030C0E0C1C1E383C301870007000
E000E000E000E000E000E0046008601030601F800F127E9112>I<01F007080C08180438
08300870307FC0E000E000E000E000E000E0046008601030600F800E127E9113>101
D<0001E0000630000E78000CF0001C60001C00001C00001C00003C0000380000380003FF
C000380000380000700000700000700000700000700000E00000E00000E00000E00000E0
0001C00001C00001C00001C00001C000018000038000038000630000F30000F60000E400
0078000015257E9C14>I<007180018B800307800607800E07000C07001C07001C070038
0E00380E00380E00380E00381C00381C00381C00183C0008F80007380000380000380000
7000607000F06000F0E000E180007E0000111A7F9114>I<0FC00001C00001C000038000
0380000380000380000700000700000700000700000E3E000EC3000F03800E03801E0380
1C03801C03801C0380380700380700380700380E00700E20700E20701C20701C40E00C80
600700131D7E9C18>I<381F81F04E20C6184640E81C4680F01C8F00F01C8E00E01C0E00
E01C0E00E01C1C01C0381C01C0381C01C0381C01C0703803807138038071380380E13803
80E2700700643003003820127E9124>109 D<381F004E61804681C04701C08F01C08E01
C00E01C00E01C01C03801C03801C03801C0700380710380710380E10380E207006403003
8014127E9119>I<07078009C86008D03008E03011C03011C03801C03801C03803807003
80700380700380600700E00700C00701800783000E86000E78000E00000E00001C00001C
00001C00001C00003C0000FF8000151A819115>112 D<1C00C02701C04701C04701C087
03808703800E03800E03801C07001C07001C07001C0700180E20180E20180E201C1E200C
264007C38013127E9118>117 D<1C02270747074703870187010E010E011C021C021C02
1C041804180818081C100C2007C010127E9114>I<1C00C0802701C1C04701C1C04701C0
C087038040870380400E0380400E0380401C0700801C0700801C0700801C070100180601
00180602001C0E02001C0F04000E13080003E1F0001A127E911E>I<07878008C84010F0
C020F1E020E3C040E18000E00000E00001C00001C00001C00001C000638080F38080F381
00E5810084C60078780013127E9118>I<1C00C02701C04701C04701C08703808703800E
03800E03801C07001C07001C07001C0700180E00180E00180E001C1E000C3C0007DC0000
1C00001800603800F03000F06000E0C0004180003E0000121A7E9114>I<038107C10FE6
081C10080010002000400080010002000400080410042C1877F843F081C010127E9113>
I E /Fi 58 122 df<003FC00001F0300003C0380007C07C000F807C000F807C000F8038
000F8000000F8000000F8000000F800000FFFFFC00FFFFFC000F807C000F807C000F807C
000F807C000F807C000F807C000F807C000F807C000F807C000F807C000F807C000F807C
000F807C000F807C007FE1FF807FE1FF80191D809C1B>12 D<003C000000E3000001C100
0003C18000038180000781800007C1800007C3000007C2000007C4000007C8000003F001
FF03E001FF03E0003003F0006001F000C003F800C004FC01801CFC0300387E0300783F06
00781F8C00F81FD800F80FF000FC07F0067C01F8067E07FE1C1FFE3FF807F007F0201D7E
9C25>38 D<0020004001800380030006000E001C001C003C0038003800780078007800F8
00F000F000F000F000F000F000F000F000F000F800780078007800380038003C001C001C
000E000600030003800180004000200B297C9E13>40 D<800040003000380018000C000E
000700070007800380038003C003C003C003E001E001E001E001E001E001E001E001E001
E003E003C003C003C0038003800780070007000E000C00180038003000400080000B297D
9E13>I<01C00003E00001C00041C100F1C780F9CF80FDDF803EBE0007F00007F0003EBE
00FDDF80F9CF80F1C78041C10001C00003E00001C00011127D9E18>I<78FCFCFEFE7A02
02040408083040070E7D850D>44 D<FFE0FFE0FFE0FFE00B047F8A10>I<78FCFCFCFC78
06067D850D>I<00600001E0000FE000FFE000F3E00003E00003E00003E00003E00003E0
0003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E0
0003E00003E00003E0007FFF807FFF80111B7D9A18>49 D<07F8001FFE00383F80780FC0
FC07C0FC07E0FC03E0FC03E07803E00007E00007C00007C0000F80001F00001E00003800
00700000E0000180600300600600600800E01FFFC03FFFC07FFFC0FFFFC0FFFFC0131B7E
9A18>I<03F8001FFE003C1F003C0F807C07C07E07C07C07C03807C0000F80000F80001E
00003C0003F800001E00000F800007C00007C00007E03007E07807E0FC07E0FC07E0FC07
C0780F80781F001FFE0007F800131B7E9A18>I<000180000380000780000F80001F8000
3F80006F8000CF80008F80018F80030F80060F800C0F80180F80300F80600F80C00F80FF
FFF8FFFFF8000F80000F80000F80000F80000F80000F8001FFF801FFF8151B7F9A18>I<
1801801FFF001FFE001FFC001FF8001FC00018000018000018000018000019F8001E0E00
180F801007800007C00007E00007E00007E07807E0F807E0F807E0F807C0F007C0600F80
381F001FFE0007F000131B7E9A18>I<007E0003FF000781800F03C01E07C03C07C03C03
80780000780000F80000F8F800FB0E00FA0780FC0380FC03C0F803E0F803E0F803E0F803
E07803E07803E07803C03C03C03C07801E0F0007FE0003F800131B7E9A18>I<6000007F
FFE07FFFE07FFFC07FFF807FFF80E00300C00600C00C00C0180000300000300000600000
E00000E00001E00001C00003C00003C00003C00003C00007C00007C00007C00007C00007
C00007C000038000131C7D9B18>I<78FCFCFCFC7800000000000078FCFCFCFC7806127D
910D>58 D<00038000000380000007C0000007C0000007C000000FE000000FE000001FF0
00001BF000001BF0000031F8000031F8000061FC000060FC0000E0FE0000C07E0000C07E
0001803F0001FFFF0003FFFF8003001F8003001F8006000FC006000FC00E000FE00C0007
E0FFC07FFEFFC07FFE1F1C7E9B24>65 D<001FE02000FFF8E003F80FE007C003E00F8001
E01F0000E03E0000E03E0000607E0000607C000060FC000000FC000000FC000000FC0000
00FC000000FC000000FC000000FC0000007C0000607E0000603E0000603E0000C01F0000
C00F80018007C0030003F80E0000FFFC00001FE0001B1C7D9B22>67
D<FFFFF800FFFFFF000FC01FC00FC007E00FC001F00FC001F80FC000F80FC000FC0FC000
7C0FC0007C0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0FC000
7E0FC0007C0FC0007C0FC0007C0FC000F80FC000F80FC001F00FC007E00FC01FC0FFFFFF
00FFFFF8001F1C7E9B25>I<FFFFFF00FFFFFF000FC01F000FC007000FC003000FC00380
0FC003800FC181800FC181800FC181800FC180000FC380000FFF80000FFF80000FC38000
0FC180000FC180000FC180600FC180600FC000E00FC000C00FC000C00FC001C00FC001C0
0FC003C00FC00F80FFFFFF80FFFFFF801B1C7E9B1F>I<FFFFFF00FFFFFF000FC01F000F
C007000FC003000FC003800FC003800FC001800FC181800FC181800FC180000FC180000F
C380000FFF80000FFF80000FC380000FC180000FC180000FC180000FC180000FC000000F
C000000FC000000FC000000FC000000FC00000FFFF0000FFFF0000191C7E9B1E>I<FFFC
3FFFFFFC3FFF0FC003F00FC003F00FC003F00FC003F00FC003F00FC003F00FC003F00FC0
03F00FC003F00FC003F00FFFFFF00FFFFFF00FC003F00FC003F00FC003F00FC003F00FC0
03F00FC003F00FC003F00FC003F00FC003F00FC003F00FC003F00FC003F0FFFC3FFFFFFC
3FFF201C7E9B25>72 D<FFFF00FFFF000FC0000FC0000FC0000FC0000FC0000FC0000FC0
000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0030FC0030FC0030FC0
070FC0070FC0060FC00E0FC01E0FC07EFFFFFEFFFFFE181C7E9B1D>76
D<FFE003FFFFE003FF0FF000300FF800300DFC00300CFE00300C7E00300C3F00300C1F80
300C1FC0300C0FE0300C07F0300C03F0300C01F8300C01FC300C00FE300C007F300C003F
300C001FB00C001FF00C000FF00C0007F00C0003F00C0001F00C0000F00C0000F0FFC000
70FFC00030201C7E9B25>78 D<003FE00001F07C0003C01E000F800F801F0007C01E0003
C03E0003E07E0003F07C0001F07C0001F0FC0001F8FC0001F8FC0001F8FC0001F8FC0001
F8FC0001F8FC0001F8FC0001F87C0001F07E0003F07E0003F03E0003E03F0007E01F0007
C00F800F8003C01E0001F07C00003FE0001D1C7D9B24>I<FFFFF800FFFFFE000FC03F80
0FC00F800FC007C00FC007E00FC007E00FC007E00FC007E00FC007E00FC007C00FC007C0
0FC00F800FC03F000FFFFC000FC000000FC000000FC000000FC000000FC000000FC00000
0FC000000FC000000FC000000FC000000FC00000FFFC0000FFFC00001B1C7E9B21>I<FF
FFF00000FFFFFE00000FC03F00000FC00F80000FC007C0000FC007E0000FC007E0000FC0
07E0000FC007E0000FC007E0000FC007C0000FC00F80000FC03E00000FFFF000000FC07C
00000FC03E00000FC03F00000FC01F80000FC01F80000FC01F80000FC01F80000FC01F80
000FC01F80000FC01F81800FC01F81800FC00FC180FFFC07C300FFFC01FE00211C7E9B24
>82 D<07F8201FFEE03C07E07801E07000E0F000E0F00060F00060F80000FE0000FFE000
7FFE003FFF003FFF800FFFC007FFE0007FE00003F00001F00000F0C000F0C000F0C000E0
E000E0F001C0FC03C0EFFF0083FC00141C7D9B1B>I<7FFFFFE07FFFFFE0781F81E0701F
80E0601F8060E01F8070C01F8030C01F8030C01F8030C01F8030001F8000001F8000001F
8000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F
8000001F8000001F8000001F8000001F800007FFFE0007FFFE001C1C7E9B21>I<FFFC01
FF80FFFC01FF800FC000180007E000300007E000300007F000700003F000600003F800E0
0001F800C00001FC00C00000FC01800000FC018000007E030000007E030000007F070000
003F060000003F8E0000001F8C0000001FCC0000000FD80000000FD800000007F0000000
07F000000007F000000003E000000003E000000001C000000001C00000211C7F9B24>86
D<7FFE1FFE007FFE1FFE0007F001800003F803800001FC07000000FC06000000FE0C0000
007F1C0000003F380000003FB00000001FE00000000FE00000000FE000000007F0000000
03F800000007F80000000FFC0000000CFE000000187E000000387F000000703F80000060
1F800000C01FC00001C00FE000018007F000030007F000FFF03FFF80FFF03FFF80211C7F
9B24>88 D<FEFEFEE0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0
E0E0E0E0E0E0E0FEFEFE07297C9E0D>91 D<FEFEFE0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E
0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0EFEFEFE07297F9E0D>93
D<020007000F801DC078F0E03840100D077B9C18>I<0FF8001C1E003E0F803E07803E07
C01C07C00007C0007FC007E7C01F07C03C07C07C07C0F807C0F807C0F807C0780BC03E13
F80FE1F815127F9117>97 D<FF0000FF00001F00001F00001F00001F00001F00001F0000
1F00001F00001F00001F3F801FE1E01F80701F00781F003C1F003C1F003E1F003E1F003E
1F003E1F003E1F003E1F003C1F003C1F00781F80701EC1E01C3F00171D7F9C1B>I<03FC
000E0E001C1F003C1F00781F00780E00F80000F80000F80000F80000F80000F800007800
007801803C01801C03000E0E0003F80011127E9115>I<000FF0000FF00001F00001F000
01F00001F00001F00001F00001F00001F00001F001F9F00F07F01C03F03C01F07801F078
01F0F801F0F801F0F801F0F801F0F801F0F801F07801F07801F03C01F01C03F00F0FFE03
F9FE171D7E9C1B>I<01FC000F07001C03803C01C07801C07801E0F801E0F801E0FFFFE0
F80000F80000F800007800007C00603C00601E00C00F038001FC0013127F9116>I<007F
0001E38003C7C00787C00F87C00F83800F80000F80000F80000F80000F8000FFF800FFF8
000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80
000F80000F80007FF8007FF800121D809C0F>I<03F8F00E0F381E0F381C07303C07803C
07803C07803C07801C07001E0F000E0E001BF8001000001800001800001FFF001FFFC00F
FFE01FFFF07801F8F00078F00078F000787000707800F01E03C007FF00151B7F9118>I<
FF0000FF00001F00001F00001F00001F00001F00001F00001F00001F00001F00001F0FC0
1F31E01F40F01F80F81F80F81F00F81F00F81F00F81F00F81F00F81F00F81F00F81F00F8
1F00F81F00F81F00F8FFE7FFFFE7FF181D7F9C1B>I<1E003F003F003F003F001E000000
00000000000000000000FF00FF001F001F001F001F001F001F001F001F001F001F001F00
1F001F001F00FFE0FFE00B1E7F9D0E>I<007800FC00FC00FC00FC007800000000000000
000000000003FC03FC007C007C007C007C007C007C007C007C007C007C007C007C007C00
7C007C007C007C007C707CF87CF878F8F070E01F800E26839D0F>I<FF0000FF00001F00
001F00001F00001F00001F00001F00001F00001F00001F00001F0FF81F0FF81F03801F07
001F0C001F18001F70001FF8001FFC001FBC001F3E001F1F001F0F001F0F801F07C01F03
E0FFC7FCFFC7FC161D7F9C19>I<FF00FF001F001F001F001F001F001F001F001F001F00
1F001F001F001F001F001F001F001F001F001F001F001F001F001F001F001F00FFE0FFE0
0B1D7F9C0E>I<FF0FC07E00FF31E18F001F40F207801F80FC07C01F80FC07C01F00F807
C01F00F807C01F00F807C01F00F807C01F00F807C01F00F807C01F00F807C01F00F807C0
1F00F807C01F00F807C01F00F807C0FFE7FF3FF8FFE7FF3FF825127F9128>I<FF0FC0FF
31E01F40F01F80F81F80F81F00F81F00F81F00F81F00F81F00F81F00F81F00F81F00F81F
00F81F00F81F00F8FFE7FFFFE7FF18127F911B>I<01FC000F07801C01C03C01E07800F0
7800F0F800F8F800F8F800F8F800F8F800F8F800F87800F07800F03C01E01E03C00F0780
01FC0015127F9118>I<FF3F80FFE1E01F80F01F00781F007C1F003C1F003E1F003E1F00
3E1F003E1F003E1F003E1F003C1F007C1F00781F80F01FC1E01F3F001F00001F00001F00
001F00001F00001F0000FFE000FFE000171A7F911B>I<FE3E00FE47001E8F801E8F801E
8F801F07001F00001F00001F00001F00001F00001F00001F00001F00001F00001F0000FF
F000FFF00011127F9114>114 D<1FD830786018E018E018F000FF807FE07FF01FF807FC
007CC01CC01CE01CE018F830CFC00E127E9113>I<0300030003000300070007000F000F
003FFCFFFC1F001F001F001F001F001F001F001F001F001F0C1F0C1F0C1F0C0F08079803
F00E1A7F9913>I<FF07F8FF07F81F00F81F00F81F00F81F00F81F00F81F00F81F00F81F
00F81F00F81F00F81F00F81F00F81F01F80F01F80786FF01F8FF18127F911B>I<FFC1FC
FFC1FC1F00601F80E00F80C00FC0C007C18007C18003E30003E30001F60001F60001FE00
00FC0000FC0000780000780000300016127F9119>I<FF8FF8FEFF8FF8FE1F03E0301F03
E0301F83E0700F83F0600F86F06007C6F0C007CEF8C007EC79C003EC7D8003F83D8001F8
3F0001F83F0001F01F0000F01E0000E00E0000E00E001F127F9122>I<FFC7FCFFC7FC1F
81800F838007C70003EE0001FC0001F80000F800007C0000FE0001DF00039F00070F8006
07C00C03E0FF07FCFF07FC16127F9119>I<FFC1FCFFC1FC1F00601F80E00F80C00FC0C0
07C18007C18003E30003E30001F70001F60000FE0000FC0000FC00007800007800003000
003000007000706000F86000F8C000F980007300003E0000161A7F9119>I
E /Fj 5 54 df<0C003C00CC000C000C000C000C000C000C000C000C000C000C000C000C
00FF8009107E8F0F>49 D<1F00618040C08060C0600060006000C00180030006000C0010
2020207FC0FFC00B107F8F0F>I<1F00218060C060C000C0008001800F00008000400060
C060C060804060801F000B107F8F0F>I<0300030007000F000B001300330023004300C3
00FFE003000300030003001FE00B107F8F0F>I<20803F002C002000200020002F003080
2040006000600060C06080C061801F000B107F8F0F>I E /Fk 77
126 df<60F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0600000000060F0F0600419779816>33
D<E038F078F078F078F078F078F078F078E038E03860300D0B7C9816>I<038700038700
0387000387000387000387007FFFC0FFFFE0FFFFE0070E00070E00070E000E1C000E1C00
0E1C000E1C00FFFFE0FFFFE07FFFC01C38001C38001C38001C38001C38001C380013197F
9816>I<3801807C03807C0380EE0700EE0700EE0E00EE0E00EE0E00EE1C007C1C007C38
0038380000700000700000700000E00000E00001C00001C00001C0000380000383800707
C00707C00E0EE00E0EE00E0EE01C0EE01C0EE03807C03807C018038013207F9C16>37
D<00E001E0038007000E001C001C0038003800700070007000E000E000E000E000E000E0
00E000E000E000700070007000380038001C001C000E000700038001E000E00B217A9C16
>40 D<C000E000700038001C000E000E000700070003800380038001C001C001C001C001
C001C001C001C001C0038003800380070007000E000E001C0038007000E000C0000A217B
9C16>I<01C00001C00001C00001C00071C700F9CF807FFF001FFC0007F00007F0001FFC
007FFF00F9CF8071C70001C00001C00001C00001C00011127E9516>I<01C00001C00001
C00001C00001C00001C00001C00001C000FFFF80FFFF80FFFF8001C00001C00001C00001
C00001C00001C00001C00001C00011137E9516>I<387C7E7E3E0E1E1C78F060070B7984
16>I<FFFF80FFFF80FFFF8011037E8D16>I<70F8F8F8700505788416>I<000180000380
000380000700000700000E00000E00001C00001C0000380000380000700000700000E000
00E00001C00001C0000380000380000700000700000E00000E00001C00001C0000380000
380000700000700000E00000E00000C0000011207E9C16>I<03E0000FF8001FFC001E3C
00380E00780F00700700700700E00380E00380E00380E00380E00380E00380E00380E003
80F00780700700700700780F003C1E001E3C001FFC000FF80003E00011197E9816>I<01
800380038007800F807F80FF807380038003800380038003800380038003800380038003
800380038003807FF87FFC7FF80E197C9816>I<07E0001FF8003FFC00783E00E00700F0
0780F00380600380000380000380000700000700000E00001C0000380000700000E00001
C0000380000F00001E03803803807FFF80FFFF807FFF8011197E9816>I<07E0001FF800
3FFC00781E00780700300700000700000700000E00003E0007FC0007F00007FC00001E00
000700000300000380000380600380F00380E00700781E003FFC001FF80007E00011197E
9816>I<007C0000FC0000DC0001DC00039C00039C00071C000F1C000E1C001E1C003C1C
00381C00781C00F01C00FFFFE0FFFFE0FFFFE0001C00001C00001C00001C00001C0001FF
C001FFC001FFC013197F9816>I<3FFE003FFE003FFE0038000038000038000038000038
00003800003800003BF0003FFC003FFE003C0F00300700000380000380600380F00380F0
0380E00700781E003FFC001FF80007E00011197E9816>I<00F80003FC0007FE000F0700
1C0F00380F00780600700000700000E3F800EFFC00FFFE00F80F00F00700F00380E00380
E003807003807003807007803807003C1E001FFC000FF80003E00011197E9816>I<E000
00FFFF80FFFF80FFFF80E00F00E01E00001C0000380000780000700000E00000E00001C0
0001C00001C0000380000380000380000380000700000700000700000700000700000700
00070000111A7E9916>I<07F0001FFC003FFE007C1F00F00780E00380E00380E0038070
07007C1F001FFC0007F0001FFC003C1E00700700F00780E00380E00380E00380F0078070
07007C1F003FFE001FFC0007F00011197E9816>I<03E0000FF8001FFC003C1E00700E00
700700E00700E00780E00380E00380E00780700780780F803FFF801FFB800FE380000700
000700300700780E00781C007078003FF0001FE0000F800011197E9816>I<70F8F8F870
000000000000000070F8F8F8700512789116>I<387C7C7C38000000000000000038787C
7C3C1C1C3870E0400618799116>I<000180000780001F80003E0000F80001F00007C000
0F80003E0000FC0000F00000FC00003E00000F800007C00001F00000F800003E00001F80
00078000018011157E9616>I<7FFF00FFFF80FFFF800000000000000000000000000000
00FFFF80FFFF807FFF00110B7E9116>I<C00000F00000FC00003E00000F800007C00001
F00000F800003E00001F80000780001F80003E0000F80001F00007C0000F80003E0000FC
0000F00000C0000011157E9616>I<00E00001F00001F00001B00001B00003B80003B800
03B800031800071C00071C00071C00071C00071C000E0E000E0E000FFE000FFE001FFF00
1C07001C07001C07007F1FC0FF1FE07F1FC013197F9816>65 D<01F18007FB800FFF801F
0F803C0780380380700380700380F00000E00000E00000E00000E00000E00000E00000E0
0000F000007003807003803803803C07001F0F000FFE0007FC0001F00011197E9816>67
D<7FF800FFFE007FFF001C0F001C07801C03C01C01C01C01C01C01E01C00E01C00E01C00
E01C00E01C00E01C00E01C00E01C00E01C01C01C01C01C03C01C07801C0F807FFF00FFFE
007FF8001319809816>I<7FFFC0FFFFC07FFFC01C01C01C01C01C01C01C01C01C00001C
00001C1C001C1C001FFC001FFC001FFC001C1C001C1C001C00001C00E01C00E01C00E01C
00E01C00E07FFFE0FFFFE07FFFE013197F9816>I<FFFFE0FFFFE0FFFFE01C00E01C00E0
1C00E01C00E01C00001C00001C1C001C1C001FFC001FFC001FFC001C1C001C1C001C0000
1C00001C00001C00001C00001C0000FF8000FFC000FF800013197F9816>I<FFFEFFFEFF
FE0380038003800380038003800380038003800380038003800380038003800380038003
800380FFFEFFFEFFFE0F197D9816>73 D<07FE07FF07FE00380038003800380038003800
380038003800380038003800380038003800386038F038F0707FF07FE01F8010197D9816
>I<7F0FE0FF8FF07F0FE01C07801C0F001C0E001C1C001C3C001C78001CF0001CE0001D
F0001FF0001FF8001F38001E1C001C1C001C0E001C0E001C07001C07001C03807F07E0FF
8FF07F07E01419809816>I<FFC000FFC000FFC0001C00001C00001C00001C00001C0000
1C00001C00001C00001C00001C00001C00001C00001C00001C00001C00401C00E01C00E0
1C00E01C00E0FFFFE0FFFFE0FFFFE013197F9816>I<FC07E0FE0FE0FE0FE03A0B803B1B
803B1B803B1B803B1B803B1B803BBB8039B38039B38039B38039B38039F38038E38038E3
80380380380380380380380380380380FE0FE0FE0FE0FE0FE013197F9816>I<7E1FC0FF
3FE07F1FC01D07001D87001D87001D87001DC7001DC7001CC7001CC7001CE7001CE7001C
E7001C67001C67001C77001C77001C37001C37001C37001C17007F1F00FF9F007F0F0013
197F9816>I<1FFC003FFE007FFF00780F00F00780E00380E00380E00380E00380E00380
E00380E00380E00380E00380E00380E00380E00380E00380E00380F00780F00780780F00
7FFF003FFE001FFC0011197E9816>I<7FF800FFFE007FFF001C0F801C03801C03C01C01
C01C01C01C01C01C03C01C03801C0F801FFF001FFE001FF8001C00001C00001C00001C00
001C00001C00001C00007F0000FF80007F000012197F9816>I<7FE000FFF8007FFC001C
1E001C0F001C07001C07001C07001C07001C0F001C1E001FFC001FF8001FFC001C1C001C
0E001C0E001C0E001C0E001C0E201C0E701C0E707F07E0FF87E07F03C014197F9816>82
D<07E3001FFF003FFF00781F00F00700E00700E00700E00000F000007800003F80001FF0
0007FC0000FE00000F00000700000380000380600380E00380E00700F80F00FFFE00FFFC
00C7F00011197E9816>I<7FFFE0FFFFE0FFFFE0E0E0E0E0E0E0E0E0E0E0E0E000E00000
E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000
E00000E00007FC000FFE0007FC0013197F9816>I<FE0FE0FF1FE0FE0FE03803801C0700
1C07001C07001C07000E0E000E0E000E0E000E0E00060C00071C00071C00071C00071C00
03180003B80003B80003B80001B00001F00001F00000E00013197F9816>86
D<FC07E0FE0FE0FC07E07001C07001C07001C030018038038038038038038038E38039F3
8039F38039B38019B30019B30019B30019B30019B30019B3001913001B1B000F1E000F1E
000E0E0013197F9816>I<7FFF80FFFF80FFFF80E00700E00F00E01E00E01C00003C0000
780000700000F00001E00001C00003C0000780000700000F00001E03801C03803C038078
0380700380FFFF80FFFF80FFFF8011197E9816>90 D<FFF0FFF0FFF0E000E000E000E000
E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000
E000E000E000E000FFF0FFF0FFF00C20789C16>I<C00000E00000E00000700000700000
3800003800001C00001C00000E00000E000007000007000003800003800001C00001C000
00E00000E000007000007000003800003800001C00001C00000E00000E00000700000700
00038000038000018011207E9C16>I<FFF0FFF0FFF00070007000700070007000700070
007000700070007000700070007000700070007000700070007000700070007000700070
0070FFF0FFF0FFF00C207F9C16>I<03000F803FE0FDF8F07840100D067C9816>I<1FE000
3FF0007FF800783C00300E00000E00000E0003FE001FFE003E0E00700E00E00E00E00E00
E00E00783E007FFFE03FE7E00F83E013127E9116>97 D<7E0000FE00007E00000E00000E
00000E00000E00000E3E000EFF000FFF800F83C00F00E00E00E00E00700E00700E00700E
00700E00700E00700E00E00F01E00F83C00FFF800EFF00063C001419809816>I<03F80F
FC1FFE3C1E780C7000E000E000E000E000E000F000700778073E0E1FFC0FF803F010127D
9116>I<003F00007F00003F0000070000070000070000070003C7000FF7001FFF003C1F
00780F00700700E00700E00700E00700E00700E00700E00700700F00700F003C1F001FFF
E00FE7F007C7E014197F9816>I<03E00FF81FFC3C1E780E7007E007FFFFFFFFFFFFE000
E000700778073C0F1FFE0FFC03F010127D9116>I<001F00007F8000FF8001E78001C300
01C00001C0007FFF00FFFF00FFFF0001C00001C00001C00001C00001C00001C00001C000
01C00001C00001C00001C00001C0003FFE007FFF003FFE0011197F9816>I<03E3C007F7
E00FFFE01C1CC0380E00380E00380E00380E00380E001C1C000FF8001FF0001BE0003800
001800001FFC001FFF003FFF807803C0E000E0E000E0E000E0E000E07001C07C07C03FFF
800FFE0003F800131C7F9116>I<7E0000FE00007E00000E00000E00000E00000E00000E
3C000EFE000FFF000F87800F03800E03800E03800E03800E03800E03800E03800E03800E
03800E03800E03807FC7F0FFE7F87FC7F01519809816>I<018003C003C0018000000000
000000007FC07FC07FC001C001C001C001C001C001C001C001C001C001C001C001C07FFF
FFFF7FFF101A7D9916>I<7E0000FE00007E00000E00000E00000E00000E00000E7FE00E
7FE00E7FE00E0F000E1E000E3C000E78000EF0000FF0000FF8000FBC000F1E000E0E000E
07000E07807F87F0FFCFF07F87F01419809816>107 D<FFC000FFC000FFC00001C00001
C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001
C00001C00001C00001C00001C00001C000FFFF80FFFF80FFFF8011197E9816>I<F9C380
FFEFC0FFFFE03C78E03C78E03870E03870E03870E03870E03870E03870E03870E03870E0
3870E03870E0FE7CF8FE7CF8FE3C781512809116>I<7E3C00FEFE007FFF000F87800F03
800E03800E03800E03800E03800E03800E03800E03800E03800E03800E03807FC7F0FFE7
F87FC7F01512809116>I<03E0000FF8001FFC003C1E00780F00700700E00380E00380E0
0380E00380E00380F00780700700780F003C1E001FFC000FF80003E00011127E9116>I<
7E3E00FEFF007FFF800F83C00F00E00E00E00E00700E00700E00700E00700E00700E0070
0E00E00F01E00F83C00FFF800EFF000E3C000E00000E00000E00000E00000E00000E0000
7FC000FFE0007FC000141B809116>I<FF0FC0FF3FE0FF7FE007F04007C0000780000780
00070000070000070000070000070000070000070000070000FFFC00FFFC00FFFC001312
7F9116>114 D<0FEC3FFC7FFCF03CE01CE01C70007F801FF007F8003C600EE00EF00EF8
1EFFFCFFF8C7E00F127D9116>I<0300000700000700000700000700007FFF00FFFF00FF
FF0007000007000007000007000007000007000007000007010007038007038007038007
870003FE0001FC0000F80011177F9616>I<7E1F80FE3F807E1F800E03800E03800E0380
0E03800E03800E03800E03800E03800E03800E03800E03800E0F800FFFF007FBF803E3F0
1512809116>I<7F1FC0FF1FE07F1FC01C07001E0F000E0E000E0E000E0E00071C00071C
00071C00071C0003B80003B80003B80001F00001F00000E00013127F9116>I<FF1FE0FF
BFE0FF1FE038038038038038038038038038E38019F30019F30019B3001DB7001DB7001D
B7001DB7000F1E000F1E000F1E0013127F9116>I<7F1FC07F3FC07F1FC00F1C00073C00
03B80003F00001F00000E00001E00001F00003B800073C00071C000E0E007F1FC0FF3FE0
7F1FC013127F9116>I<7F1FC0FF9FE07F1FC01C07000E07000E0E000E0E00070E00071C
00071C00039C00039C0003980001B80001B80000F00000F00000F00000E00000E00000E0
0001C00079C0007BC0007F80003F00003C0000131B7F9116>I<3FFFC07FFFC07FFFC070
0780700F00701E00003C0000780001F00003E0000780000F00001E01C03C01C07801C0FF
FFC0FFFFC0FFFFC012127F9116>I<001F80007F8000FF8001E00001C00001C00001C000
01C00001C00001C00001C00001C00001C00003C0007F8000FF0000FF00007F800003C000
01C00001C00001C00001C00001C00001C00001C00001C00001C00001E00000FF80007F80
001F8011207E9C16>I<E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0E0
E0E0E0E0E0E00320779C16>I<7C0000FF0000FF800003C00001C00001C00001C00001C0
0001C00001C00001C00001C00001C00001E00000FF00007F80007F8000FF0001E00001C0
0001C00001C00001C00001C00001C00001C00001C00001C00003C000FF8000FF00007C00
0011207E9C16>I E /Fl 48 128 df<0001FC000703000C03001C07001C030018000038
0000380000380000380000700007FFFC00701C00701C00701C00E03800E03800E03800E0
3800E07001C07001C07001C07001C0E201C0E201C0E20380E40380640380380380000300
00070000060000C60000E40000CC00007000001825819C17>12 D<000100000300000300
000300000300000600000600000600000600000C00000C00000C00FFFFFFFFFFFF001800
001800001800003000003000003000003000006000006000006000006000004000181A7A
9620>43 D<FFC0FFC0FFC00A037D890F>45 D<3078F06005047C830D>I<003C0000C600
0183000303000603000603800E03800C03801C03801C0300380700380700380700380700
700E00700E00700E00700E00E01C00E01C00E01C00E03800E03800E03000C06000E06000
60C0007180001E0000111D7B9B15>48 D<00020006000C001C007C039C00380038003800
38007000700070007000E000E000E000E001C001C001C001C003800380038003800780FF
F00F1C7C9B15>I<003C0000C3000101800201800201C00441C00441C00841C00841C008
41C01083801083801107000E0600000C0000180000300000C00001000006000008000010
01001002002002004006007E0C00C7F80083F80080E000121D7C9B15>I<001E00006100
0081800180800300C00300C006018006018006018007030007860003CC0003F00001F000
037800063C00081E00180E00300E00600600600600600600C00C00C00C00C01800601000
60200030C0000F0000121D7C9B15>56 D<003C0000C6000183000303000603000E03000C
03801C03801C03001C0300380700380700380700380F00380E00181E00181E000C6C0007
9C00001C00001800003800003000006000E0C000E0C0008180008600007C0000111D7B9B
15>I<0000180000001800000038000000380000007800000078000000B8000001B80000
0138000002380000023C0000041C0000041C0000081C0000181C0000101C0000201C0000
201C00007FFC0000401C0000801C0001801C0001001C0002001C0002001C0004000E000C
000E001C001E00FF00FFC01A1D7E9C1F>65 D<01FFFE00003C0780003803C0003801C000
3801C0003801C0007001C0007003C0007003C00070078000E0070000E00E0000E03C0000
FFF80001C01C0001C00E0001C00F0001C00F0003800F0003800F0003800F0003800F0007
001E0007001C0007003C00070078000E01E000FFFF80001A1C7D9B1D>I<0003F020001E
0C60003002E000E003C001C001C0038001C0070000C00E0000801E0000801C0000803C00
00803C000000780000007800000078000000F0000000F0000000F0000000F0000000F000
0400F0000400F0000400F0000800700008007000100038002000180040000C0180000706
000001F800001B1E7A9C1E>I<01FFFE00003C0780003801C0003801C0003800E0003800
E0007000F00070007000700070007000F000E000F000E000F000E000F000E000F001C001
E001C001E001C001E001C001C0038003C003800380038007800380070007000E0007001C
0007003800070070000E01C000FFFF00001C1C7D9B1F>I<01FFFFE0003C00E000380060
0038004000380040003800400070004000700040007020400070200000E0400000E04000
00E0C00000FFC00001C0800001C0800001C0800001C08000038101000380010003800200
03800200070004000700040007000C00070018000E007800FFFFF0001B1C7D9B1C>I<01
FFC0003C0000380000380000380000380000700000700000700000700000E00000E00000
E00000E00001C00001C00001C00001C00003800003800003800003800007000007000007
00000700000F0000FFE000121C7E9B10>73 D<01FFE0003C000038000038000038000038
0000700000700000700000700000E00000E00000E00000E00001C00001C00001C00001C0
000380080380080380080380100700100700300700600700E00E03C0FFFFC0151C7D9B1A
>76 D<01FE0007F8003E000780002E000F00002E001700002E001700002E002700004E00
2E00004E004E00004E004E00004E008E00008E011C00008E011C00008E021C00008E021C
000107043800010704380001070838000107103800020710700002072070000207207000
0207407000040740E000040780E000040700E0000C0700E0001C0601E000FF861FFC0025
1C7D9B25>I<01FC03FE001C0070003C0060002E0040002E0040002E0040004700800047
008000470080004380800083810000838100008181000081C1000101C2000101C2000100
E2000100E2000200E4000200740002007400020074000400380004003800040038000C00
18001C001000FF8010001F1C7D9B1F>I<0007F000001C1C0000700E0000E0070001C003
8003800380070003800E0003C01E0003C01C0003C03C0003C03C0003C0780003C0780003
C0780003C0F0000780F0000780F0000780F0000F00F0000F00F0000E00F0001E00F0003C
0070003800700070007800E0003801C0001C0380000E0E000003F800001A1E7A9C20>I<
01FFFC00003C070000380380003801C0003801C0003801C0007003C0007003C0007003C0
0070038000E0078000E0070000E00E0000E0380001FFE00001C0000001C0000001C00000
03800000038000000380000003800000070000000700000007000000070000000F000000
FFE000001A1C7D9B1C>I<000F8400304C00403C00801801001803001803001806001006
001006000007000007000003E00003FC0001FF00007F800007C00001C00001C00000C000
00C02000C02000C0600180600180600300600200F00400CC180083E000161E7D9C17>83
D<1FFFFFC01C0701C0300E00C0200E0080600E0080400E0080401C0080801C0080801C00
80001C000000380000003800000038000000380000007000000070000000700000007000
0000E0000000E0000000E0000000E0000001C0000001C0000001C0000001C0000003C000
007FFE00001A1C799B1E>I<7FF0FF800F001C000E0018000E0010000E0010000E001000
1C0020001C0020001C0020001C0020003800400038004000380040003800400070008000
700080007000800070008000E0010000E0010000E0010000E0020000E0020000E0040000
E00400006008000030300000104000000F800000191D779B1F>I<03CC063C0C3C181C38
38303870387038E070E070E070E070E0E2C0E2C0E261E462643C380F127B9115>97
D<3F00070007000E000E000E000E001C001C001C001C0039C03E60383038307038703870
387038E070E070E070E060E0E0C0C0C1C0618063003C000D1D7B9C13>I<01F007080C08
181C3838300070007000E000E000E000E000E000E008E010602030C01F000E127B9113>
I<001F80000380000380000700000700000700000700000E00000E00000E00000E0003DC
00063C000C3C00181C00383800303800703800703800E07000E07000E07000E07000E0E2
00C0E200C0E20061E4006264003C3800111D7B9C15>I<01E007100C1018083810701070
607F80E000E000E000E000E000E0086010602030C01F000D127B9113>I<0003C0000670
000C70001C60001C00001C0000380000380000380000380000380003FF80007000007000
00700000700000700000E00000E00000E00000E00000E00001C00001C00001C00001C000
01C000038000038000038000030000030000070000C60000E60000CC0000780000142581
9C0D>I<00F3018F030F06070E0E0C0E1C0E1C0E381C381C381C381C3838303830381878
18F00F700070007000E000E0C0C0E1C0C3007E00101A7D9113>I<0FC00001C00001C000
0380000380000380000380000700000700000700000700000E78000E8C000F0E000E0E00
1C0E001C0E001C0E001C0E00381C00381C00381C00383800703880703880707080707100
E03200601C00111D7D9C15>I<01800380010000000000000000000000000000001C0026
00470047008E008E000E001C001C001C0038003800710071007100720072003C00091C7C
9B0D>I<0FC00001C00001C0000380000380000380000380000700000700000700000700
000E0F000E11000E23800E43801C83001C80001D00001E00003F800039C00038E00038E0
0070E20070E20070E20070E400E06400603800111D7D9C13>107
D<1F800380038007000700070007000E000E000E000E001C001C001C001C003800380038
0038007000700070007000E400E400E400E40068003800091D7C9C0B>I<3C1E07802663
18C04683A0E04703C0E08E0380E08E0380E00E0380E00E0380E01C0701C01C0701C01C07
01C01C070380380E0388380E0388380E0708380E0710701C0320300C01C01D127C9122>
I<3C3C002646004687004707008E07008E07000E07000E07001C0E001C0E001C0E001C1C
00381C40381C40383840383880701900300E0012127C9117>I<01E007180C0C180C380C
300E700E700EE01CE01CE01CE018E038E030E06060C031801E000F127B9115>I<078700
04D98008E0C008E0C011C0E011C0E001C0E001C0E00381C00381C00381C0038180070380
0703000707000706000E8C000E70000E00000E00001C00001C00001C00001C00003C0000
FF8000131A7F9115>I<3C3C26C2468747078E068E000E000E001C001C001C001C003800
3800380038007000300010127C9112>114 D<01F006080C080C1C18181C001F001FC00F
F007F0007800386030E030C030806060C01F000E127D9111>I<00C001C001C001C00380
038003800380FFE00700070007000E000E000E000E001C001C001C001C00384038403840
388019000E000B1A7D990E>I<1E0300270700470700470700870E00870E000E0E000E0E
001C1C001C1C001C1C001C1C003838803838801838801839001C5900078E0011127C9116
>I<1E06270E470E4706870287020E020E021C041C041C041C0818083808181018200C40
07800F127C9113>I<1E01832703874703874703838707018707010E07010E07011C0E02
1C0E021C0E021C0E04180C04181C04181C081C1C100C263007C3C018127C911C>I<070E
0019910010E38020E38041C30041C00001C00001C0000380000380000380000380000702
00670200E70400CB04008B080070F00011127D9113>I<1E03270747074707870E870E0E
0E0E0E1C1C1C1C1C1C1C1C38383838183818381C7007F00070007000E0E0C0E1C0818047
003C00101A7C9114>I<038207C20FEC0838100800100020004000800100020004000808
1008383067F043E081C00F127D9111>I<6180F3C0E3C0C1800A04749C15>127
D E /Fm 13 117 df<01020408103020606040C0C0C0C0C0C0C0C0C0C040606020301008
040201081E7E950D>40 D<80402010080C0406060203030303030303030303020606040C
0810204080081E7E950D>I<006000006000006000006000006000006000006000006000
006000006000FFFFF0FFFFF0006000006000006000006000006000006000006000006000
00600000600014167E9119>43 D<0F0030C0606060604020C030C030C030C030C030C030
C030C030C03040206060606030C00F000C137E9211>48 D<0C001C00EC000C000C000C00
0C000C000C000C000C000C000C000C000C000C000C000C00FFC00A137D9211>I<1F0060
C06060F070F030603000700070006000C001C00180020004000810101020207FE0FFE00C
137E9211>I<0FC030707038703870380038003000E00FC0007000380018001C601CF01C
F018E03860701FC00E137F9211>I<006000E000E00160026006600C6008601060206060
60C060FFFC0060006000600060006003FC0E137F9211>I<60607FC07F80440040004000
40004F0070C040E0006000700070E070E070E06040E021C01F000C137E9211>I<07C00C
201070207060006000C000CF00D0C0E060C020C030C030C03040306020206010C00F000C
137E9211>I<7FFFE0FFFFF0000000000000000000000000000000000000FFFFF07FFFE0
140A7E8B19>61 D<F00030003000300030003000300033E0343038183018301830183018
30183018301830183018FC7E0F147F9312>104 D<10001000100030007000FF80300030
003000300030003000300030803080308011000E0009127F910D>116
D E /Fn 86 125 df<007E1F0001C1B1800303E3C00703C3C00E03C1800E01C0000E01C0
000E01C0000E01C0000E01C0000E01C000FFFFFC000E01C0000E01C0000E01C0000E01C0
000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0
000E01C0000E01C0000E01C0007F87FC001A1D809C18>11 D<007E0001C1800301800703
C00E03C00E01800E00000E00000E00000E00000E0000FFFFC00E01C00E01C00E01C00E01
C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01
C07F87F8151D809C17>I<007FC001C1C00303C00703C00E01C00E01C00E01C00E01C00E
01C00E01C00E01C0FFFFC00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E
01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C07FCFF8151D809C17>I<003F07
E00001C09C18000380F018000701F03C000E01E03C000E00E018000E00E000000E00E000
000E00E000000E00E000000E00E00000FFFFFFFC000E00E01C000E00E01C000E00E01C00
0E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E
00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C007FC7FCFF80211D
809C23>I<60F0F0F0F0F0F0F060606060606060606060606060000000000060F0F06004
1E7C9D0C>33 D<6060F0F0F8F86868080808080808101010102020404080800D0C7F9C15
>I<60F0F8680808081010204080050C7C9C0C>39 D<004000800100020006000C000C00
18001800300030007000600060006000E000E000E000E000E000E000E000E000E000E000
E000E000600060006000700030003000180018000C000C00060002000100008000400A2A
7D9E10>I<800040002000100018000C000C000600060003000300038001800180018001
C001C001C001C001C001C001C001C001C001C001C001C001800180018003800300030006
0006000C000C00180010002000400080000A2A7E9E10>I<000600000006000000060000
000600000006000000060000000600000006000000060000000600000006000000060000
00060000FFFFFFE0FFFFFFE0000600000006000000060000000600000006000000060000
000600000006000000060000000600000006000000060000000600001B1C7E9720>43
D<60F0F0701010101020204080040C7C830C>I<FFE0FFE00B0280890E>I<60F0F0600404
7C830C>I<00010003000600060006000C000C000C001800180018003000300030006000
6000C000C000C0018001800180030003000300060006000C000C000C0018001800180030
0030003000600060006000C000C00010297E9E15>I<03C00C301818300C300C700E6006
6006E007E007E007E007E007E007E007E007E007E007E007E007E00760066006700E300C
300C18180C3007E0101D7E9B15>I<030007003F00C70007000700070007000700070007
000700070007000700070007000700070007000700070007000700070007000F80FFF80D
1C7C9B15>I<07C01830201C400C400EF00FF80FF807F8077007000F000E000E001C001C
00380070006000C00180030006010C01180110023FFE7FFEFFFE101C7E9B15>I<07E018
30201C201C781E780E781E381E001C001C00180030006007E00030001C001C000E000F00
0F700FF80FF80FF80FF00E401C201C183007E0101D7E9B15>I<000C00000C00001C0000
3C00003C00005C0000DC00009C00011C00031C00021C00041C000C1C00081C00101C0030
1C00201C00401C00C01C00FFFFC0001C00001C00001C00001C00001C00001C00001C0001
FFC0121C7F9B15>I<300C3FF83FF03FC020002000200020002000200023E02430281830
1C200E000E000F000F000F600FF00FF00FF00F800E401E401C2038187007C0101D7E9B15
>I<00F0030C06040C0E181E301E300C700070006000E3E0E430E818F00CF00EE006E007
E007E007E007E007600760077006300E300C18180C3003E0101D7E9B15>I<4000007FFF
807FFF007FFF0040020080040080040080080000100000100000200000600000400000C0
0000C00001C0000180000180000380000380000380000380000780000780000780000780
00078000078000030000111D7E9B15>I<03E00C301008200C2006600660066006700678
0C3E083FB01FE007F007F818FC307E601E600FC007C003C003C003C00360026004300C1C
1007E0101D7E9B15>I<03C00C301818300C700C600EE006E006E007E007E007E007E007
6007700F300F18170C2707C700060006000E300C780C78187010203030C00F80101D7E9B
15>I<60F0F0600000000000000000000060F0F06004127C910C>I<60F0F0600000000000
000000000060F0F0701010101020204080041A7C910C>I<7FFFFFC0FFFFFFE000000000
00000000000000000000000000000000000000000000000000000000FFFFFFE07FFFFFC0
1B0C7E8F20>61 D<003F800000C0600003001800040004000800020010000100201F0080
2070808040E0404040C0384041C038408180382083803820838038208380382083803820
838038208180382041C0382040C0384040E0784020709880201F0F001000000008000000
04000000030001E000C01F80003FF0001B1D7E9C20>64 D<000600000006000000060000
000F0000000F0000000F00000017800000178000001780000023C0000023C0000023C000
0041E0000041E0000041E0000080F0000080F0000180F8000100780001FFF80003007C00
02003C0002003C0006003E0004001E0004001E000C001F001E001F00FF80FFF01C1D7F9C
1F>I<FFFFC00F00F00F00380F003C0F001C0F001E0F001E0F001E0F001E0F001C0F003C
0F00780F01F00FFFE00F00780F003C0F001E0F000E0F000F0F000F0F000F0F000F0F000F
0F001E0F001E0F003C0F0078FFFFE0181C7E9B1D>I<001F808000E06180018019800700
07800E0003801C0003801C00018038000180780000807800008070000080F0000000F000
0000F0000000F0000000F0000000F0000000F0000000F000000070000080780000807800
0080380000801C0001001C0001000E000200070004000180080000E03000001FC000191E
7E9C1E>I<FFFFC0000F00F0000F003C000F000E000F0007000F0007000F0003800F0003
C00F0001C00F0001C00F0001E00F0001E00F0001E00F0001E00F0001E00F0001E00F0001
E00F0001E00F0001C00F0001C00F0003C00F0003800F0007800F0007000F000E000F001C
000F007000FFFFC0001B1C7E9B20>I<FFFFFC0F003C0F000C0F00040F00040F00060F00
020F00020F02020F02000F02000F02000F06000FFE000F06000F02000F02000F02000F02
010F00010F00020F00020F00020F00060F00060F000C0F003CFFFFFC181C7E9B1C>I<FF
FFF80F00780F00180F00080F00080F000C0F00040F00040F02040F02000F02000F02000F
06000FFE000F06000F02000F02000F02000F02000F00000F00000F00000F00000F00000F
00000F00000F8000FFF800161C7E9B1B>I<001F808000E0618001801980070007800E00
03801C0003801C00018038000180780000807800008070000080F0000000F0000000F000
0000F0000000F0000000F0000000F000FFF0F0000F807000078078000780780007803800
07801C0007801C0007800E00078007000B800180118000E06080001F80001C1E7E9C21>
I<FFF3FFC00F003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C
000F003C000F003C000F003C000F003C000FFFFC000F003C000F003C000F003C000F003C
000F003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C
00FFF3FFC01A1C7E9B1F>I<FFF00F000F000F000F000F000F000F000F000F000F000F00
0F000F000F000F000F000F000F000F000F000F000F000F000F000F000F00FFF00C1C7F9B
0F>I<1FFF00F80078007800780078007800780078007800780078007800780078007800
7800780078007800787078F878F878F878F0F040E021C01F00101D7F9B15>I<FFF03FE0
0F000F000F000C000F0008000F0010000F0020000F0040000F0080000F0100000F020000
0F0400000F0E00000F1F00000F2F00000F2780000F4780000F83C0000F01E0000F01E000
0F00F0000F00F8000F0078000F003C000F003C000F001E000F001F000F001F80FFF07FF0
1C1C7E9B20>I<FFF8000F80000F00000F00000F00000F00000F00000F00000F00000F00
000F00000F00000F00000F00000F00000F00000F00000F00000F00080F00080F00080F00
180F00180F00100F00300F00700F01F0FFFFF0151C7E9B1A>I<FF8000FF800F8000F800
0F8000F8000BC00178000BC00178000BC001780009E002780009E002780008F004780008
F004780008F0047800087808780008780878000878087800083C107800083C107800083C
107800081E207800081E207800081E207800080F407800080F4078000807807800080780
7800080780780008030078001C03007800FF8307FF80211C7E9B26>I<FF007FC00F800E
000F8004000BC0040009E0040009E0040008F0040008F8040008780400083C0400083C04
00081E0400080F0400080F0400080784000807C4000803C4000801E4000801E4000800F4
0008007C0008007C0008003C0008003C0008001C0008000C001C000C00FF8004001A1C7E
9B1F>I<003F800000E0E0000380380007001C000E000E001C0007003C00078038000380
780003C0780003C0700001C0F00001E0F00001E0F00001E0F00001E0F00001E0F00001E0
F00001E0F00001E0700001C0780003C0780003C0380003803C0007801C0007000E000E00
07001C000380380000E0E000003F80001B1E7E9C20>I<FFFF800F00E00F00780F003C0F
001C0F001E0F001E0F001E0F001E0F001E0F001C0F003C0F00780F00E00FFF800F00000F
00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0000FFF00017
1C7E9B1C>I<003F800000E0E0000380380007001C000E000E001C0007003C0007803800
0380780003C0780003C0700001C0F00001E0F00001E0F00001E0F00001E0F00001E0F000
01E0F00001E0F00001E0700001C0780003C0780003C0380003803C0E07801C1107000E20
8E0007205C0003A0780000F0E020003FE0200000602000003060000038E000003FC00000
3FC000001F8000000F001B257E9C20>I<FFFF00000F01E0000F0078000F003C000F001C
000F001E000F001E000F001E000F001E000F001C000F003C000F0078000F01E0000FFF00
000F03C0000F00E0000F00F0000F0078000F0078000F0078000F0078000F0078000F0078
000F0078100F0078100F0038100F003C20FFF01C20000007C01C1D7E9B1F>I<07E0801C
1980300580700380600180E00180E00080E00080E00080F00000F800007C00007FC0003F
F8001FFE0007FF0000FF80000F800007C00003C00001C08001C08001C08001C0C00180C0
0180E00300D00200CC0C0083F800121E7E9C17>I<7FFFFFC0700F01C0600F00C0400F00
40400F0040C00F0020800F0020800F0020800F0020000F0000000F0000000F0000000F00
00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00
00000F0000000F0000000F0000000F0000001F800003FFFC001B1C7F9B1E>I<FFF07FC0
0F000E000F0004000F0004000F0004000F0004000F0004000F0004000F0004000F000400
0F0004000F0004000F0004000F0004000F0004000F0004000F0004000F0004000F000400
0F0004000F0004000F0004000700080007800800038010000180100000C020000070C000
001F00001A1D7E9B1F>I<FFE00FF01F0003C00F0001800F0001000F8003000780020007
80020003C0040003C0040003C0040001E0080001E0080001F0080000F0100000F0100000
F830000078200000782000003C4000003C4000003C4000001E8000001E8000001F800000
0F0000000F00000006000000060000000600001C1D7F9B1F>I<FFE0FFE0FF1F001F003C
1E001E00180F001F00100F001F00100F001F001007801F00200780278020078027802003
C027804003C043C04003C043C04003E043C04001E081E08001E081E08001E081E08000F1
00F10000F100F10000F100F100007900FA00007A007A00007A007A00003E007C00003C00
3C00003C003C00003C003C00001800180000180018000018001800281D7F9B2B>I<7FF0
FFC00FC03E000780180003C0180003E0100001E0200001F0600000F0400000788000007D
8000003D0000001E0000001F0000000F0000000F8000000F80000013C0000023E0000021
E0000041F00000C0F8000080780001007C0003003C0002001E0006001F001F003F80FFC0
FFF01C1C7F9B1F>I<FFF007FC0F8001E00780008007C0018003C0010003E0020001F002
0000F0040000F8040000780800007C1800003C1000001E2000001F2000000F4000000FC0
000007800000078000000780000007800000078000000780000007800000078000000780
000007800000078000007FF8001E1C809B1F>I<7FFFF07C01F07001E06003C06003C040
0780400F80400F00401E00001E00003C00007C0000780000F00000F00001E00003E00003
C0100780100780100F00101F00301E00203C00203C00607800E0F803E0FFFFE0141C7E9B
19>I<FEFEC0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
C0C0C0C0C0C0FEFE07297C9E0C>I<08081010202040404040808080808080B0B0F8F878
7830300D0C7A9C15>I<FEFE060606060606060606060606060606060606060606060606
06060606060606060606060606FEFE0729809E0C>I<0C0012002100408080400A057B9B
15>I<1FC000307000783800781C00301C00001C00001C0001FC000F1C00381C00701C00
601C00E01C40E01C40E01C40603C40304E801F870012127E9115>97
D<FC00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C7C
001D86001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00
C01C01C01C01801E030019060010F800131D7F9C17>I<07E00C301878307870306000E0
00E000E000E000E000E00060007004300418080C3007C00E127E9112>I<003F00000700
00070000070000070000070000070000070000070000070000070003E7000C1700180F00
300700700700600700E00700E00700E00700E00700E00700E00700600700700700300700
180F000C370007C7E0131D7E9C17>I<03E00C301818300C700E6006E006FFFEE000E000
E000E00060007002300218040C1803E00F127F9112>I<00F8018C071E061E0E0C0E000E
000E000E000E000E00FFE00E000E000E000E000E000E000E000E000E000E000E000E000E
000E000E000E007FE00F1D809C0D>I<00038003C4C00C38C01C3880181800381C00381C
00381C00381C001818001C38000C300013C0001000003000001800001FF8001FFF001FFF
803003806001C0C000C0C000C0C000C06001803003001C0E0007F800121C7F9215>I<FC
00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C7C001C
87001D03001E03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C
03801C03801C03801C0380FF9FF0141D7F9C17>I<18003C003C00180000000000000000
00000000000000FC001C001C001C001C001C001C001C001C001C001C001C001C001C001C
001C001C00FF80091D7F9C0C>I<00C001E001E000C00000000000000000000000000000
0FE000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E0
00E000E000E060E0F0C0F1C061803E000B25839C0D>I<FC00001C00001C00001C00001C
00001C00001C00001C00001C00001C00001C00001C3FC01C0F001C0C001C08001C10001C
20001C40001CE0001DE0001E70001C78001C38001C3C001C1C001C0E001C0F001C0F80FF
9FE0131D7F9C16>I<FC001C001C001C001C001C001C001C001C001C001C001C001C001C
001C001C001C001C001C001C001C001C001C001C001C001C001C001C00FF80091D7F9C0C
>I<FC7E07E0001C838838001D019018001E01E01C001C01C01C001C01C01C001C01C01C
001C01C01C001C01C01C001C01C01C001C01C01C001C01C01C001C01C01C001C01C01C00
1C01C01C001C01C01C001C01C01C00FF8FF8FF8021127F9124>I<FC7C001C87001D0300
1E03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C0380
1C03801C0380FF9FF014127F9117>I<03F0000E1C00180600300300700380600180E001
C0E001C0E001C0E001C0E001C0E001C06001807003803003001806000E1C0003F0001212
7F9115>I<FC7C001D86001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C
00E01C00E01C01C01C01C01C01801E03001D06001CF8001C00001C00001C00001C00001C
00001C00001C0000FF8000131A7F9117>I<03C1000C3300180B00300F00700700700700
E00700E00700E00700E00700E00700E00700600700700700300F00180F000C370007C700
000700000700000700000700000700000700000700003FE0131A7E9116>I<FCE01D301E
781E781C301C001C001C001C001C001C001C001C001C001C001C001C00FFC00D127F9110
>I<1F9030704030C010C010E010F8007F803FE00FF000F880388018C018C018E010D060
8FC00D127F9110>I<04000400040004000C000C001C003C00FFE01C001C001C001C001C
001C001C001C001C001C101C101C101C101C100C100E2003C00C1A7F9910>I<FC1F801C
03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C
03801C07800C07800E1B8003E3F014127F9117>I<FF07E03C03801C01001C01000E0200
0E020007040007040007040003880003880003D80001D00001D00000E00000E00000E000
00400013127F9116>I<FF3FCFE03C0F03801C0701801C0701001C0B01000E0B82000E0B
82000E1182000711C4000711C4000720C40003A0E80003A0E80003C0680001C0700001C0
700001803000008020001B127F911E>I<7F8FF00F03800F030007020003840001C80001
D80000F00000700000780000F800009C00010E00020E000607000403801E07C0FF0FF815
12809116>I<FF07E03C03801C01001C01000E02000E0200070400070400070400038800
03880003D80001D00001D00000E00000E00000E000004000004000008000008000F08000
F10000F300006600003C0000131A7F9116>I<7FFC70386038407040F040E041C003C003
8007000F040E041C043C0C380870087038FFF80E127F9112>I<FFFFF01401808B15>I<FF
FFFFFFFF802901808B2A>I E /Fo 26 121 df<000E00001E00007E0007FE00FFFE00FF
FE00F8FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000
FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000
FE0000FE0000FE0000FE0000FE0000FE0000FE007FFFFE7FFFFE7FFFFE17277BA622>49
D<00FF800007FFF0000FFFFC001E03FE003800FF807C003F80FE003FC0FF001FC0FF001F
E0FF000FE0FF000FE07E000FE03C001FE000001FE000001FC000001FC000003F8000003F
0000007E000000FC000000F8000001F0000003E00000078000000F0000001E0000003C00
E0007000E000E000E001C001C0038001C0060001C00FFFFFC01FFFFFC03FFFFFC07FFFFF
C0FFFFFF80FFFFFF80FFFFFF801B277DA622>I<007F800003FFF00007FFFC000F80FE00
1F007F003F807F003F803F803F803F803F803F801F803F801F003F8000007F0000007F00
00007E000000FC000001F8000007F00000FFC00000FFC0000001F80000007E0000003F00
00003F8000001FC000001FC000001FE000001FE03C001FE07E001FE0FF001FE0FF001FE0
FF001FC0FF003FC0FE003F807C007F003F00FE001FFFFC0007FFF00000FF80001B277DA6
22>I<00000E0000001E0000003E0000007E000000FE000000FE000001FE000003FE0000
077E00000E7E00000E7E00001C7E0000387E0000707E0000E07E0000E07E0001C07E0003
807E0007007E000E007E000E007E001C007E0038007E0070007E00E0007E00FFFFFFF8FF
FFFFF8FFFFFFF80000FE000000FE000000FE000000FE000000FE000000FE000000FE0000
00FE00007FFFF8007FFFF8007FFFF81D277EA622>I<FFFFFFFFE0FFFFFFFFE0FFFFFFFF
E003FC001FE003FC0007F003FC0001F003FC0001F003FC0000F003FC00007003FC000070
03FC00007003FC01C07803FC01C03803FC01C03803FC01C03803FC03C00003FC03C00003
FC0FC00003FFFFC00003FFFFC00003FFFFC00003FC0FC00003FC03C00003FC03C00003FC
01C00E03FC01C00E03FC01C00E03FC01C01C03FC00001C03FC00001C03FC00001C03FC00
003C03FC00003803FC00007803FC0000F803FC0001F803FC0003F803FC001FF8FFFFFFFF
F0FFFFFFFFF0FFFFFFFFF027297EA82C>69 D<FFFFFFFFC0FFFFFFFFC0FFFFFFFFC003FC
003FC003FC000FE003FC0003E003FC0001E003FC0001E003FC0000E003FC0000E003FC00
00E003FC0000F003FC01C07003FC01C07003FC01C07003FC01C00003FC03C00003FC03C0
0003FC0FC00003FFFFC00003FFFFC00003FFFFC00003FC0FC00003FC03C00003FC03C000
03FC01C00003FC01C00003FC01C00003FC01C00003FC00000003FC00000003FC00000003
FC00000003FC00000003FC00000003FC00000003FC00000003FC000000FFFFFC0000FFFF
FC0000FFFFFC000024297EA82A>I<FFFFFCFFFFFCFFFFFC01FE0001FE0001FE0001FE00
01FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE00
01FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE0001FE00
01FE0001FE0001FE0001FE0001FE0001FE0001FE00FFFFFCFFFFFCFFFFFC16297FA819>
73 D<FFFFFFE00000FFFFFFFE0000FFFFFFFF800003FC003FE00003FC000FF00003FC00
07F80003FC0003FC0003FC0001FC0003FC0001FE0003FC0001FE0003FC0001FE0003FC00
01FE0003FC0001FE0003FC0001FE0003FC0001FC0003FC0003F80003FC0007F80003FC00
0FE00003FC003FC00003FFFFFE000003FFFFFE000003FC00FF800003FC003FC00003FC00
1FE00003FC000FF00003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC00
07F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80003FC0007F80E03FC00
07F80E03FC0003F80E03FC0001FC1CFFFFF000FE1CFFFFF0007FF8FFFFF0000FE02F297E
A832>82 D<00FF00C003FFE1C00FFFF9C01F80FFC03F003FC03E000FC07C0007C07C0007
C0FC0003C0FC0003C0FC0001C0FE0001C0FE0001C0FF000000FFC000007FFC00007FFFE0
003FFFF8001FFFFE001FFFFF0007FFFF8003FFFFC000FFFFC0000FFFE000007FE000001F
F000000FF0000007F0E00003F0E00003F0E00003F0E00003F0F00003E0F00003E0F80007
E0FC0007C0FF000F80FFE01F80E3FFFF00E1FFFC00C01FF0001C297CA825>I<03FF8000
0FFFF0001F01FC003F80FE003F807F003F803F003F803F801F003F8000003F8000003F80
00003F8000003F80003FFF8001FC3F800FE03F801F803F803F003F807E003F80FC003F80
FC003F80FC003F80FC003F80FC005F807E00DF803F839FFC1FFE0FFC03F803FC1E1B7E9A
21>97 D<003FF00001FFFC0003F03E000FC07F001F807F003F007F003F007F007F003E00
7E0000007E000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000
7E0000007E0000007F0000003F0003803F8003801F8007000FE00E0003F83C0001FFF800
003FC000191B7E9A1E>99 D<00007FF000007FF000007FF0000007F0000007F0000007F0
000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0
003F87F001FFF7F007F03FF00FC00FF01F8007F03F0007F03F0007F07E0007F07E0007F0
7E0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0
7E0007F07E0007F03F0007F03F0007F01F800FF00FC01FF007E07FFF01FFE7FF007F87FF
202A7EA925>I<003FC00001FFF00003E07C000F803E001F801F001F001F003F000F807E
000F807E000FC07E000FC0FE0007C0FE0007C0FFFFFFC0FFFFFFC0FE000000FE000000FE
0000007E0000007E0000007F0000003F0001C01F0001C00F80038007C0070003F01E0000
FFFC00003FE0001A1B7E9A1F>I<0007F8003FFC007E3E01FC7F03F87F03F07F07F07F07
F03E07F00007F00007F00007F00007F00007F00007F000FFFFC0FFFFC0FFFFC007F00007
F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007F00007
F00007F00007F00007F00007F00007F00007F00007F0007FFF807FFF807FFF80182A7EA9
15>I<FFE00000FFE00000FFE000000FE000000FE000000FE000000FE000000FE000000F
E000000FE000000FE000000FE000000FE000000FE000000FE000000FE07E000FE1FF800F
E30FC00FE40FE00FE807E00FF807F00FF007F00FF007F00FE007F00FE007F00FE007F00F
E007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00F
E007F00FE007F00FE007F00FE007F0FFFE3FFFFFFE3FFFFFFE3FFF202A7DA925>104
D<07000F801FC03FE03FE03FE01FC00F8007000000000000000000000000000000FFE0FF
E0FFE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00F
E00FE00FE00FE00FE0FFFEFFFEFFFE0F2B7EAA12>I<FFE0FFE0FFE00FE00FE00FE00FE0
0FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE0
0FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE00FE0FFFEFFFEFFFE0F2A
7EA912>108 D<FFC07F001FC000FFC1FFC07FF000FFC307E0C1F8000FC407F101FC000F
C803F200FC000FD803FE00FE000FD003FC00FE000FD003FC00FE000FE003F800FE000FE0
03F800FE000FE003F800FE000FE003F800FE000FE003F800FE000FE003F800FE000FE003
F800FE000FE003F800FE000FE003F800FE000FE003F800FE000FE003F800FE000FE003F8
00FE000FE003F800FE000FE003F800FE000FE003F800FE000FE003F800FE00FFFE3FFF8F
FFE0FFFE3FFF8FFFE0FFFE3FFF8FFFE0331B7D9A38>I<FFC07E00FFC1FF80FFC30FC00F
C40FE00FC807E00FD807F00FD007F00FD007F00FE007F00FE007F00FE007F00FE007F00F
E007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00F
E007F00FE007F00FE007F0FFFE3FFFFFFE3FFFFFFE3FFF201B7D9A25>I<003FE00001FF
FC0003F07E000FC01F801F800FC03F0007E03F0007E07E0003F07E0003F07E0003F0FE00
03F8FE0003F8FE0003F8FE0003F8FE0003F8FE0003F8FE0003F8FE0003F87E0003F07E00
03F03F0007E03F0007E01F800FC00FC01F8007F07F0001FFFC00003FE0001D1B7E9A22>
I<FFE1FE00FFE7FF80FFFE0FE00FF803F00FF001F80FE001FC0FE000FC0FE000FE0FE000
FE0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE0007F0FE000
7E0FE000FE0FE000FE0FE000FC0FE001FC0FF001F80FF803F00FFC0FE00FEFFF800FE1FC
000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000
00FFFE0000FFFE0000FFFE000020277E9A25>I<FFC3E0FFC7F8FFCC7C0FD8FE0FD0FE0F
D0FE0FF0FE0FE07C0FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000F
E0000FE0000FE0000FE0000FE0000FE0000FE000FFFF00FFFF00FFFF00171B7E9A1B>
114 D<03FE300FFFF03E03F07800F07000F0F00070F00070F80070FE0000FFE0007FFF00
7FFFC03FFFE01FFFF007FFF800FFF80007FC0000FCE0007CE0003CF0003CF00038F80038
FC0070FF01E0E7FFC0C1FF00161B7E9A1B>I<00700000700000700000700000F00000F0
0000F00001F00003F00003F00007F0001FFFE0FFFFE0FFFFE007F00007F00007F00007F0
0007F00007F00007F00007F00007F00007F00007F00007F00007F00007F07007F07007F0
7007F07007F07007F07007F07003F0E001F8C000FFC0003F0014267FA51A>I<FFE07FF0
FFE07FF0FFE07FF00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F0
0FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F00FE007F0
0FE007F00FE007F00FE00FF00FE00FF007E017F003F067FF01FFC7FF007F87FF201B7D9A
25>I<FFFC1FFEFFFC1FFEFFFC1FFE07F0078003F8070001FC0F0001FE1E0000FE3C0000
7F7800003FF800003FF000001FE000000FE0000007F0000007F800000FF800001FFC0000
3DFE000038FF0000787F0000F03F8001E03FC003C01FE003800FE0FFF03FFFFFF03FFFFF
F03FFF201B7F9A23>120 D E /Fp 30 122 df<70F8FCFC740404040408081010204006
0F7C840E>44 D<01F000071C000C06001803003803803803807001C07001C07001C07001
C0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001
E0F001E0F001E07001C07001C07001C07803C03803803803801C07000C0600071C0001F0
0013227EA018>48 D<008003800F80F38003800380038003800380038003800380038003
800380038003800380038003800380038003800380038003800380038003800380038007
C0FFFE0F217CA018>I<03F8000C1E001007002007804007C07807C07803C07807C03807
C0000780000780000700000F00000E0000380003F000001C00000F000007800007800003
C00003C00003E02003E07003E0F803E0F803E0F003C04003C0400780200780100F000C1C
0003F00013227EA018>51 D<01F000060C000C0600180700380380700380700380F001C0
F001C0F001C0F001E0F001E0F001E0F001E0F001E07001E07003E03803E01805E00C05E0
0619E003E1E00001C00001C00001C0000380000380300300780700780600700C00201800
1030000FC00013227EA018>57 D<0001800000018000000180000003C0000003C0000003
C0000005E0000005E000000DF0000008F0000008F0000010F80000107800001078000020
3C0000203C0000203C0000401E0000401E0000401E0000800F0000800F0000FFFF000100
078001000780030007C0020003C0020003C0040003E0040001E0040001E00C0000F00C00
00F03E0001F8FF800FFF20237EA225>65 D<0007E0100038183000E0063001C001700380
00F0070000F00E0000701E0000701C0000303C0000303C0000307C000010780000107800
0010F8000000F8000000F8000000F8000000F8000000F8000000F8000000F80000007800
0000780000107C0000103C0000103C0000101C0000201E0000200E000040070000400380
008001C0010000E0020000381C000007E0001C247DA223>67 D<FFFFF0000F801E000780
0700078003C0078001C0078000E0078000F007800078078000780780007C0780003C0780
003C0780003C0780003E0780003E0780003E0780003E0780003E0780003E0780003E0780
003E0780003E0780003C0780003C0780007C0780007807800078078000F0078000E00780
01E0078003C0078007000F801E00FFFFF8001F227EA125>I<FFFFFFC00F8007C0078001
C0078000C007800040078000400780006007800020078000200780002007802020078020
000780200007802000078060000780E00007FFE0000780E0000780600007802000078020
000780200007802008078000080780000807800010078000100780001007800030078000
3007800070078000E00F8003E0FFFFFFE01D227EA121>I<0007F008003C0C1800E00218
01C001B8038000F8070000780F0000381E0000381E0000183C0000183C0000187C000008
7800000878000008F8000000F8000000F8000000F8000000F8000000F8000000F8000000
F8001FFF780000F8780000787C0000783C0000783C0000781E0000781E0000780F000078
07000078038000B801C000B800E00318003C0C080007F00020247DA226>71
D<03FFF0001F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F
00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F
00000F00000F00700F00F80F00F80F00F80E00F01E00401C0020380018700007C0001423
7EA119>74 D<FFFC03FF000FC000F8000780006000078000400007800080000780010000
078002000007800400000780080000078010000007802000000780400000078080000007
818000000783C000000787E000000789E000000788F000000790F0000007A078000007C0
3C000007803C000007801E000007800F000007800F00000780078000078007C000078003
C000078001E000078001E000078000F000078000F8000FC000FC00FFFC07FF8021227EA1
26>I<FFFE00000FC0000007800000078000000780000007800000078000000780000007
800000078000000780000007800000078000000780000007800000078000000780000007
800000078000000780000007800000078000000780008007800080078000800780008007
8001800780018007800100078003000780030007800F000F803F00FFFFFF0019227EA11E
>I<FFC00003FF0FC00003F007C00003E005E00005E005E00005E004F00009E004F00009
E004F00009E004780011E004780011E004780011E0043C0021E0043C0021E0043C0021E0
041E0041E0041E0041E0040F0081E0040F0081E0040F0081E004078101E004078101E004
078101E00403C201E00403C201E00401E401E00401E401E00401E401E00400F801E00400
F801E00400F801E004007001E00E007001E01F007003F0FFE0203FFF28227EA12D>I<FF
8007FF07C000F807C0007005E0002004F0002004F0002004780020047C0020043C002004
1E0020041F0020040F002004078020040780200403C0200401E0200401E0200400F02004
00F8200400782004003C2004003E2004001E2004000F2004000F20040007A0040003E004
0003E0040001E0040001E0040000E00E0000601F000060FFE0002020227EA125>I<000F
E00000783C0000E00E0003C00780078003C00F0001E00E0000E01E0000F03C0000783C00
00787C00007C7C00007C7800003C7800003CF800003EF800003EF800003EF800003EF800
003EF800003EF800003EF800003EF800003E7800003C7C00007C7C00007C3C0000783E00
00F81E0000F00F0001E00F0001E0078003C003C0078000E00E0000783C00000FE0001F24
7DA226>I<7FFFFFF87807807860078018400780084007800840078008C007800C800780
048007800480078004800780040007800000078000000780000007800000078000000780
000007800000078000000780000007800000078000000780000007800000078000000780
00000780000007800000078000000780000007800000078000000FC00003FFFF001E227E
A123>84 D<FFF03FFC03FE1F8007E000F80F0003C000700F0003C000200F0003C0002007
8001E00040078001E00040078001E0004003C002F0008003C002F0008003C002F0008001
E00478010001E00478010001E00478010000F0083C020000F0083C020000F0083C020000
F8183E06000078101E04000078101E0400007C101E0400003C200F0800003C200F080000
3C200F0800001E40079000001E40079000001E40079000000F8003E000000F8003E00000
0F8003E00000070001C00000070001C00000070001C0000003000180000002000080002F
237FA132>87 D<0FE0001838003C0C003C0E0018070000070000070000070000FF0007C7
001E07003C0700780700700700F00708F00708F00708F00F087817083C23900FC1E01515
7E9418>97 D<01FE000703000C07801C0780380300780000700000F00000F00000F00000
F00000F00000F00000F000007000007800403800401C00800C010007060001F80012157E
9416>99 D<01FC000707000C03801C01C03801C07801E07000E0F000E0FFFFE0F00000F0
0000F00000F00000F000007000007800203800201C00400E008007030000FC0013157F94
16>101 D<0E0000FE00001E00000E00000E00000E00000E00000E00000E00000E00000E
00000E00000E00000E00000E1F800E60C00E80E00F00700F00700E00700E00700E00700E
00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E0070FF
E7FF18237FA21B>104 D<1C003E003E003E001C00000000000000000000000000000000
000E00FE001E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E
000E000E00FFC00A227FA10E>I<0E00FE001E000E000E000E000E000E000E000E000E00
0E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00
0E000E000E000E000E00FFE00B237FA20E>108 D<0E1F80FE60C01E80E00F00700F0070
0E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E0070
0E00700E00700E0070FFE7FF18157F941B>110 D<01FC000707000C01801800C03800E0
700070700070F00078F00078F00078F00078F00078F00078F000787000707800F03800E0
1C01C00E038007070001FC0015157F9418>I<0E3CFE461E8F0F0F0F060F000E000E000E
000E000E000E000E000E000E000E000E000E000E000F00FFF010157F9413>114
D<02000200020002000600060006000E001E003E00FFF80E000E000E000E000E000E000E
000E000E000E000E000E040E040E040E040E040E040708030801F00E1F7F9E13>116
D<0E0070FE07F01E00F00E00700E00700E00700E00700E00700E00700E00700E00700E00
700E00700E00700E00700E00700E00F00E00F006017003827800FC7F18157F941B>I<FF
C1FE1E00780E00300E00200E002007004007004003808003808003808001C10001C10000
E20000E20000E20000740000740000380000380000380000100000100000200000200000
2000004000F04000F08000F180004300003C0000171F7F941A>121
D E /Fq 39 122 df<0001FE01F8000701C704001C002E0E007800FC1F00F001F81F00E0
01F81F01E001F00E03C000F00003C000F00003C000F00003C000F00003C000F00003C000
F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F000FFFFFFFF
F0FFFFFFFFF003C000F00003C000F00003C000F00003C000F00003C000F00003C000F000
03C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003
C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C0
00F00003C000F00003C000F00003C000F00003C000F00003C000F00007E001F8007FFE1F
FFC07FFE1FFFC028327FB126>11 D<78FCFCFEFE7A020202020204040408081020204007
147AB112>39 D<0000070000000000070000000000070000000000070000000000070000
000000070000000000070000000000070000000000070000000000070000000000070000
000000070000000000070000000000070000000000070000000000070000000000070000
00000007000000000007000000000007000000000007000000FFFFFFFFFFF0FFFFFFFFFF
F0FFFFFFFFFFF00000070000000000070000000000070000000000070000000000070000
000000070000000000070000000000070000000000070000000000070000000000070000
000000070000000000070000000000070000000000070000000000070000000000070000
000000070000000000070000000000070000000000070000002C2D7CA734>43
D<78FCFCFEFE7A020202020204040408081020204007147A8512>I<FFFF80FFFF80FFFF
8011037F9016>I<78FCFCFCFC780000000000000000000000000000000000000078FCFC
FCFC78061F7A9E12>58 D<00000300000000000300000000000300000000000780000000
000780000000000FC0000000000FC0000000000FC00000000017E00000000013E0000000
0013E00000000023F00000000021F00000000021F00000000040F80000000040F8000000
0040F800000000807C00000000807C00000001807E00000001003E00000001003E000000
02003F00000002001F00000002001F00000004000F80000004000F80000004000F800000
080007C00000080007C00000180007E000001FFFFFE000001FFFFFE00000200003F00000
200001F00000200001F00000400001F80000400000F80000400000F800008000007C0000
8000007C00008000007C00010000003E00010000003E00030000003F00030000001F0007
0000001F001F8000003F80FFE00003FFFCFFE00003FFFC2E327EB132>65
D<00003FE0010001FFF8030007F01E03001F800307003E000087007800004F00F000002F
01E000001F03C000000F078000000F0F800000070F000000071F000000031E000000033E
000000033C000000017C000000017C000000017C000000017800000000F800000000F800
000000F800000000F800000000F800000000F800000000F800000000F800000000F80000
0000F800000000F80000000078000000007C000000007C000000017C000000013C000000
013E000000011E000000011F000000020F000000020F80000006078000000403C0000008
01E000000800F00000100078000020003E0000C0001F8003800007F00F000001FFFC0000
003FE00028337CB130>67 D<FFFFFFE00000FFFFFFFC000007E0007F000003E0000F8000
03E00003C00003E00001E00003E00000F00003E00000780003E000003C0003E000001E00
03E000001E0003E000000F0003E000000F0003E000000F8003E00000078003E0000007C0
03E0000007C003E0000003C003E0000003C003E0000003E003E0000003E003E0000003E0
03E0000003E003E0000003E003E0000003E003E0000003E003E0000003E003E0000003E0
03E0000003E003E0000003E003E0000003C003E0000003C003E0000007C003E0000007C0
03E00000078003E00000078003E000000F8003E000000F0003E000001F0003E000001E00
03E000003C0003E00000780003E00000F80003E00001F00003E00003E00003E0000F8000
07E0003F0000FFFFFFFC0000FFFFFFE000002B317CB033>I<FFFFFFFFC0FFFFFFFFC007
E0001FC003E00003C003E00001E003E00000E003E000006003E000006003E000002003E0
00002003E000002003E000002003E000001003E000001003E000001003E000801003E000
800003E000800003E000800003E000800003E001800003E001800003E007800003FFFF80
0003FFFF800003E007800003E001800003E001800003E000800003E000800003E0008000
03E000800003E000800003E000000003E000000003E000000003E000000003E000000003
E000000003E000000003E000000003E000000003E000000003E000000003E000000003E0
00000007F0000000FFFFC00000FFFFC0000024317CB02B>70 D<00001FE000800000FFFC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>I<FFFF80FFFF8007F00003E00003E00003E00003E000
03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000
03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000
03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000
03E00003E00003E00007F000FFFF80FFFF8011317DB017>73 D<FFFF80007FF0FFFF8000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>75 D<FFFFC00000FFFFC0000007F000000003E000000003E000000003E000000003E0
00000003E000000003E000000003E000000003E000000003E000000003E000000003E000
000003E000000003E000000003E000000003E000000003E000000003E000000003E00000
0003E000000003E000000003E000000003E000000003E000000003E000000003E0000000
03E000000003E000000003E000000003E000004003E000004003E000004003E000004003
E000008003E000008003E000008003E000008003E000018003E000018003E000038003E0
00038003E000078003E0000F0003E0003F0007E000FF00FFFFFFFF00FFFFFFFF0022317C
B029>I<FFF00000007FF8FFF00000007FF807F00000007F0002F8000000BE0002F80000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>I<FFFFFFC000FF
FFFFF80007E0007E0003E0001F0003E000078003E00003C003E00001E003E00001F003E0
0001F003E00000F003E00000F803E00000F803E00000F803E00000F803E00000F803E000
00F803E00000F003E00001F003E00001E003E00003E003E00003C003E000078003E0001F
0003E0007C0003FFFFF00003E000000003E000000003E000000003E000000003E0000000
03E000000003E000000003E000000003E000000003E000000003E000000003E000000003
E000000003E000000003E000000003E000000003E000000003E000000003E000000003E0
00000003E000000007F0000000FFFF800000FFFF80000025317CB02D>80
D<7FFFFFFFFFE07FFFFFFFFFE07E000F8007E078000F8001E070000F8000E060000F8000
6040000F80002040000F800020C0000F800030C0000F80003080000F80001080000F8000
1080000F80001080000F80001080000F80001080000F80001000000F80000000000F8000
0000000F80000000000F80000000000F80000000000F80000000000F80000000000F8000
0000000F80000000000F80000000000F80000000000F80000000000F80000000000F8000
0000000F80000000000F80000000000F80000000000F80000000000F80000000000F8000
0000000F80000000000F80000000000F80000000000F80000000000F80000000000F8000
0000000F80000000000F80000000000F80000000000F80000000001FC00000000FFFFF80
00000FFFFF80002C317EB030>84 D<FFFF8007FFC0FFFF8007FFC007F000007C0003E000
00380003E00000100003E00000100003E00000100003E00000100003E00000100003E000
00100003E00000100003E00000100003E00000100003E00000100003E00000100003E000
00100003E00000100003E00000100003E00000100003E00000100003E00000100003E000
00100003E00000100003E00000100003E00000100003E00000100003E00000100003E000
00100003E00000100003E00000100003E00000100003E00000100003E00000100003E000
00100003E00000100003E00000100003E00000100001E00000200001F00000200001F000
00200000F00000400000F000004000007800008000003C00018000003C00010000001E00
0600000007800C00000003E07800000000FFF0000000003F8000002A327CB032>I<7FFF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>88 D<FFFE000007FFFFFE000007FF0FF0000001F803F0000000E0
03F0000000C001F80000008000F80000018000FC00000100007E00000200007E00000200
003F00000400001F80000C00001F80000800000FC00010000007C00010000007E0002000
0003F00060000001F00040000001F80080000000FC0080000000FC01000000007E030000
00003E02000000003F04000000001F84000000000F88000000000FD80000000007F00000
000007E00000000003E00000000003E00000000003E00000000003E00000000003E00000
000003E00000000003E00000000003E00000000003E00000000003E00000000003E00000
000003E00000000003E00000000003E00000000003E00000000003E00000000003E00000
000007F000000000FFFF80000000FFFF800030317FB032>I<3FFFFFFF003FFFFFFF003F
E0003E003F00003E003C00007C00380000FC00300000F800300001F000600001F0006000
03E000600003E000600007C00040000FC00040000F800040001F000040001F000000003E
000000007E000000007C00000000F800000000F800000001F000000001F000000003E000
000007E000000007C00000000F800000000F800000001F000000001F000000003E000080
007E000080007C00008000F800008000F800008001F000008003F000018003E000018007
C000018007C00001000F800003000F800003001F000007003F00000F003E00001F007C00
003F007C0001FF00FFFFFFFF00FFFFFFFF0021317CB028>I<00FE00000303C0000C00E0
0010007000100038003C003C003E001C003E001E003E001E0008001E0000001E0000001E
0000001E00000FFE0000FC1E0003E01E000F801E001F001E003E001E003C001E007C001E
00F8001E04F8001E04F8001E04F8003E04F8003E0478003E047C005E043E008F080F0307
F003FC03E01E1F7D9E21>97 D<07800000FF800000FF8000000F80000007800000078000
000780000007800000078000000780000007800000078000000780000007800000078000
00078000000780000007800000078000000781FC0007860700078801C0079000E007A000
7007C00078078000380780003C0780003C0780001E0780001E0780001F0780001F078000
1F0780001F0780001F0780001F0780001F0780001F0780001F0780001E0780003E078000
3C0780003C0780007807C00070072000F0072001E00618038006060F000401F80020327E
B125>I<003F8000E0600380180700040F00041E001E1C003E3C003E7C003E7C00087800
00F80000F80000F80000F80000F80000F80000F80000F80000F800007800007C00007C00
003C00011E00011E00020F000207000403801800E060003F80181F7D9E1D>I<000001E0
00003FE000003FE0000003E0000001E0000001E0000001E0000001E0000001E0000001E0
000001E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0000001E0
001F81E000F061E001C019E0078005E00F0003E00E0003E01E0001E03C0001E03C0001E0
7C0001E0780001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0F80001E0
F80001E0F80001E0780001E0780001E03C0001E03C0001E01C0001E01E0003E00E0005E0
070009E0038011F000E061FF003F81FF20327DB125>I<003F800000E0E0000380380007
003C000E001E001E001E001C000F003C000F007C000F0078000F8078000780F8000780F8
000780FFFFFF80F8000000F8000000F8000000F8000000F8000000F8000000780000007C
0000003C0000003C0000801E0000800E0001000F0002000780020001C00C0000F0300000
1FC000191F7E9E1D>I<0007E0001C1000383800707C00E07C01E07C01C03803C00003C0
0003C00003C00003C00003C00003C00003C00003C00003C00003C00003C000FFFFC0FFFF
C003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C0
0003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C0
0003C00003C00007E0007FFF007FFF0016327FB114>I<000000F0007F030801C1C41C03
80E81C070070080F0078001E003C001E003C003E003E003E003E003E003E003E003E003E
003E003E003E001E003C001E003C000F007800070070000780E00009C1C000087F000018
000000180000001800000018000000180000001C0000000E0000000FFFF80007FFFF0003
FFFF800E000FC0180001E0300000F070000070E0000038E0000038E0000038E0000038E0
0000387000007070000070380000E01C0001C00700070001C01C00003FE0001E2F7E9F21
>I<0F001F801F801F801F800F0000000000000000000000000000000000000000000000
0780FF80FF800F8007800780078007800780078007800780078007800780078007800780
07800780078007800780078007800780078007800FC0FFF8FFF80D307EAF12>105
D<0780FF80FF800F80078007800780078007800780078007800780078007800780078007
800780078007800780078007800780078007800780078007800780078007800780078007
80078007800780078007800780078007800780078007800FC0FFFCFFFC0E327EB112>
108 D<0780FE001FC000FF83078060F000FF8C03C18078000F9001E2003C0007A001E400
3C0007A000F4001E0007C000F8001E0007C000F8001E00078000F0001E00078000F0001E
00078000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E00
078000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E0007
8000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E000780
00F0001E00078000F0001E00078000F0001E000FC001F8003F00FFFC1FFF83FFF0FFFC1F
FF83FFF0341F7E9E38>I<0780FE0000FF83078000FF8C03C0000F9001E00007A001E000
07A000F00007C000F00007C000F000078000F000078000F000078000F000078000F00007
8000F000078000F000078000F000078000F000078000F000078000F000078000F0000780
00F000078000F000078000F000078000F000078000F000078000F000078000F000078000
F000078000F0000FC001F800FFFC1FFF80FFFC1FFF80211F7E9E25>I<001FC00000F078
0001C01C00070007000F0007801E0003C01C0001C03C0001E03C0001E0780000F0780000
F0780000F0F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000F8F80000
F8780000F07C0001F03C0001E03C0001E01E0003C01E0003C00F00078007800F0001C01C
0000F07800001FC0001D1F7E9E21>I<0781FC00FF860700FF8803C00F9001E007A000F0
07C00078078000780780003C0780003C0780003E0780001E0780001F0780001F0780001F
0780001F0780001F0780001F0780001F0780001F0780001F0780003E0780003E0780003C
0780007C0780007807C000F007A000F007A001E00798038007860F000781F80007800000
078000000780000007800000078000000780000007800000078000000780000007800000
078000000FC00000FFFC0000FFFC0000202D7E9E25>I<0783E0FF8C18FF907C0F907C07
A07C07C03807C00007C00007C00007800007800007800007800007800007800007800007
80000780000780000780000780000780000780000780000780000780000780000780000F
C000FFFE00FFFE00161F7E9E19>114 D<01FC100E03301800F0300070600030E00030E0
0010E00010E00010F00010F800007E00003FF0001FFF000FFFC003FFE0003FF00001F800
00F880003C80003C80001CC0001CC0001CE0001CE00018F00038F00030CC0060C301C080
FE00161F7E9E1A>I<00400000400000400000400000400000C00000C00000C00001C000
01C00003C00007C0000FC0001FFFE0FFFFE003C00003C00003C00003C00003C00003C000
03C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C01003C010
03C01003C01003C01003C01003C01003C01001C02001E02000E0400078C0001F00142C7F
AB19>I<078000F000FF801FF000FF801FF0000F8001F000078000F000078000F0000780
00F000078000F000078000F000078000F000078000F000078000F000078000F000078000
F000078000F000078000F000078000F000078000F000078000F000078000F000078000F0
00078000F000078000F000078001F000078001F000078001F000038002F00003C004F000
01C008F800007030FF80001FC0FF80211F7E9E25>I<FFF801FF80FFF801FF800FC0007C
00078000380007C000300003C000200003C000200001E000400001E000400001F0004000
00F000800000F000800000780100000078010000007C010000003C020000003C02000000
1E040000001E040000001F040000000F080000000F080000000790000000079000000007
D000000003E000000003E000000001C000000001C000000001C000000000800000000080
000000010000000001000000000100000000020000000002000000000400000070040000
00F80C000000F808000000F810000000703000000030400000001F80000000212D7F9E23
>121 D E end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300dpi
TeXDict begin

%%EndSetup
%%Page: 1 1
1 0 bop 61 482 a Fq(MXYZPTLK:)21 b(A)h(Practical,)g(User-F)-6
b(riendly)21 b(C)1311 476 y(++)1436 482 y(Implemen)n(tation)646
573 y(of)h(Di\013eren)n(tial)f(Algebra:)791 664 y(User's)g(Guide)820
785 y Fp(Leo)c(Mic)o(helotti)793 882 y(Jan)o(uary)g(31,)f(1990)0
1060 y Fo(1)67 b(In)n(tro)r(duction)0 1151 y Fn(Except)15
b(for)e(Section)h(3,)f(whic)o(h)g(is)h(in)o(tended)g(to)f(motiv)n(ate)f
(as)h(w)o(ell)g(as)h(to)f(inform,)e(this)j(note)g(is)f(written)h(for)f
(p)q(eople)h(who)0 1201 y(already)e(\(a\))h(ha)o(v)o(e)f(heard)i(ab)q
(out)e(di\013eren)o(tial)h(algebra)f(and)g(w)o(an)o(t)h(to)f(use)i(it)e
(and)g(\(b\))h(write)g(programs)f(in)g(C)1739 1197 y(++)1817
1201 y(.)g(Those)0 1251 y(who)f(ha)o(v)o(e)h(not)g(y)o(et)g(b)q(een)h
(exp)q(osed)f(to)g(these)h(topics)f(are)g(in)o(vited)g(to)f(read)h(the)
h(references)h(in)d(the)i(bibliograph)o(y)m(.)i(Here)e(w)o(e)0
1301 y(shall)f(only)g(describ)q(e)j(ho)o(w)d(to)h(use)h(V)m(ersion)f
(1.0)f(of)g(MXYZPTLK,)i(a)e(di\013eren)o(tial)h(algebra)f(to)q(olkit)
1583 1286 y Fm(1)1614 1301 y Fn(programmed)e(using)0
1351 y(GNU)k(C)139 1347 y(++)218 1351 y(on)g(a)g(SUN)g(w)o(orkstation.)
19 b(The)c(to)q(olkit)e(implem)o(en)o(ts)g(t)o(w)o(o)g(classes,)i(D)o
(A)f(and)g(LieOp)q(erator,)h(whic)o(h)f(mo)q(del)0 1400
y(the)j(n)o(um)o(b)q(ers)f(of)f(di\013eren)o(tial)h(algebra,)g(just)h
(as)f(\\double")g(v)n(ariables)f(mo)q(del)g(real)h(n)o(um)o(b)q(ers.)25
b(As)17 b(its)f(name)f(suggests,)0 1450 y(a)j(LieOp)q(erator)h(con)o
(tains,)g(as)f Fl(p)n(art)j Fn(of)d(its)g(structure,)j(an)d(arra)o(y)g
(of)f(D)o(A)h(v)n(ariables;)h(it)f(is)g(in)o(tro)q(duced)h(primarily)c
(for)0 1500 y(concatenation.)62 1550 y(In)d(a)f(previous)i(pap)q(er[7])
e(I)g(describ)q(ed)j(a)d(C)736 1546 y(++)813 1550 y(class,)h
Fk(nstd)p Fn(,)f(whic)o(h)g(directly)h(and)g(v)o(ery)g(straigh)o(tforw)
o(ardly)e(mo)q(delled)0 1600 y(\\prolonged")g(n)o(um)o(b)q(ers,)h(an)f
(ob)r(ject)i(whic)o(h)f(w)o(e)g(shall)f(review)i(brie\015y)f(b)q(elo)o
(w,)g(as)g(a)f(w)o(a)o(y)g(of)h(doing)f(di\013eren)o(tial)h
(arithmetic.)0 1650 y(This)f(concept,)h(whic)o(h)f(merely)f(extended)i
(Rall's)d([11)o(])h(p)q(edagogical)g(metho)q(ds)g(to)h(higher)f
(dimensions,)g(pro)o(vided)h(an)f(easily)0 1699 y(grasp)q(ed)k
(construct)h(for)d(understanding)i(ho)o(w)f(the)h(most)e(basic)h(op)q
(erations)g(of)g(di\013eren)o(tial)g(algebra)f(w)o(ork.)17
b(I)c(had)e(hop)q(ed)0 1749 y(also)h(that)g(it)g(w)o(ould)f(motiv)n
(ate)f(p)q(eople)j(to)f(learn)h(more)e(ab)q(out)h(ob)r(ject-orien)o
(ted)h(programming,)c(esp)q(ecially)j(as)h(it)f(is)g(done)0
1799 y(in)k(C)81 1795 y(++)163 1799 y(.)26 b(Ho)o(w)o(ev)o(er,)18
b(the)f Fk(nstd)f Fn(class)h(w)o(as)g(thro)o(wn)g(together)h(in)e(a)h
(few)f(w)o(eeks,)i(and)f(although)f(it)g(could)h(do)f(simple)0
1849 y(calculations)11 b(on)g(lo)o(w)f(dimensional)f(spaces,)j(it)f(w)o
(as)h Fl(not)j Fn(\(and)c(w)o(as)g(nev)o(er)h(in)o(tended)g(to)f(b)q
(e\))h(a)f(practical)g(implemen)o(tation)0 1899 y(for)j(more)g
(sophisticated)h(problems:)j(\(a\))d(it)f(used)i(to)q(o)e(m)o(uc)o(h)f
(memory)m(,)f(m)o(uc)o(h)h(of)h(whic)o(h)g(accomplished)g(nothing)g
(more)0 1948 y(than)g(storing)g(zero)q(es;)i(\(b\))e(the)h(arithmetic)e
(rules)i(sp)q(en)o(t)g(m)o(uc)o(h)e(of)h(their)g(time)f(op)q(erating)h
(on)g(these)i(useless)g(zero)q(es;)f(\(c\))0 1998 y(w)o(orst)i(of)e
(all,)g(the)i(maxim)n(um)12 b(\\w)o(eigh)o(t")j(of)h(an)g
Fk(nstd)f Fn(v)n(ariable)g(|)h(the)h(highest)g(order)f(of)g(deriv)n
(ativ)o(es)g(stored)h(|)f(w)o(as)0 2048 y(sp)q(eci\014ed)f(in)f(the)g
(class)g(de\014nition)f(rather)i(than)f(b)o(y)f(the)h(application)f
(program;)f(\(d\))i(most)e(of)h(the)i(more)d(p)q(o)o(w)o(erful,)h(and)0
2098 y(corresp)q(ondingly)h(more)f(useful,)g(di\013eren)o(tial)g
(algebra)g(op)q(erations,)h(suc)o(h)g(as)g(concatenation)g(and)f
(di\013eren)o(tiation,)g(w)o(ere)0 2148 y(a)o(wkw)o(ard)g(to)h
(implemen)o(t.)62 2197 y(MXYZPTLK)i(corrects)h(these)f(de\014ciencies.)
22 b(The)15 b(classes)h(D)o(A)f(and)f(LieOp)q(erator)i(mo)q(del)d
(prolonged)i(n)o(um)o(b)q(ers)f(as)0 2247 y(dynamically)c(allo)q(cated)
j(\(and)h(deallo)q(cated\))f(doubly)g(link)o(ed)f(lists)i(|)f(whic)o(h)
g(w)o(e)g(shall)g(call)f(simply)g(\\c)o(hains")h(|)f(whose)0
2297 y(attributes)h(are)f(de\014ned)i(at)e(run)o(time.)k(Uninformativ)o
(e)10 b(zero)q(es)k(are)e(neither)h(stored)g(nor)f(op)q(erated)h(up)q
(on,)f(the)h(maxim)n(um)0 2347 y(w)o(eigh)o(t)i(stored)i(is)e(sp)q
(eci\014ed)j(b)o(y)d(the)h(user,)h(and)f(all)e(di\013eren)o(tial)i
(algebra)f(op)q(erations)h(are)g(implemen)o(ted)d(easily)m(.)23
b(Eac)o(h)p 0 2382 780 2 v 46 2415 a Fj(1)64 2427 y Fn(Or)14
b(to)q(ol;)f(I)g(ha)o(v)o(e)h(di\016cult)o(y)f(distinguishing)g(b)q(et)
o(w)o(een)i(the)g(t)o(w)o(o.)965 2574 y(1)p eop
%%Page: 2 2
2 1 bop 0 307 a Fn(link)16 b(in)h(a)h(c)o(hain)f(con)o(tains)g(the)h
(\\index)f(arra)o(y")g(\(to)h(b)q(e)g(de\014ned)g(b)q(elo)o(w\))f(for)g
(a)h(particular)f Fl(non-zer)n(o)j Fn(deriv)n(ativ)o(e)d(and)0
357 y(its)i(v)n(alue.)34 b(When)20 b(it)f(is)g(\014rst)h(declared,)h
(the)f(v)n(ariable)e(is)i(\\n)o(ull,")e(a)h(c)o(hain)g(with)g(no)g
(links.)34 b(Its)20 b(links)f(are)g(created)0 407 y(dynamically)14
b(as)i(calculations)g(pro)q(ceed)j(in)d(the)h(application)e(program.)25
b(Run)o(time)15 b(attributes)j(are)f(sp)q(eci\014ed)h(using)e(a)0
457 y Fi(D)o(ASetup)11 b Fn(function,)i(after)h(whic)o(h)g(arithmetic)f
(and)h(analytic)f(op)q(erations)h(pro)q(ceed)h(in)f(a)f(transparen)o(t)
i(manner.)62 506 y(This)c(transparency)h(is)f(imp)q(ortan)o(t;)e
(MXYZPTLK)j(has)f(b)q(een)h(designed)f(for)g(\\user-friendliness";)h
(this)f(User's)g(Guide)0 556 y(should)i(pro)o(vide)h(enough)f
(information)e(to)i(start)i(using)e(the)h(D)o(A)f(and)h(LieOp)q(erator)
g(classes)h(immediately)l(.)g(The)f(syn)o(tax)0 606 y(and)f(notation)e
(is)i(as)g(close)g(to)g(\\exp)q(ected")h(as)f(I)f(could)h(mak)o(e)e
(it,)h(and)h(eac)o(h)g(v)n(ariable)f(k)o(eeps)i(trac)o(k)f(of)f(suc)o
(h)h(attributes)h(as)0 656 y(its)g(accuracy)i(or)e(its)g(\\reference)j
(p)q(oin)o(t")c(\(see)j(b)q(elo)o(w\),)d(freeing)i(the)g(application)e
(program)f(from)h(routine)h(b)q(o)q(okk)o(eeping)0 706
y(tasks.)27 b(D)o(A)16 b(and)h(LieOp)q(erator)h(v)n(ariables)e(are)h
(declared)g(in)g(the)g(usual)f(w)o(a)o(y)m(.)26 b(Once)18
b(declared,)f(the)h(comp)q(onen)o(ts)e(of)g(a)0 756 y(LieOp)q(erator)j
(ma)o(y)c(b)q(e)j(accessed)i(just)e(as)g(though)f(it)g(w)o(ere)i(an)e
(arra)o(y)m(,)g(as)h(demonstrated)f(in)g(the)i(follo)o(wing)c(program)0
805 y(fragmen)o(t.)132 848 y Fk(...)132 897 y(DA)21 b(x,)g(y,)h(z;)132
947 y(LieOperator)d(u;)132 997 y(...)132 1047 y(x)i(=)h(u[0];)132
1097 y(y)f(=)h(u[1];)132 1147 y(z)f(=)h(u[2];)0 1231
y Fn(Ho)o(w)o(ev)o(er,)c(a)g(statemen)o(t)f(lik)o(e)g(\\)p
Fk(u[1])j(=)i(y)p Fn(")17 b(is)g(not)h(allo)o(w)o(ed;)f(this)h(t)o(yp)q
(e)g(of)f(assignmen)o(t)f(is)h(handled)h(b)o(y)f(a)g
Fi(.setV)l(ari-)0 1281 y(able)g Fn(metho)q(d,)g(to)h(b)q(e)g(describ)q
(ed)i(b)q(elo)o(w.)29 b(Notice)18 b(in)f(the)i(fragmen)o(t)d(that)i
Fk(u)f Fn(is)h Fl(not)k Fn(declared)d(with)e(the)i(statemen)o(t,)0
1331 y(\\)p Fk(DA)i(u[3])p Fn(.)o(")12 b(Suc)o(h)h(a)f(declaration)g(w)
o(ould)f(pro)o(vide)h(for)g(an)h(arra)o(y)f(of)f(D)o(A)h(v)n(ariables)g
(but)h(w)o(ould)e(not)h(sp)q(ecify)h(one)g(of)f(class)0
1381 y(LieOp)q(erator.)62 1430 y(The)k(rest)h(of)e(this)h(note)g
(describ)q(es)i(ho)o(w)d(to)h(use)g(these)h(classes)g(in)e(C)1173
1426 y(++)1253 1430 y(programs.)22 b(Before)17 b(b)q(eginning,)e(ho)o
(w)o(ev)o(er,)0 1480 y(w)o(e)j(shall)e(review)i(a)f(few)h(pieces)g(of)f
(jargon,)g(some)g(of)g(whic)o(h)g(w)o(e)h(ha)o(v)o(e)f(used)h(already)m
(.)28 b(With)17 b(an)o(y)g(smo)q(oth)f(function,)0 1530
y Fh(f)g Fn(:)i Fh(U)f Fg(\022)12 b Fh(R)187 1515 y Ff(N)229
1530 y Fg(!)f Fh(R;)j Fn(w)o(e)h(asso)q(ciate)h(its)f(\\prolongation,")
d(whic)o(h)j(explicitly)e(stores)j(information)c(on)j(deriv)n(ativ)o
(es)f(of)g(the)0 1580 y(function.)161 1565 y Fm(2)664
1619 y Fn(^)655 1630 y Fh(f)i Fg(\021)c(h)7 b Fh(f)r(;)21
b Fg(r)p Fh(f)r(;)f Fg(rr)p Fh(f)r(;)g Fg(rrr)p Fh(f)r(;)g(:)7
b(:)g(:)e Fg(i)28 b Fh(:)0 1702 y Fn(The)16 b(\014rst)h(mem)o(b)q(er)d
(of)h(this)h(structure,)i(its)e(\\standard)g(part,")f(is)h(the)g
(function)g Fh(f)k Fn(itself,)c(the)g(second)h(is)f(its)g(gradien)o(t,)
0 1752 y(the)i(third)f(is)g(its)g(hessian,)h(and)f(so)h(forth.)27
b(Ev)o(erything)18 b(except)g(the)g(standard)g(part)f(is)g(the)h
(\\nilp)q(oten)o(t")1736 1737 y Fm(3)1771 1752 y Fn(part;)g(it)f(is)0
1802 y(also)c(called)g(the)h(\\di\013eren)o(tial")e(or)i
(\\in\014nitesimal")c(or)j(\\nonstandard")g(part.)18
b(Ev)n(aluating)12 b(a)h(prolonged)g(function)g(at)g(a)0
1852 y(\\reference)j(p)q(oin)o(t")d(|)h(sa)o(y)m(,)f(^)-22
b Fh(a)12 b Fn(=)546 1841 y(^)537 1852 y Fh(f)t Fn(\()p
Fh(w)p 577 1859 31 2 v 1 w Fn(\))i(|)g(pro)q(duces)h(a)f(\\prolonged)f
(n)o(um)o(b)q(er.")319 1944 y(^)-22 b Fh(a)12 b Fn(=)404
1933 y(^)395 1944 y Fh(f)5 b Fn(\()p Fh(w)p 436 1951
V 1 w Fn(\))12 b(=)g Fg(h)7 b Fh(f)t Fn(\()p Fh(w)p 602
1951 V 2 w Fn(\))p Fh(;)20 b Fg(r)p Fh(f)t Fn(\()p Fh(w)p
757 1951 V 1 w Fn(\))p Fh(;)h Fg(rr)p Fh(f)t Fn(\()p
Fh(w)p 947 1951 V 1 w Fn(\))p Fh(;)f Fg(rrr)p Fh(f)t
Fn(\()p Fh(w)p 1171 1951 V 1 w Fn(\))p Fh(;)g(:)7 b(:)g(:)e
Fg(i)12 b Fn(=)g Fg(h)7 b Fh(a;)g(a)p 1441 1951 22 2
v -1 w(;)g(a)p 1481 1951 V 1481 1959 V(;)g(:)g(:)g(:)e
Fg(i)27 b Fh(:)0 2031 y Fn(The)20 b Fk(nstd)e Fn(class)i(describ)q(ed)h
(in)e([7)o(])g(mo)q(delled)f(this)h(\(truncated\))i(structure)h
(exactly;)g(the)e(c)o(hains)f(of)g(the)h(D)o(A)f(class)0
2081 y(pro)o(vide)14 b(greater)h(e\016ciency)m(.)20 b(The)14
b(underlying)g(subset,)h Fh(U)i Fg(\022)11 b Fh(R)1033
2066 y Ff(N)1065 2081 y Fh(;)i Fn(whic)o(h)i(is)f(the)g(domain)e(of)i
(our)g(prolonged)g(functions)0 2131 y(is)i(the)g(\\problem)e(space.")24
b(As)16 b(determined)g(b)o(y)f(the)i(application,)d(it)h(splits)h(in)o
(to)f(t)o(w)o(o)g(\\sectors")i(whic)o(h)e(comprise)g(the)0
2181 y(\\dynamical")c(and)k(\\con)o(trol")e(co)q(ordinates,)i(and)f
(accordingly)m(,)f Fh(N)k Fn(=)11 b Fh(N)1173 2187 y
Ff(d)1202 2181 y Fn(+)f Fh(N)1277 2187 y Ff(c)1294 2181
y Fh(:)k Fn(\(F)m(or)g(example,)f(supp)q(ose)j(that)e(w)o(e)h(are)0
2231 y(studying)j(the)g(restricted)i(three-b)q(o)q(dy)f(problem:)25
b(sa)o(y)m(,)17 b(the)i(motion)c(of)i(a)h(small)d(satellite)j(under)h
(the)f(in\015uence)h(of)e(a)p 0 2264 780 2 v 46 2294
a Fj(2)64 2306 y Fn(My)d(using)h(this)g(term)f(is)h(an)f(abuse)i(of)e
(terminology)f(in)o(tro)q(duced)i(on)g(page)g(3)f(of)g(reference)k([1)o
(].)i(The)c(w)o(ord)e(already)0 2356 y(has)g(sev)o(eral)g(meanings,)e
(dep)q(ending)j(on)f(con)o(text;)g(this)g(just)g(adds)g(one)g(more.)46
2388 y Fj(3)64 2399 y Fn(So-called)c(b)q(ecause)j(under)f(the)f(rules)h
(of)e(di\013eren)o(tial)h(arithmetic,)f(a)h(truncated)h(prolongation)e
(whose)h(standard)h(part)0 2449 y(is)i(zero)g(ev)o(en)o(tually)g(v)n
(anishes)g(under)h(rep)q(eated)g(m)o(ultiplication.)965
2574 y(2)p eop
%%Page: 3 3
3 2 bop 0 307 a Fn(planet)13 b(and)h(its)f(mo)q(on.)j(The)e(dynamical)d
(sector)k(w)o(ould)d(represen)o(t)k(the)e(six-dimensional)d(phase)j
(space,)g(corresp)q(onding)0 357 y(to)j(the)h(initial)e(momen)o(tum)d
(and)18 b(p)q(osition)f(of)f(the)j(satellite.)28 b(Ho)o(w)o(ev)o(er,)19
b(if)d(w)o(e)i(w)o(an)o(ted)g(to)f(examine)f(suc)o(h)i(questions)0
407 y(as)h(the)h(sensitivit)o(y)f(of)f(the)i(\014nal)e(state)i(to)f
(the)h(masses)f(of)f(the)i(planet)f(and)g(mo)q(on,)f(then)i(w)o(e)f(w)o
(ould)f(add)h(these)i(as)0 457 y(\\con)o(trol")14 b(co)q(ordinates)h
(of)f(the)h(problem)e(space.\))21 b(The)15 b(\\index)g(arra)o(y")f
(asso)q(ciated)h(with)f(a)g(deriv)n(ativ)o(e)g(is)h(the)g(ordered)0
506 y(arra)o(y)j(of)g(in)o(tegers)h(whic)o(h)g(sp)q(ecify)g(the)g
(deriv)n(ativ)o(e.)31 b(\(F)m(or)18 b(example,)g(if)g(the)h(problem)e
(space)j(is)e(3)g(dimensional,)f(sa)o(y)0 556 y Fh(x)p
0 563 24 2 v 11 w Fn(=)12 b(\()p Fh(x)119 562 y Fm(0)138
556 y Fh(;)7 b(x)181 562 y Fm(1)198 556 y Fh(;)g(x)241
562 y Fm(2)259 556 y Fn(\))p Fh(;)17 b Fn(then)g(the)h(index)e(arra)o
(y)h(asso)q(ciated)g(with)g Fh(@)1024 541 y Fm(6)1043
556 y Fh(f)t Fn(\()p Fh(x)p 1083 563 V 1 w Fn(\))p Fh(=@)r(x)1193
562 y Fm(0)1211 556 y Fh(@)r(x)1259 541 y Fm(3)1259 567
y(1)1278 556 y Fh(@)r(x)1326 541 y Fm(2)1326 567 y(2)1361
556 y Fn(w)o(ould)f(b)q(e)i(\(1)p Fh(;)7 b Fn(3)p Fh(;)g
Fn(2\))p Fh(:)15 b Fn(\))h(The)i(sum)e(of)0 606 y(the)e(indices)g
(\(the)g(comp)q(onen)o(ts)g(of)f(an)g(index)h(arra)o(y\))f(will)f(b)q
(e)i(v)n(aryingly)e(referred)j(to)f(as)g(the)g(deriv)n(ativ)o(e's)f
(\\w)o(eigh)o(t,")f(its)0 656 y(\\order,")i(or)g(its)f(\\degree.")0
793 y Fo(2)67 b(F)-6 b(unctions)24 b(and)f(metho)r(ds)0
884 y Fn(In)14 b(this)f(section)i(w)o(e)e(describ)q(e)j(the)e
(functions)g(and)f(metho)q(ds)976 869 y Fm(4)1008 884
y Fn(curren)o(tly)h(a)o(v)n(ailable)e(in)h(MXYZPTLK,)h(arranged)g(in)f
(the)0 934 y(order)i(in)e(whic)o(h)h(they)g(probably)f(w)o(ould)h(b)q
(e)g(used)h(in)e(most)g(programs.)0 1050 y Fe(2.1)74
b(Setup)19 b(functions)0 1127 y Fi(\(a\))c(v)o(oid)g(D)o(ASetup\()e(in)
o(t)g(n,)j(in)o(t)e(w)i(\))0 1177 y(\(b\))115 b(D)o(ASetup\()13
b(in)o(t)g(n,)j(in)o(t)e(w,)j(double*)c(r)j(\))0 1226
y(\(c\))121 b(D)o(ASetup\()13 b(in)o(t)g(n,)j(in)o(t)e(w,)j(in)o(t)d(s)
h(\))0 1276 y(\(d\))115 b(D)o(ASetup\()13 b(in)o(t)g(n,)j(in)o(t)e(w,)j
(in)o(t)d(s,)i(double*)d(r)j(\))p 0 1367 945 12 v 62
1492 a Fn(Before)g(D)o(A)f(v)n(ariables)f(can)h(b)q(e)h(used,)g(the)f
(application)f(program)f(m)o(ust)h(pro)o(vide)h(information)d(on)j(the)
g(dimensions)0 1542 y(of)f(the)h(problem)e(space)i(and)g(on)f(an)g
(initial)e(reference)17 b(p)q(oin)o(t.)i(This)c(is)f(done)h(b)o(y)f
(four)g Fi(Setup)e Fn(functions,)j(one)f(of)g(whic)o(h)0
1592 y(m)o(ust)f(b)q(e)i(in)o(v)o(ok)o(ed)f(b)q(efore)h(using)f(D)o(A)g
(v)n(ariables)g(in)g(arithmetic)f(or)i(analytic)e(op)q(erations.)20
b(The)15 b(formal)d(argumen)o(ts,)h(all)0 1641 y(input,)g(are)i(in)o
(terpreted)g(as)f(follo)o(ws.)0 1716 y Fi(in)o(t)g(n)p
Fn(:)45 b(Dimension)12 b(of)h(the)i(problem)d(space,)j(the)f(total)f(n)
o(um)o(b)q(er)h(of)f(dynamical)e(and)j(con)o(trol)g(co)q(ordinates.)0
1791 y Fi(in)o(t)g(w)p Fn(:)47 b(The)15 b(maxim)n(um)9
b(deriv)n(ativ)o(e)14 b(w)o(eigh)o(t)g(to)g(b)q(e)g(carried)h(b)o(y)f
(D)o(A)g(v)n(ariables.)j(If)d(w)o(e)g(in)o(terpret)i(a)d(D)o(A)h(v)n
(ariable)f(as)h(a)0 1841 y(m)o(ultinom)o(ia)o(l,)c(then)15
b(its)f(degree)h(will)d(b)q(e)j Fg(\024)d Fi(w)q Fh(:)0
1915 y Fi(in)o(t)g(s)p Fn(:)42 b(The)12 b(n)o(um)o(b)q(er)g(of)f
(dynamical)f(co)q(ordinates,)j(i.e.,)e(the)i(dimension)e(of)g(the)i
(dynamical)d(sector,)k(or)e(\\phase)h(space.")0 2040
y Fi(double)g(r[n])p Fn(:)46 b(An)14 b(arra)o(y)f(con)o(taining)g(the)i
(reference)h(p)q(oin)o(t.)62 2164 y(If)g(form)d(\(a\))j(or)g(\(b\))f
(is)h(used,)g(so)g(that)g Fi(s)f Fn(is)h(not)f(declared)i(explicitly)m
(,)d(the)i(default)f(option)g(sets)i Fi(s)12 b Fn(=)f(0)p
Fh(:)k Fn(In)h(practice)0 2214 y(this)f(means)g(that)g(all)g(v)n
(ariables)f(are)i(considered)h(to)e(b)q(e)h(con)o(trol)f(v)n(ariables,)
g(and)g(neither)h(concatenation)g(nor)f(P)o(oisson)0
2264 y(brac)o(k)o(ets)h(will)d(b)q(e)i(allo)o(w)o(ed)f(\(see)i
(Sections)f(2.7)f(and)h(2.8\).)20 b(If)14 b(form)f(\(a\))i(or)f(\(c\))i
(is)e(used,)i(so)f(that)f(the)i(reference)h(p)q(oin)o(t)d(is)0
2314 y(not)f(declared,)g(it)f(is)h(set)h(to)e(the)h(\\origin,")e(an)i
(arra)o(y)f(of)g(zero)q(es.)20 b(When)12 b(form)f(\(c\))j(or)e(\(d\))h
(is)g(used,)g(so)g(that)g Fi(s)f Fn(is)h(sp)q(eci\014ed,)0
2364 y Fi(D)o(ASetup)e Fn(will)i(stop)h(the)g(application)f(program)f
(if)h(its)h(argumen)o(ts)f Fi(s)h Fn(and)f Fi(n)h Fn(do)g(not)f
(satisfy)h(1)d Fg(\024)h Fi(s)f Fg(\024)h Fi(n)p Fh(:)p
0 2398 780 2 v 46 2432 a Fj(4)64 2444 y Fn(A)h(\\metho)q(d")g(is)h(a)f
(public)h(mem)o(b)q(er)e(function)i(of)f(either)i(the)f(D)o(A)g(or)g
(LieOp)q(erator)h(class.)965 2574 y(3)p eop
%%Page: 4 4
4 3 bop 62 307 a Fn(In)14 b(principle,)g Fi(D)o(ASetup)d
Fn(should)j(b)q(e)h(in)o(v)o(ok)o(ed)e(b)q(efore)i(the)f(formal)e
(declaration)i(of)f(D)o(A)h(v)n(ariables,)f(but)h(this)g(is)g(not)0
357 y(alw)o(a)o(ys)f(p)q(ossible.)18 b(F)m(or)c(example,)e(an)h
(application)g(program)f(ma)o(y)g(con)o(tain)h(a)h(fragmen)o(t)e(lik)o
(e)i(this:)132 419 y Fk(DA)21 b(x;)132 469 y(DA)g(y;)132
569 y(main\(\))f({)132 619 y(DASetup\(\);)132 669 y(...)0
747 y Fn(Here,)g Fk(x)e Fn(and)h Fk(y)f Fn(are)h(mean)o(t)e(to)h(b)q(e)
h(global)e(v)n(ariables,)h(so)g(they)h(are)g(initialized)e(when)i(the)g
(program)e(b)q(egins)h(to)h(run)0 797 y(and)f Fl(b)n(efor)n(e)i
Fn(the)f Fi(D)o(ASetup)c Fn(function)j(can)g(b)q(e)g(in)o(v)o(ok)o(ed.)
30 b(What)17 b(happ)q(ens)i(in)e(suc)o(h)i(a)f(case)g(is)g(this:)26
b(the)19 b(C)1806 793 y(++)1888 797 y(D)o(A)0 847 y(constructors)c
(only)e Fl(p)n(artial)r(ly)i Fn(initialize)d(these)j(v)n(ariables)d
(and)h(load)f(their)i(addresses)h(in)o(to)e(a)g(queue.)18
b(When)c Fi(D)o(ASetup)0 897 y Fn(is)k(\014nally)e(in)o(v)o(ok)o(ed,)i
(this)g(queue)g(is)g(tra)o(v)o(ersed,)h(and)f(the)h(initialization)c
(of)i(an)o(y)g(v)n(ariable)g(whic)o(h)g(had)h(b)q(een)h(declared)0
947 y(previously)14 b(is)f(completed.)0 1063 y Fe(2.2)56
b(Setting)17 b(the)i(reference)d(p)r(oin)n(t)0 1139 y
Fi(\(a\))31 b(v)o(oid)15 b(D)o(AFixReference\()d(double*)i(r)h(\))0
1189 y(\(b\))131 b(D)o(AFixReference\()12 b(D)o(A&)k(x)g(\))0
1239 y(\(c\))137 b(D)o(AFixReferenceA)o(t)o(St)o(art\()12
b(LieOp)q(erator&)i(x)i(\))0 1289 y(\(d\))131 b(D)o(AFixReferenceA)o(t)
o(End)o(\()13 b(LieOp)q(erator&)g(x)k(\))0 1338 y(\(e\))32
b(v)o(oid)15 b(D)o(A::\014xReference\(\))0 1388 y(\(f)5
b(\))209 b(::\014xReference\()14 b(double*)f(r)j(\))0
1438 y(\(g\))205 b(::\014xReference\()14 b(D)o(A&)h(x)i(\))0
1488 y(\(h\))202 b(::\014xReferenceA)o(tStart)o(\()13
b(LieOp)q(erator&)g(x)j(\))0 1538 y(\(i\))215 b(::\014xReferenceA)o
(tEnd\()13 b(LieOp)q(erator&)g(x)j(\))0 1588 y(\(j\))39
b(v)o(oid)15 b(LieOp)q(erator::\014xRef)o(eren)o(ce\(\))0
1637 y(\(k\))387 b(::\014xReference\()14 b(double*)f(r)j(\))0
1687 y(\(l\))398 b(::\014xReference\()14 b(D)o(A&)h(x)i(\))0
1737 y(\(m\))372 b(::\014xReferenceA)o(tStart)o(\()13
b(LieOp)q(erator&)g(x)j(\))0 1787 y(\(n\))385 b(::\014xReferenceA)o
(tEnd\()13 b(LieOp)q(erator&)g(x)j(\))p 0 1876 945 12
v 62 2001 a Fn(A)e(default)g(reference)i(p)q(oin)o(t)d(is)h
(established)h(initially)c(b)o(y)j(a)f Fi(D)o(ASetup)e
Fn(fuction;)j(v)n(ariables)f(declared)h(either)h(b)q(efore)0
2051 y(or)10 b(after)h(its)f(in)o(v)o(o)q(cation)g(are)g(assigned)h
(this)g(reference)h(p)q(oin)o(t)e(as)h(their)g(o)o(wn.)16
b(Ho)o(w)o(ev)o(er,)11 b(the)g(default)f(reference)j(p)q(oin)o(t)d(ma)o
(y)0 2100 y(b)q(e)j(c)o(hanged)g(b)o(y)g(one)f(of)g(the)i(\014rst)f
(four)f(functions.)18 b(The)13 b(\014rst)g(sets)h(it)f(v)n(alue)e(to)i
(that)g(of)f(an)g(arra)o(y)g(pro)o(vided)h(b)o(y)f(the)h(user.)0
2150 y(Changing)e(this)h(arra)o(y)f(later)h(in)g(the)g(application)f
(program)f(will)h(not,)g(b)o(y)h(itself,)g(c)o(hange)g(the)g(default)g
(reference;)j(another)0 2200 y(in)o(v)o(o)q(cation)g(of)h
Fi(D)o(AFixReference)d Fn(w)o(ould)i(b)q(e)i(required.)26
b(F)m(orm)15 b(\(b\))h(of)g(this)g(function)g(sets)i(\(or)e(resets\))i
(the)f(default)0 2250 y(reference)g(p)q(oin)o(t)c(to)h(that)h(of)e(an)h
(already)g(de\014ned)h(D)o(A)f(v)n(ariable.)k(The)d(third)f(function,)f
Fi(D)o(AFixReferenceA)o(tS)o(tart)o Fn(,)0 2300 y(sets)20
b(the)g(default)f(reference)j(to)d(the)h(reference)h(p)q(oin)o(t)e(of)f
(its)i(argumen)o(t;)g(the)g(fourth,)g Fi(D)o(AFixReferenceA)n(tEnd)o
Fn(,)0 2350 y(sets)e(it)f(to)g(the)h Fl(standar)n(d)g(p)n(art)j
Fn(of)16 b(its)h(argumen)o(t.)27 b(F)m(or)17 b(example,)f(supp)q(ose)i
(the)g(\014rst)g(comp)q(onen)o(t)f(of)f(a)h(LieOp)q(erator)0
2399 y Fk(u)j Fn(prolongs)f(the)h(function)g(cos\()p
Fh(xy)11 b Fn(+)f Fh(\031)q(=)p Fn(2\))p Fh(;)19 b Fn(while)g(the)h
(second)h(comp)q(onen)o(t)e(prolongs)h(sin\()p Fh(xy)11
b Fn(+)e Fh(\031)q(=)p Fn(2\))p Fh(;)19 b Fn(b)q(oth)h(ab)q(out)0
2449 y(the)g(p)q(oin)o(t)e(\()p Fh(x;)7 b(y)q Fn(\))12
b(=)g(\()358 2419 y Fg(p)p 393 2419 26 2 v 30 x Fh(\031)q(;)7
b Fg(\000)469 2419 y(p)p 503 2419 V 503 2449 a Fh(\031)q
Fn(\))p Fh(:)19 b Fn(Then)h(\\)p Fk(DAFixReference)o(AtSta)o(rt\()f(u)i
(\))p Fn(")e(w)o(ould)f(set)i(the)g(default)f(reference)i(to)965
2574 y(4)p eop
%%Page: 5 5
5 4 bop 0 307 a Fn(\()16 277 y Fg(p)p 51 277 26 2 v 30
x Fh(\031)q(;)7 b Fg(\000)127 277 y(p)p 161 277 V 161
307 a Fh(\031)q Fn(\))p Fh(;)15 b Fn(while)f(\\)p Fk(DAFixRefernceAtE)o
(nd\()19 b(u)i(\))p Fn(")14 b(w)o(ould)g(set)i(it)e(to)h(\(0)p
Fh(;)7 b Fg(\000)p Fn(1\))p Fh(:)14 b Fn(The)h(latter)g(function)f(is)h
(essen)o(tial)g(for)0 357 y(doing)e(concatenation)h(correctly)h(\(see)h
(Sections)e(2.7)f(and)h(3.3\).)62 407 y(The)c(ten)g(metho)q(ds)f
(\(e\)-\(n\))h(are)g(public)e(mem)o(b)q(ers)g(of)h(the)h(D)o(A)f(and)g
(LieOp)q(erator)h(classes.)18 b(They)10 b(p)q(erform)e(analagously)0
457 y(to)15 b(the)g(\014rst)h(four,)f(but)g(rather)h(than)f(acting)f
(on)h(the)h(default)e(reference)k(p)q(oin)o(t,)c(these)i(mem)o(b)q(ers)
e(adjust)h(the)g(reference)0 506 y(p)q(oin)o(t)e(of)h(the)g(individual)
e(v)n(ariables.)17 b(F)m(or)d(example,)e(in)h(the)i(fragmen)o(t)132
569 y Fk(DA)21 b(x,)g(y,)h(z;)132 619 y(...)132 669 y(x.fixReference\()
c(y)k(\);)132 718 y(z.fixReference\()o(\);)0 803 y Fn(the)e
Fi(.\014xReference)e Fn(mem)o(b)q(er)g(sets)j(the)f(reference)i(p)q
(oin)o(t)d(of)g Fk(x)g Fn(to)g(that)h(of)f Fk(y)p Fn(,)h(while)f(the)h
(reference)i(p)q(oin)o(t)d(of)g Fk(z)g Fn(is)0 853 y(set)c(to)f(the)g
(curren)o(t)h(default)f(reference.)0 969 y Fe(2.3)56
b(Initializing)16 b(a)j(calculation:)24 b(co)r(ordinates)0
1046 y Fi(v)o(oid)14 b(D)o(A::setV)l(ariable\()f(in)o(t)h(j)i(\))175
1095 y(::setV)l(ariable\()d(double)h(x,)32 b(in)o(t)14
b(j)h(\))0 1145 y(v)o(oid)f(LieOp)q(erator::setV)l(ariabl)o(e\()e(D)o
(A&)k(x,)g(in)o(t)e(j)h(\))358 1195 y(::setV)l(ariable\()e(double)h(x,)
i(in)o(t)e(j)h(\))p 0 1286 945 12 v 62 1411 a Fn(D)o(A)f(v)n(ariables)g
(mo)q(del)f(prolonged)h(n)o(um)o(b)q(ers.)19 b(Arithmetic)13
b(m)o(ust)h(b)q(egin)g(b)o(y)g(iden)o(tifying)f(a)h(set)h(of)f(v)n
(ariables)g(as)g(pro-)0 1461 y(longed)j(co)q(ordinates.)28
b(The)17 b(b)q(est)h(w)o(a)o(y)f(of)f(doing)g(this)h(is)g(\014rst)h(to)
f(set)h(the)f(default)g(reference)i(p)q(oin)o(t)e(with)g
Fi(D)o(ASetup)0 1511 y Fn(or)d Fi(D)o(AFixReference)p
Fn(.)j(Then)e(one)f(simply)f(assigns)h(an)g(\\index")g(to)h(eac)o(h)f
(co)q(ordinate)h(v)n(ariable,)e(as)i(in)e(the)i(fragmen)o(t)0
1560 y(b)q(elo)o(w.)132 1595 y Fk(...)132 1644 y(double)20
b(r[3];)132 1744 y(r[0])g(=)44 b(0.0;)132 1794 y(r[1])20
b(=)44 b(1.0;)132 1844 y(r[2])20 b(=)i(-1.0;)132 1943
y(DASetup\()e(3,)h(12,)g(r)h(\);)132 2043 y(DA)f(x,)g(y,)h(z,)f(f;)132
2143 y(x.setVariable\()d(0)k(\);)132 2192 y(y.setVariable\()c(1)k(\);)
132 2242 y(z.setVariable\()c(2)k(\);)132 2342 y(f)f(=)h(exp\()f(x*y)g
(+)g(z)h(\);)0 2430 y Fn(This)15 b(iden)o(ti\014es)h(the)g(phase)g
(space)g(co)q(ordinate)g(arra)o(y)m(,)e Fh(u)p 898 2437
24 2 v 11 w Fg(\021)e Fn(\()p Fh(x;)7 b(y)q(;)g(z)r Fn(\))p
Fh(:)15 b Fn(The)g(v)n(ariable)g Fk(f)g Fn(will)e(con)o(tain)i(data)g
(on)g(the)h(pro-)965 2574 y(5)p eop
%%Page: 6 6
6 5 bop 0 307 a Fn(longed)18 b(function,)h Fh(f)t Fn(\()p
Fh(u)p 356 314 24 2 v 1 w Fn(\))12 b(=)f Fh(e)471 292
y Ff(xy)q Fm(+)p Ff(z)553 307 y Fh(;)18 b Fn(with)h(deriv)n(ativ)o(es)f
(ev)n(aluated)g(at)h(the)g(p)q(oin)o(t)f Fh(u)p 1329
314 V 12 w Fn(=)11 b(\(0)p Fh(;)c Fn(1)p Fh(;)g Fg(\000)p
Fn(1\))p Fh(:)17 b Fn(These)j(data)e(can)h(b)q(e)0 357
y(accessed)f(through)e(a)f(selection)h(metho)q(d)f(\(explained)h(in)f
(Section)h(2.6\))f(b)o(y)g(using)h(the)g(indices)g(that)g(w)o(ere)g
(assigned)g(b)o(y)0 407 y Fi(.setV)l(ariable)p Fn(.)62
457 y(A)e(second)h(w)o(a)o(y)d(of)h(initializing)e(a)j(D)o(A)f
(calculation)f(emplo)o(ys)g(the)j(second)f(form)e(of)h
Fi(.setV)l(ariable)e Fn(to)j(declare)g(a)f(D)o(A)0 506
y(v)n(ariable)g(as)i(a)f(co)q(ordinate)h(while)f(sim)o(ultaneously)f
(setting)i(its)g(v)n(alue.)k(This)14 b(metho)q(d)g(is)h(not)f
(recommended:)19 b(it)14 b(resets)0 556 y(the)i(default)f(reference)j
(p)q(oin)o(t)d(one)g(comp)q(onen)o(t)g(at)g(a)g(time,)f(so)i(that)f(a)g
(in)o(v)o(oking)f Fi(.\014xReference)f Fn(w)o(ould)i(b)q(e)h(required)0
606 y(after)e(the)h(fact.)132 640 y Fk(...)132 690 y(DASetup\()20
b(3,)h(12)g(\);)132 740 y(DA)g(x,)g(y,)h(z,)f(f;)132
840 y(x.setVariable\()d(0.0,)j(0)h(\);)132 889 y(y.setVariable\()c
(1.0,)j(1)h(\);)132 939 y(z.setVariable\()c(-1.0,)j(2)h(\);)132
1039 y(x.fixReference\()o(\);)132 1089 y(y.fixReference\()o(\);)132
1188 y(f)f(=)h(exp\()f(x*y)g(+)g(z)h(\);)62 1326 y Fn(The)d(t)o(w)o(o)g
(LieOp)q(erator)g(metho)q(ds)g(enable)g(one)g(to)f(declare)i(a)e(comp)q
(onen)o(t)g(of)g(a)h(LieOp)q(erator)h(v)n(ariable)d(to)i(b)q(e)g(a)0
1376 y(co)q(ordinate)d(|)g(whic)o(h)g(is)g(useful)g(in)f(the)i(con)o
(trol)e(sector)j(|)d(or)h(to)g(load)f(D)o(A)h(v)n(ariables)f(in)o(to)g
(sp)q(eci\014c)j(comp)q(onen)o(ts)d(|)0 1426 y(prior)f(to)f
(concatenation,)h(for)g(example.)i(Their)f(use)f(will)f(b)q(e)h
(illustrated)g(in)f(Section)i(3.)0 1542 y Fe(2.4)56 b(Op)r(erators)0
1619 y Fn(Logical)15 b(and)h(arithmetic)f(binary)h(op)q(erators)h(act)f
(the)h(w)o(a)o(y)f(one)g(naturally)f(exp)q(ects.)27 b(The)17
b(replacemen)o(t)f(op)q(erator,)h Fk(=)p Fn(,)0 1668
y(enables)d(the)h(replacemen)o(t)f(of)f(one)h(D)o(A,)f(or)h(LieOp)q
(erator,)g(v)n(ariable)f(b)o(y)g(another,)h(while)g(the)g(logical)e(op)
q(erators)j Fk(==)e Fn(and)0 1718 y Fk(!=)d Fn(test)h(whether)h(t)o(w)o
(o)e(v)n(ariables)g(are)h(equiv)n(alen)o(t.)16 b(Arithmetic)10
b(op)q(erators)h Fk(+,)21 b(-,)h(*)10 b Fn(and)g Fk(/)p
Fn(,)h(when)g(sandwic)o(hed)g(b)q(et)o(w)o(een)0 1768
y(t)o(w)o(o)i(D)o(A)h(v)n(ariables,)e(activ)n(ate)i(the)g(corresp)q
(onding)g(arithmetic)f(op)q(erations)h(of)f(addition,)f(subtraction,)i
(m)o(ultiplicatio)o(n,)0 1818 y(and)c(division.)16 b(In)10
b(addition,)f(the)i(subtraction)g(sym)o(b)q(ol,)e Fk(-)p
Fn(,)g(also)h(acts)h(as)f(a)g(unary)h(op)q(erator)f(on)g(D)o(A)g(v)n
(ariables,)g(indicating)0 1868 y(that)k(they)g(are)h(to)e(b)q(e)i
(negated.)k(The)14 b(C)646 1864 y(++)724 1868 y(op)q(erators)h
Fk(+=,)21 b(-=,)g(*=,)14 b Fn(and)f Fk(/=)h Fn(are)g(a)o(v)n(ailable)e
(as)i(w)o(ell.)62 1917 y(When)d(placed)g(b)q(et)o(w)o(een)h(t)o(w)o(o)e
(LieOp)q(erator)h(v)n(ariables,)f(the)h(\\m)o(ultiplicatio)o(n")d(op)q
(erator,)j Fk(*)p Fn(,)f(initiates)g(concatenation)0
1967 y(rather)15 b(than)f(m)o(ultipli)o(cation.)h(This)f(will)e(b)q(e)j
(discussed)g(in)f(detail)f(in)h(Section)g(2.7.)62 2017
y(Comp)q(onen)o(ts)f(of)h(a)f(LieOp)q(erator)i(can)f(b)q(e)h(accessed)h
(b)o(y)e(the)g(p)q(ost\014x)g(unary)g(op)q(erator,)g
Fk([)51 b(])p Fn(.)13 b(F)m(or)g(example,)132 2080 y
Fk(DA)21 b(x,)g(y,)h(z;)132 2129 y(LieOperator)d(u;)132
2179 y(...)132 2229 y(x)i(=)h(u[0];)132 2279 y(y)f(=)h(u[1];)132
2329 y(z)f(=)h(u[2];)132 2378 y(...)965 2574 y Fn(6)p
eop
%%Page: 7 7
7 6 bop 0 307 a Fn(will)12 b(load)h(the)i(zeroth)g(comp)q(onen)o(t)e
(of)g Fk(u)h Fn(in)o(to)f Fk(x)p Fn(,)g(the)i(\014rst)f(in)o(to)g
Fk(y)p Fn(,)f(and)g(so)h(forth.)62 357 y(In)f(addition)f(to)h(these,)h
(the)g(binary)e(op)q(erator)i(caret,)f Fk(^)22 b Fn(,)12
b(placed)i(b)q(et)o(w)o(een)g(t)o(w)o(o)f(LieOp)q(erators)h(p)q
(erforms)e(a)h(P)o(oisson)0 407 y(brac)o(k)o(et.)19 b(W)m(e)13
b(dela)o(y)h(its)f(description)i(to)f(Section)g(2.8.)62
457 y(All)g(binary)g(op)q(erators)h Fl(exc)n(ept)h(c)n(onc)n(atenation)
s Fn(,)g(whic)o(h)e(has)h(its)f(o)o(wn)g(subtleties,)i(c)o(hec)o(k)f
(to)f(b)q(e)h(sure)h(that)f(their)f(t)o(w)o(o)0 506 y(op)q(erands)j(ha)
o(v)o(e)e(the)h(same)f(reference)j(p)q(oin)o(t.)23 b(If)15
b(they)h(do)g(not,)f(then)i(an)e(error)i(message)e(is)h(written)g(on)f
(the)i(standard)0 556 y(output,)d(and)f(the)i(application)d(program)g
(is)i(stopp)q(ed.)19 b(Of)14 b(course,)h(the)f(replacemen)o(t)g(op)q
(erator,)g Fk(=)p Fn(,)f(automatically)e(sets)0 606 y(the)j(reference)j
(p)q(oin)o(t)c(of)h(its)f(left-hand)h(op)q(erand)g(to)g(that)g(of)f
(the)i(righ)o(t-hand)e(one.)0 722 y Fe(2.5)56 b(T)-5
b(ranscenden)n(tal)18 b(functions)0 799 y Fn(Ideally)m(,)13
b(all)g(C)233 795 y(++)313 799 y(transcenden)o(tal)i(functions)g(a)o(v)
n(ailable)e(for)h(\\)p Fk(double)p Fn(")f(v)n(ariables)h(should)g(b)q
(e)h(a)o(v)n(ailable)e(for)h(D)o(A)g(v)n(ari-)0 849 y(ables)e(as)h(w)o
(ell.)k(Ho)o(w)o(ev)o(er,)12 b(the)h(only)f(ones)h(written)f(for)g(V)m
(ersion)h(1.0)e(are)i(the)g(exp)q(onen)o(tial)f(and)g(circular)h
(functions,)f Fi(cos,)0 898 y(cosh,)j(exp,)f(sin,)g(sinh,)f(tan,)i
(tanh.)i Fn(Eac)o(h)c(tak)o(es)g(a)g(single)f(D)o(A)h(v)n(ariable)e(as)
i(its)g(argumen)o(t)e(and)i(returns)h(a)f(single)f(D)o(A)0
948 y(v)n(ariable)f(as)i(its)f(result.)19 b(The)12 b(C)505
944 y(++)582 948 y(functions)h(most)e(conspicuously)i(missing)e(are)h
Fi(p)q(o)o(w)h Fn(and)f Fi(log)p Fn(.)k(These)e(will)d(b)q(e)i(made)0
998 y(a)o(v)n(ailable)f(in)h(V)m(ersion)h(1.1,)e(and)i(more)f(will)f(b)
q(e)j(added)f(to)g(subsequen)o(t)i(v)o(ersions)e(of)f(this)h(to)q
(olkit.)0 1114 y Fe(2.6)74 b(Selection)17 b(metho)r(ds)0
1191 y Fi(double)c(D)o(A::standardP)o(art\(\))226 1241
y(::deriv)m(ativ)o(e\()g(in)o(t*)h(m)i(\))226 1290 y(::w)o(eigh)o
(tedDeri)o(v)m(ativ)o(e)o(\()d(in)o(t*)h(m)h(\))0 1340
y(D)o(A)82 b(D)o(A::\014lter\()14 b(in)o(t)g(wgtLo,)h(in)o(t)f(wgtHi)i
(\))0 1390 y(v)o(oid)65 b(LieOp)q(erator::standard)o(P)o(art)o(\()13
b(double*)g(x)j(\))409 1440 y(::deriv)m(ativ)o(e\()e(in)o(t*)f(m,)j
(double*)e(x)i(\))409 1490 y(::w)o(eigh)o(tedDeri)o(v)m(ativ)o(e)o(\()d
(in)o(t*)h(m,)i(double*)d(x)j(\))p 0 1581 945 12 v 62
1705 a Fn(A)i(n)o(um)o(b)q(er)e(of)h(metho)q(ds)g(access)i(parts)e(of)g
(D)o(A)g(v)n(ariables)f(without)h(c)o(hanging)g(the)h(v)n(ariable.)27
b(As)17 b(a)g(D)o(A)g(metho)q(d,)0 1755 y Fi(.standardP)o(art)p
Fn(,)10 b(returns)16 b(as)e(its)f(v)n(alue)h(the)g(standard)g(part)g
(of)f(the)i(v)n(ariable;)d(as)i(a)g(LieOp)q(erator)g(metho)q(d,)f(it)g
(accepts)0 1805 y(an)f(arra)o(y)g(p)q(oin)o(ter)g(\(that)h(is,)f(the)g
(name)f(of)h(an)g(arra)o(y\))g(argumen)o(t)f(and)h(loads)g(the)g
(standard)h(parts)g(of)e(all)g(its)h(comp)q(onen)o(ts)0
1855 y(in)o(to)h(this)h(arra)o(y)m(.)j(F)m(or)d(example:)132
1897 y Fk(...)132 1947 y(double)20 b(z,)h(x[8];)132 1997
y(LieOperator)e(y;)132 2046 y(...)132 2096 y(y.standartPart\()f(x)k
(\);)132 2146 y(z)f(=)h(y[3].standartPar)o(t\(\);)132
2196 y(if\()f(z)g(==)h(x[3])f(\))g(cout)g(<<)h("All)f(is)g(OK\\n")132
2246 y(...)62 2300 y Fn(The)f Fi(.deriv)m(ativ)o(e)d
Fn(and)h Fi(.w)o(eigh)o(tedDeri)o(v)m(ativ)o(e)e Fn(routines)j(return)h
(the)g(v)n(alue)e(of)h(a)f(sp)q(eci\014ed)j(deriv)n(ativ)o(e.)33
b(The)0 2350 y(argumen)o(t)16 b(is)h(a)g(p)q(oin)o(ter)g(to)g(\(name)f
(of)s(\))h(an)g(in)o(teger)g(arra)o(y)g(con)o(taining)f(the)h(indices)h
(of)e(the)i(desired)g(deriv)n(ativ)o(e.)27 b(F)m(or)0
2399 y(example,)11 b(if)g Fk(f)h Fn(represen)o(ts)j(the)e(D)o(A)f(ev)n
(aluation)e(of)i(a)g(prolonged)g(function)g(of)f(three)j(v)n(ariables,)
d Fh(f)t Fn(,)i(at)f(the)h(p)q(oin)o(t)e Fh(w)p 1814
2406 31 2 v 1 w Fn(,)h(then)0 2449 y(the)i(deriv)n(ativ)o(e)35
b Fh(@)307 2434 y Fm(6)326 2449 y Fh(f)t Fn(\()p Fh(x)p
366 2456 24 2 v Fn(\))p Fh(=@)r(x)475 2455 y Fm(0)494
2449 y Fh(@)r(x)542 2434 y Fm(3)542 2459 y(1)561 2449
y Fh(@)r(x)609 2434 y Fm(2)609 2459 y(2)627 2449 y Fg(j)639
2455 y Ff(x)p 639 2462 19 2 v Fm(=)p Ff(w)p 683 2462
25 2 v 745 2449 a Fn(can)14 b(b)q(e)g(obtained)g(as)g(follo)o(ws.)965
2574 y(7)p eop
%%Page: 8 8
8 7 bop 132 271 a Fk(...)132 321 y(DA)21 b(f;)132 370
y(double)f(d,)h(w[3];)132 420 y(int)g(m[3];)132 470 y(...)132
520 y(DASetup\()f(3,)h(10,)g(w)h(\);)132 570 y(...)132
620 y(m[0])e(=)i(1;)132 669 y(m[1])e(=)i(3;)132 719 y(m[2])e(=)i(2;)132
769 y(d)f(=)h(f.derivative\()d(m)i(\);)132 819 y(...)0
898 y Fn(The)13 b Fi(.w)o(eigh)o(tedDeri)o(v)m(ati)o(v)o(e)d
Fn(returns)k(the)f(deriv)n(ativ)o(e)f(w)o(eigh)o(ted)g(b)o(y)g
(factorials)g(of)g(the)h(indices.)18 b(These)13 b(are)g(the)g(actual)0
947 y(co)q(e\016cien)o(ts)i(whic)o(h)g(w)o(ould)e(app)q(ear)i(in)f(a)g
(m)o(ultinom)o(i)o(al)d(represen)o(tation)16 b(of)d Fh(f)t
Fn(,)i(and)f(they)m(,)g(not)g(the)h(deriv)n(ativ)o(es,)f(are)g(the)0
997 y(actual)h(n)o(um)o(b)q(ers)h(stored)h(in)e(the)h(D)o(A)g(v)n
(ariable.)779 982 y Fm(5)820 997 y Fn(Th)o(us,)g(if)f(w)o(e)g(replace)i
Fk(.derivative)d Fn(with)h Fk(.weightedDerivati)o(ve)0
1047 y Fn(in)e(the)i(example)e(ab)q(o)o(v)o(e,)g(then)h(the)h(v)n(alue)
e(returned)j(w)o(ould)d(b)q(e)h(\(1!)7 b(3!)g(2!\))1176
1032 y Fd(\000)p Fm(1)1219 1047 y Fh(@)1243 1032 y Fm(6)1262
1047 y Fh(f)t Fn(\()p Fh(x)p 1302 1054 24 2 v Fn(\))p
Fh(=@)r(x)1411 1053 y Fm(0)1430 1047 y Fh(@)r(x)1478
1032 y Fm(3)1478 1057 y(1)1497 1047 y Fh(@)r(x)1545 1032
y Fm(2)1545 1057 y(2)1563 1047 y Fg(j)1575 1053 y Ff(x)p
1575 1060 19 2 v Fm(=)p Ff(w)p 1619 1060 25 2 v 1646
1047 a Fh(:)62 1097 y Fn(As)15 b(with)f Fi(.standardP)o(art)p
Fn(,)d(the)k(LieOp)q(erator)h(metho)q(ds)d(load)h(the)h(v)n(alues)f(of)
g(the)h(deriv)n(ativ)o(e)f(at)g(eac)o(h)h(comp)q(onen)o(t)0
1147 y(in)o(to)e(the)i(arra)o(y)e(p)q(oin)o(ted)h(to)g(b)o(y)g(the)g
(additional)e(argumen)o(t,)g Fi(double*)i(x)p Fn(.)62
1197 y(The)e Fi(.\014lter)d Fn(metho)q(d,)h(whic)o(h)h(curren)o(tly)h
(b)q(elongs)f(only)f(to)h(the)g(D)o(A)g(class,)g(returns)i(a)e(D)o(A)f
(v)n(ariable)g(whose)i(links)e(store)0 1246 y(those)k(deriv)n(ativ)o
(es)g(with)f(w)o(eigh)o(ts)h(b)q(ounded)g(b)o(y)g(the)g(argumen)o(ts,)f
Fi(wgtLo)g Fn(and)g Fi(wgtHi)p Fn(.)18 b(It)13 b(w)o(as)h(written)g
(primarily)d(for)0 1296 y(use)k(b)o(y)e(other)i(D)o(A)e(metho)q(ds,)g
(and)h(I)g(do)g(not)f(exp)q(ect)j(it)d(to)h(b)q(e)h(used)f(m)o(uc)o(h)f
(in)g(application)g(programs.)0 1412 y Fe(2.7)74 b(Ev)m(aluation)18
b(and)h(concatenation)0 1489 y Fi(double)129 b(D)o(A::op)q
(erator\(\)\()13 b(double*)h(x)i(\))0 1539 y(LieOp)q(erator)d(op)q
(erator*\()h(LieOp)q(erator&)g(x,)i(LieOp)q(erator&)d(y)k(\))p
0 1630 945 12 v 62 1755 a Fn(D)o(A)d(v)n(ariables)f(can)h(act)g(lik)o
(e)e(p)q(o)o(w)o(er)j(series.)k(The)14 b(data)f(stored)i(in)e(the)i
(links)e(of)g(a)g(D)o(A)h(v)n(ariable)e(are)i(the)h(co)q(e\016cien)o
(ts)0 1804 y(of)e(a)g(p)q(o)o(w)o(er)h(series,)g(or)f(m)o(ultinom)o
(ial)o(,)d(expansion)j(of)g(a)g(function,)g Fh(f)t Fn(,)h(ab)q(out)f
(the)h(reference)i(p)q(oin)o(t.)h(This)c(expansion)h(can)0
1854 y(b)q(e)h(ev)n(aluated)e(b)o(y)h(using)f(the)i Fi(.op)q
(erator\(\))d Fn(metho)q(d.)62 1904 y(Closely)17 b(related)g(to)g(ev)n
(aluation)e(is)i(the)h(op)q(eration)e(of)h(concatenation,)g(whic)o(h)g
(is)g(activ)n(ated)f(b)o(y)h(sandwic)o(hing)f(the)0 1954
y(\\m)o(ultiplicati)o(on")c(binary)i(op)q(erator,)h Fk(*)p
Fn(,)f(b)q(et)o(w)o(een)i(t)o(w)o(o)e(LieOp)q(erators.)22
b(Let)15 b Fh(f)p 1253 1969 25 2 v 5 w(;)7 b(g)p 1297
1969 22 2 v 12 w Fn(:)k Fh(R)1384 1939 y Ff(N)1410 1943
y Fc(d)1428 1939 y Fm(+)p Ff(N)1479 1943 y Fc(c)1509
1954 y Fg(!)g Fh(R)1594 1939 y Ff(N)1620 1943 y Fc(d)1637
1939 y Fm(+)p Ff(N)1688 1943 y Fc(c)1721 1954 y Fn(b)q(e)16
b(t)o(w)o(o)e(map-)0 2004 y(pings)j(of)g(the)h(problem)e(space)j(in)o
(to)e(itself)g Fl(which)h(act)g(like)g(the)g(identity)g(on)h(the)f(c)n
(ontr)n(ol)g(se)n(ctor.)28 b Fn(That)18 b(is,)g(only)e(the)0
2054 y(dynamical)11 b(co)q(ordinates)j(c)o(hange)g(under)h(the)f
(action)f(of)g Fh(f)p 916 2068 25 2 v 18 w Fn(and)h Fh(g)p
1035 2068 22 2 v 1 w Fn(;)f(the)h(con)o(trol)f(v)n(ariables)g(are)h
(not)g(touc)o(hed.)k(The)c(com-)0 2103 y(p)q(osite)i(map,)d
Fh(h)p 228 2110 24 2 v 12 w Fn(=)e Fh(f)p 307 2118 25
2 v 14 w Fg(\016)e Fh(g)p 371 2118 22 2 v 13 w Fn(:)i
Fh(u)p 427 2110 24 2 v 12 w Fg(7!)g Fh(f)p 516 2118 25
2 v 4 w Fn(\()p Fh(g)p 556 2118 22 2 v 2 w Fn(\()p Fh(u)p
594 2110 24 2 v Fn(\)\))p Fh(;)k Fn(is)g(a)g(mapping)e(of)i(the)g(same)
g(t)o(yp)q(e)h(and,)f(therefore,)h(also)f(represen)o(table)i(b)o(y)e(a)
0 2153 y(LieOp)q(erator.)j(Ho)o(w)o(ev)o(er,)12 b(notice)g(that)g
(although)f(the)h(reference)i(p)q(oin)o(ts)e(of)f Fh(h)p
1215 2160 V 12 w Fn(and)g Fh(g)p 1329 2168 22 2 v 13
w Fn(are)h(iden)o(tical,)f(sa)o(y)h(a)p 1676 2160 21
2 v(,)f(the)h(reference)0 2203 y(p)q(oin)o(t)h(of)h(f)p
156 2210 13 2 v 13 w(is)g Fh(g)p 224 2218 22 2 v 1 w
Fn(\()p Fh(a)p 261 2210 V Fn(\))p Fh(:)62 2253 y Fn(When)h(the)h(con)o
(trol)e(sector)j(is)d(not)h(empt)o(y)m(,)e Fl(al)r(l)j(LieOp)n(er)n
(ator)f(op)n(er)n(ations)g(and)i(metho)n(ds)f(assume)g(that)g(the)g
(\014rst)f Fh(N)1930 2259 y Ff(d)0 2303 y Fl(c)n(omp)n(onents)h(r)n
(efer)d(to)i(the)g(dynamic)n(al)h(se)n(ctor)e(and)i(the)f(\014nal)g
Fh(N)1034 2309 y Ff(c)1066 2303 y Fl(to)g(the)g(c)n(ontr)n(ol)f(se)n
(ctor.)p 0 2337 780 2 v 46 2365 a Fj(5)64 2377 y Fn(In)c(fact,)h(the)g
Fi(.deriv)m(ativ)o(e)e Fn(metho)q(d)h(\014rst)h(in)o(v)o(ok)o(es)f
Fi(.w)o(eigh)o(tedDeri)o(v)m(ativ)o(e)d Fn(and)k(then)g(m)o(ultiplies)d
(b)o(y)j(the)g(factorials.)965 2574 y(8)p eop
%%Page: 9 9
9 8 bop 62 307 a Fn(F)m(urther)14 b(description)f(of)f(these)i(metho)q
(ds)f(w)o(ould)e(b)q(e)j(a)o(wkw)o(ard)e(without)g(recourse)j(to)d
(examples;)g(w)o(e)h(shall)f(con)o(tin)o(ue)0 357 y(this)i(discussion)g
(in)g(Section)g(3.)0 471 y Fe(2.8)74 b(Di\013eren)n(tiation)17
b(and)i(P)n(oisson)g(brac)n(k)n(ets)0 548 y Fi(D)o(A)c(D)o(A::D\()g(in)
o(t*)f(m)i(\))0 598 y(D)o(A)f(op)q(erator^)g(\()g(D)o(A&)h(x,)g(D)o(A&)
f(y)h(\))p 0 678 945 12 v 62 803 a Fn(Deriv)n(ativ)o(es)e(of)f
(functions)h(are)g(themselv)o(es)g(functions,)f(and)h(D)o(A)g(v)n
(ariables)f(con)o(tain)g(a)h(metho)q(d,)e Fi(.D)p Fn(,)h(whic)o(h)h
(imple-)0 853 y(men)o(ts)9 b(this)h(op)q(eration.)17
b(F)m(or)9 b(example,)g(if)g Fh(u)h Fn(and)g Fh(v)h Fn(are)f(functions)
g(o)o(v)o(er)g Fh(R)1169 838 y Fm(2)1188 853 y Fn(,)g(and)f(w)o(e)i(w)o
(an)o(t)e(a)h(functional)e(corresp)q(ondence,)0 903 y
Fh(v)13 b Fg(\021)f Fh(@)101 888 y Fm(3)120 903 y Fh(u=@)r(x)213
888 y Fm(2)213 913 y(0)231 903 y Fh(@)r(x)279 909 y Fm(1)298
903 y Fn(,)h(this)h(w)o(ould)f(b)q(e)i(accomplished)e(as)h(follo)o(ws.)
132 947 y Fk(...)132 997 y(DA)21 b(u,)g(v;)132 1047 y(int)g(m[2];)132
1097 y(...)132 1146 y(m[0])f(=)i(2;)132 1196 y(m[1])e(=)i(1;)132
1246 y(v)f(=)h(u.D\()f(m)g(\);)0 1331 y Fn(The)14 b(D)o(A)g(v)n
(ariable)f Fk(u)g Fn(itself)h(is)g(unc)o(hanged)g(b)o(y)g(this)g(metho)
q(d.)62 1381 y(T)m(aking)d(deriv)n(ativ)o(es)i Fl(lowers)f(the)i
(maximum)g(ac)n(cur)n(ate)g(weight)i Fn(of)c(a)g(D)o(A)g(v)n(ariable.)
17 b(Th)o(us,)12 b(if)g Fk(u)g Fn(stores)i(deriv)n(ativ)o(es)f(of)0
1430 y Fh(u)p Fn(\()p Fh(x)p 40 1437 24 2 v Fn(\))e(through)h(w)o(eigh)
o(t)f Fh(w)q Fn(,)g(and)g(w)o(e)h(de\014ne)h Fh(v)g Fn(to)e(b)q(e)h(an)
g Fh(m)911 1415 y Fm(th)944 1430 y Fn(-order)g(deriv)n(ativ)o(e)f(of)g
Fh(u)p Fn(,)h(then)g Fk(v)f Fn(can)h(store)g(the)g(deriv)n(ativ)o(es)g
(of)0 1480 y Fh(v)i Fn(accurately)g(only)e(through)h(w)o(eigh)o(t)f
Fh(w)e Fg(\000)g Fh(m;)j Fn(all)e(deriv)n(ativ)o(es)i(of)f(higher)h(w)o
(eigh)o(t)g(b)q(eing)g(unkno)o(wn.)k(One)c(of)g(the)g(priv)n(ate)0
1530 y(mem)o(b)q(ers)e(of)i(eac)o(h)g(D)o(A)f(v)n(ariable)g(k)o(eeps)i
(trac)o(k)f(of)f(the)h(maxim)o(um)8 b(w)o(eigh)o(t)k(of)g(deriv)n(ativ)
o(es)h(computed)f(accurately)m(,)h(whic)o(h)0 1580 y(ma)o(y)f(b)q(e)i
(less)g(than)g(the)g(maxim)n(um)c(w)o(eigh)o(t)j(declared)h(b)o(y)g
(the)g Fi(D)o(ASetup)d Fn(function.)18 b(These)d(n)o(um)o(b)q(ers)e
(are)h(propagated)0 1630 y(through)i(arithmetic)f(op)q(erations,)h(so)g
(errors)h(will)d(not)i(arise)g(when)g(using)g(less)g(accurate)h(v)n
(ariables.)24 b(In)15 b(principle,)h(an)0 1679 y(applications)c
(program)f(can)j(request)g(a)f(di\013eren)o(tiation)g(or)g(in)o(v)o(ok)
o(e)f(a)h(selection)g(metho)q(d)g(whic)o(h)f(cannot)i(b)q(e)f(carried)h
(out)0 1729 y(accurately)m(.)30 b(If)18 b(this)g(happ)q(ens,)h(then)g
(the)f(D)o(A)g(class)g(will)f(stop)h(the)g(program)f(and)g(write)h(an)g
(error)h(message)f(to)f(the)0 1779 y(standard)d(output.)62
1829 y(If)d(the)h(dynamical)d(sector)k(has)f(ev)o(en)g(dimension,)e(sa)
o(y)h Fh(N)957 1835 y Ff(d)988 1829 y Fn(=)h(2)p Fh(n;)e
Fn(it)i(can)f(b)q(e)h(\(and)g(usually)e(is\))i(in)o(terpreted)h(as)e(a)
g(phase)0 1879 y(space)16 b(whose)g(\014rst)f Fh(n)g
Fn(comp)q(onen)o(ts)g(are)g(\\p)q(ositions")f(and)h(whose)g(second)h
(are)g(\\momen)o(ta.)o(")j(The)c(P)o(oisson)g(brac)o(k)o(et)h(of)0
1928 y(t)o(w)o(o)d(suc)o(h)i(observ)n(ables)g(is)e(an)h(observ)n(able,)
g(and)f(D)o(A)h(implemen)o(ts)d(this)j(op)q(eration)g(via)f(the)i
(binary)e(op)q(erator)h Fk(^)22 b Fn(.)132 1971 y Fk(...)132
2021 y(DA)f(f,)g(g,)h(h;)132 2070 y(...)132 2120 y(h)f(=)h(f^g;)0
2208 y Fn(Because)g(this)f(op)q(eration)f(requires)h(taking)f(deriv)n
(ativ)o(es,)h(the)g(accurate)h(w)o(eigh)o(t)e(of)f(the)i(resultan)o(t)g
(is)f(smaller)f(than)0 2258 y(that)14 b(of)f(its)h(op)q(erands,)g(and)g
(just)g(as)g(with)g Fi(.D)p Fn(,)f(if)g(the)i(op)q(eration)e(cannot)h
(b)q(e)h(carried)f(out)g(the)h(program)d(will)g(stop.)0
2373 y Fe(2.9)56 b(Miscellaneous)17 b(utilities)0 2449
y Fi(v)o(oid)d(D)o(AAb)q(out\(\))965 2574 y Fn(9)p eop
%%Page: 10 10
10 9 bop 0 307 a Fi(v)o(oid)14 b(D)o(ANews\(\))0 357
y(v)o(oid)g(D)o(A::p)q(eekA)o(t\(\))175 407 y(::clear\(\))0
457 y(v)o(oid)g(LieOp)q(erator::p)q(eekA)o(t\(\))p 0
548 945 12 v 62 672 a Fn(The)h(\014rst)h(function,)e
Fi(D)o(AAb)q(out)p Fn(,)e(prin)o(ts)j(information)d(ab)q(out)i(the)i(D)
o(A)e(implemen)o(tatio)o(n,)e(esp)q(ecially)j(the)g(v)o(ersion)0
722 y(n)o(um)o(b)q(er,)d(on)h(the)h(standard)f(output;)g(the)h(second,)
g Fi(D)o(ANews)f Fn(prin)o(ts)g(notices)h(of)f(di\013erences)i(b)q(et)o
(w)o(een)g(one)e(implemen-)0 772 y(tation)g(and)h(another,)g(as)g(w)o
(ell)f(as)h(information)d(on)j(kno)o(wn)f(bugs.)62 822
y(The)18 b Fi(.p)q(eekA)o(t)e Fn(metho)q(d)g(will)f(tra)o(v)o(erse)j(a)
f(D)o(A)f(v)n(ariable)g(and)h(write)g(information)d(on)i(eac)o(h)i
(link)d(to)i(the)h(standard)0 872 y(output,)h(including)e(the)i(index)g
(arra)o(y)f(of)f(the)i(asso)q(ciated)g(deriv)n(ativ)o(e,)g(its)f(v)n
(alue,)g(and)g(the)h(address)h(of)e(the)h(link.)30 b(It)0
922 y(pro)o(vides)14 b(a)f(w)o(a)o(y)g(of)g(lo)q(oking)f(at)i(the)g(en)
o(tire)g(v)n(ariable)f(without)g(rep)q(eated)j(use)e(of)f(the)h
Fi(.deriv)m(ativ)o(e)e Fn(metho)q(ds)h(describ)q(ed)0
971 y(in)h(Section)i(2.6.)k(The)15 b(metho)q(d)f Fi(.clear)g
Fn(returns)j(a)d(D)o(A)h(v)n(ariable)f(to)g(its)h(n)o(ull)f(state,)i(a)
e(c)o(hain)h(with)f(no)h(links.)20 b(It)15 b(should)0
1021 y(b)q(e)g(used)f(rarely)g(and)g(cautiously)m(.)0
1158 y Fo(3)89 b(Examples)0 1249 y Fn(W)m(e)18 b(displa)o(y)g(b)q(elo)o
(w)h(a)g(few)f(sample)g(programs)g(whic)o(h)g(illustrate)h(v)n(arious)f
(features)i(of)e(the)i(D)o(A)e(to)q(olkit.)32 b(They)20
b(are)0 1299 y(simple)12 b(enough)i(to)f(b)q(e)i(understandable)f
(without)f(detailed)h(kno)o(wledge)f(of)g(C)1257 1295
y(++)1336 1299 y(,)g(and)g(I)h(hop)q(e)g(that,)f(to)h(some)e(exten)o
(t,)0 1349 y(their)h(ease)h(and)f(transparency)i(will)c(help)i(motiv)n
(ate)e(those)j(who)f(con)o(tin)o(ue)g(to)g(hesitate)h(in)o(v)o(esting)e
(the)i(four)f(or)g(\014v)o(e)g(da)o(ys)0 1399 y(needed)j(to)e(learn)g
(this)g(language)g(or)g(who)g(ha)o(v)o(e)g(b)q(een)h(discouraged)g(b)o
(y)f(essa)o(ys)h([13)o(])f(suggesting)g(that)h(F)o(OR)m(TRAN)e(still)0
1449 y(p)q(ossesses)k(a)c(few)h(adv)n(an)o(tages.)0 1565
y Fe(3.1)74 b(P)n(oisson)20 b(brac)n(k)n(ets)0 1641 y
Fn(This)e(little)g(test)i(program)c(ev)n(aluates)j(the)g(P)o(oisson)f
(brac)o(k)o(et)i(of)d(t)o(w)o(o)h(functions)h(and)f(tests)i(D)o(A)e
(against)g(the)h(Jacobi)0 1691 y(iden)o(tit)o(y)13 b(in)h(a)f(four)h
(dimensional)e(phase)i(space.)19 b(The)14 b(\014rst)h(P)o(oisson)f
(brac)o(k)o(et)g(is)g(carried)h(out)f(on)f(the)i(functions)735
1783 y Fh(a)p Fn(\()p Fh(x)p 773 1790 24 2 v(;)7 b(p)p
816 1797 21 2 v Fn(\))41 b(=)h Fh(x)992 1765 y Fm(2)992
1793 y(1)1010 1783 y Fh(x)1034 1765 y Fm(3)1034 1793
y(2)1053 1783 y Fh(p)1074 1789 y Fm(1)1092 1783 y Fh(p)1113
1765 y Fm(4)1113 1793 y(2)1159 1783 y Fh(;)739 1851 y(b)p
Fn(\()p Fh(x)p 773 1858 24 2 v(;)7 b(p)p 816 1866 21
2 v Fn(\))41 b(=)h(sin\()p Fh(x)1059 1857 y Fm(1)1077
1851 y Fh(p)1098 1834 y Fm(2)1098 1862 y(2)1117 1851
y Fh(x)1141 1834 y Fm(3)1141 1862 y(2)1159 1851 y Fn(\))28
b Fh(:)0 1943 y Fn(The)14 b(brac)o(k)o(et)f(is)g(to)g(b)q(e)h(ev)n
(aluated)f(at)g(the)h(arbitrarily)e(selected)j(p)q(oin)o(t,)d(\()p
Fh(x)p 1171 1950 24 2 v(;)7 b(p)p 1214 1957 21 2 v -1
w Fn(\))12 b(=)g(\(0)p Fh(:)p Fn(32)p Fh(;)7 b Fn(0)p
Fh(:)p Fn(5)p Fh(;)g Fg(\000)p Fn(3)p Fh(:)o Fn(1)p Fh(;)f
Fn(1)p Fh(:)p Fn(5)o(\))p Fh(:)k Fn(F)m(or)j(testing)g(the)0
1993 y(Jacobi)h(iden)o(tit)o(y)m(,)e(w)o(e)i(in)o(tro)q(duce)h(a)e
(third)h(function,)f Fh(c)f Fn(=)g(exp\()p Fh(p)1023
1999 y Fm(1)1042 1993 y Fh(x)1066 1999 y Fm(1)1093 1993
y Fn(+)e Fh(p)1156 1999 y Fm(2)1174 1993 y Fh(x)1198
1999 y Fm(2)1217 1993 y Fn(\))p Fh(:)0 2150 y Fk(#include)20
b(<std.h>)0 2200 y(#include)g(<stdio.h>)0 2250 y(#include)g(<stream.h>)
0 2300 y(#include)g("mxyzptlk.rsc")172 b(//)21 b(**)g(SEE)h(COMMENT)e
(1)0 2399 y(main\(\))h({)954 2574 y Fn(10)p eop
%%Page: 11 11
11 10 bop 0 307 a Fk(double)21 b(u1,)g(u2,)g(v1,)g(v2;)0
357 y(double)g(r[4];)0 407 y(r[0])g(=)h(u1)f(=)h(0.32;)0
457 y(r[1])f(=)h(u2)f(=)h(0.5;)0 506 y(r[2])f(=)h(v1)f(=)h(-3.1;)0
556 y(r[3])f(=)h(v2)f(=)h(1.5;)0 656 y(DASetup\()e(4,)i(3,)f(4,)g(r)h
(\);)196 b(//)21 b(**)g(SEE)h(COMMENT)e(2)0 756 y(double)h(w,)g(y,)g
(z,)h(answer;)0 805 y(DA)f(a,)h(b,)f(c;)0 855 y(DA)g(x1,)h(x2,)f(p1,)g
(p2;)0 905 y(DA)g(pb;)0 1005 y(x1.setVariable\(0\))o(;)281
b(//)21 b(**)g(SEE)h(COMMENT)e(3)0 1054 y(x2.setVariable\(1\))o(;)0
1104 y(p1.setVariable\(2\))o(;)0 1154 y(p2.setVariable\(3\))o(;)676
1254 y(//)h(**)g(SEE)h(COMMENT)e(4)0 1303 y(a)i(=)f(\(x1*x1\))g(*)g
(\(x2*x2*x2\))f(*)h(p1)h(*)f(\(p2*p2*p2*p2\);)0 1353
y(b)h(=)f(sin\()g(x1)h(*)f(\(p2*p2\))f(*)i(\(x2*x2*x2\))e(\);)0
1403 y(pb)h(=)h(a^b;)0 1453 y(cout)f(<<)g("Computed)f(by)i(DA:)f(")g
(<<)h(pb.standardPart\()o(\))d(<<)i("\\n";)0 1553 y(w)h(=)f(\(u1*u1\))g
(*)g(\(u2*u2*u2\))f(*)h(v1)h(*)f(\(v2*v2*v2*v2\);)0 1602
y(y)h(=)130 b(u1)22 b(*)f(\(v2*v2\))f(*)i(\(u2*u2*u2\))42
b(;)0 1652 y(z)22 b(=)f(cos\()g(y)h(\);)0 1702 y(answer)f(=)g(w*y*z*\()
f(6.0/\(u2*v2\))g(-)i(1.0/\(u1*v1\))d(-)j(12.0/\(u2*v2\))d(\);)0
1752 y(cout)i(<<)g("Exact)g(answer)42 b(:)22 b(")f(<<)h(answer)e(<<)i
("\\n";)0 1851 y(cout)f(<<)g("And)g(also)130 b(:)22 b(")109
b(//)21 b(**)g(SEE)h(COMMENT)e(5)109 1901 y(<<)h(\()h(\()g(\(x1*x1\))e
(*)h(\(x2*x2*x2\))f(*)i(p1)f(*)h(\(p2*p2*p2*p2\))d(\))i(^)218
1951 y(\()h(sin\()e(x1)i(*)f(\(p2*p2\))g(*)g(\(x2*x2*x2\))f(\))i(\))174
2001 y(\).standardPart\(\))109 2051 y(<<)f("\\n\\n";)0
2150 y(//)g(--)h(Test)f(of)g(the)g(Jacobi)g(identity)0
2200 y(c)h(=)f(exp\()g(p1*x1)g(+)g(p2*x2)g(\);)0 2250
y(pb)g(=)h(\(a^\(b^c\)\))e(+)h(\(b^\(c^a\)\))327 2300
y(+)g(\(c^\(a^b\)\);)86 b(//)21 b(**)g(SEE)h(COMMENT)e(6)0
2350 y(cout)h(<<)g("Jacobi)g(identity\\n";)0 2399 y(pb.peekAt\(\);)412
b(//)21 b(**)g(SEE)h(COMMENT)e(7)0 2449 y(})954 2574
y Fn(11)p eop
%%Page: 12 12
12 11 bop 0 307 a Fi(Output:)230 333 y Fk(Computed)21
b(by)g(DA:)g(.125897)230 382 y(Exact)g(answer)42 b(:)22
b(.125897)230 432 y(And)g(also)129 b(:)22 b(.125897)230
532 y(Jacobi)f(identity)230 631 y(Count)43 b(=)22 b(35,)f(Weight)f(=)i
(3,)f(Max)g(accurate)g(weight)f(=)i(1)230 681 y(Reference)e(point:)230
731 y(3.200000e-01)41 b(5.000000e-01)h(-3.100000e+00)e(1.500000e+00)230
781 y(Weight:)21 b(0)65 b(Value:)20 b(2.498002e-16)42
b(||)21 b(Addresses:)f(313360)g(184296)h(184560)f(:)i(184248)230
831 y(Index:)43 b(0)g(0)g(0)h(0)230 930 y(Weight:)21
b(1)65 b(Value:)20 b(7.771561e-16)42 b(||)21 b(Addresses:)f(184296)g
(184560)h(193136)f(:)i(184512)230 980 y(Index:)43 b(0)g(0)g(0)h(1)230
1080 y(Weight:)21 b(1)65 b(Value:)20 b(1.110223e-16)42
b(||)21 b(Addresses:)f(184560)g(193136)h(191528)f(:)i(184584)230
1130 y(Index:)43 b(0)g(0)g(1)h(0)230 1229 y(Weight:)21
b(1)65 b(Value:)20 b(-1.332268e-15)41 b(||)22 b(Addresses:)d(193136)i
(191528)g(191648)f(:)i(193160)230 1279 y(Index:)43 b(0)g(1)g(0)h(0)230
1379 y(Weight:)21 b(1)65 b(Value:)20 b(-3.774758e-15)41
b(||)22 b(Addresses:)d(191528)i(191648)g(190592)f(:)i(191552)230
1428 y(Index:)43 b(1)g(0)g(0)h(0)0 1511 y Fi(Commen)o(t)15
b(1:)33 b Fn(The)15 b(D)o(A)e(header)j(\014le,)d(mxyzptlk.rsc,)g(m)o
(ust)g(b)q(e)i(included)f(at)g(the)h(top)f(of)g(an)o(y)f(application)g
(program.)0 1561 y(This)h(form)e(of)h(the)i(statemen)o(t)e(assumes,)h
(of)f(course,)i(that)f(it)f(is)h(lo)q(cated)g(in)g(the)g(same)f
(directory)i(as)f(the)g(program.)0 1636 y Fi(Commen)o(t)i(2:)35
b Fn(W)m(e)15 b(assume)f(a)h(four)f(dimensional)f(phase)i(space)h(with)
f(no)g(con)o(trol)f(sector.)23 b(Only)14 b(terms)h(up)g(through)0
1686 y(w)o(eigh)o(t)c(3)f(are)i(to)f(b)q(e)g(k)o(ept.)18
b(The)11 b(default)g(reference)j(is)c(set)i(at)f(a)g(rather)h(un)o
(usual)f(lo)q(cation)f(just)h(for)g(illustrativ)o(e)f(purp)q(oses.)0
1735 y(W)m(e)j(c)o(ho)q(ose)i(to)f(in)o(v)o(ok)o(e)f
Fi(D)o(ASetup)e Fn(b)q(efore)k(declaring)e(D)o(A)h(v)n(ariables,)e(but)
i(as)g(explained)g(in)f(Section)i(2.1,)d(this)i(is)f(not)h(a)0
1785 y(restriction.)0 1860 y Fi(Commen)o(t)g(3:)33 b
Fn(These)15 b(four)f(statemen)o(ts)g(initialize)e(the)j(calculation)d
(b)o(y)i(establishing)g(co)q(ordinates.)0 1935 y Fi(Commen)o(t)i(4:)37
b Fn(The)15 b(P)o(oisson)g(brac)o(k)o(et)h(is)f(computed)g(t)o(w)o(o)g
(w)o(a)o(ys:)20 b(\(1\))c(here,)g(using)f(the)h(binary)f(op)q(erator)g
Fk(^)37 b Fn(on)15 b(D)o(A)0 1984 y(v)n(ariables)d Fk(a)h
Fn(and)f Fk(b)h Fn(and)f(\(2\))h(b)q(elo)o(w,)f(for)h(comparison,)e
(using)h(its)h(algebraic)g(expansion)f(on)h(v)n(ariables)f(of)g(t)o(yp)
q(e)h(double.)0 2059 y Fi(Commen)o(t)f(5:)29 b Fn(This)12
b(third)f(calculation)g(emphasizes)h(that)g(D)o(A)f(metho)q(ds)g(and)h
(op)q(erators)h(w)o(ork)e(not)h(only)e(on)i(formally)0
2109 y(declared)19 b(D)o(A)f(v)n(ariables)f Fl(but)i(also)g(on)h(expr)n
(essions)f(which)f(evaluate)i(to)e(D)o(A)h(variables.)31
b Fn(It)18 b(is)g(carried)h(out)f(without)0 2159 y(in)o(tro)q(ducing)c
(auxiliary)e(v)n(ariables,)g(suc)o(h)j(as)f Fk(a)p Fn(,)f
Fk(b)p Fn(,)g(or)h Fk(pb)p Fn(.)0 2234 y Fi(Commen)o(t)20
b(6:)46 b Fn(The)19 b(extra)g(paren)o(theses)h(mak)o(e)d(certain)i
(that)g(ev)o(erything)g(gets)g(ev)n(aluated)f(in)g(the)h(prop)q(er)h
(order.)0 2283 y(Not)13 b(only)f(is)h(the)h(P)o(oisson)e(brac)o(k)o(et)
i(op)q(eration)f(non-asso)q(ciativ)o(e)g(\(and)g(non-comm)o(utati)o(v)o
(e\),)d(its)j(precedence)j(relativ)o(e)d(to)0 2333 y(addition)g(is)g
(am)o(biguous.)0 2408 y Fi(Commen)o(t)k(7:)38 b Fn(The)16
b(output)g(from)e(this)i(in)o(v)o(o)q(cation)f(of)g Fi(.p)q(eekA)o(t)g
Fn(sho)o(ws)h(that)g Fk(pb)f Fn(con)o(tains)h(35)f(links.)24
b(Only)15 b(those)954 2574 y(12)p eop
%%Page: 13 13
13 12 bop 0 307 a Fn(whose)20 b(w)o(eigh)o(ts)g(are)g(not)f(ab)q(o)o(v)
o(e)h(the)g(maxim)n(um)15 b(accurate)21 b(w)o(eigh)o(t)f(are)g(displa)o
(y)o(ed)f(here.)36 b(The)20 b(fact)g(that)g(the)g(rest)0
357 y(con)o(tin)o(ue)13 b(to)f(b)q(e)h(stored)g(is)f(a)g(\015a)o(w)g
(\(but)h(not)f(a)g(bug\))h(in)e(the)i(to)q(olkit)f(whic)o(h)g(will)f(b)
q(e)i(remo)o(v)o(ed)e(from)g(V)m(ersion)h(1.1.)17 b(By)12
b(the)0 407 y(Jacobi)g(iden)o(tit)o(y)m(,)f(all)h(links)f(of)h
Fk(pb)g Fn(should)g(store)h(a)g(zero,)g(whic)o(h)f(means)f(that)i(they)
g(should)f(not)g(b)q(e)h(presen)o(t,)h(since)f(zero)q(es)0
457 y(are)i(not)g(stored)h(b)q(ey)o(ond)f(the)g(standard)g(part.)21
b(Ho)o(w)o(ev)o(er,)15 b(b)q(ecause)i(of)d(n)o(umerical)g(roundo\013)g
(errors,)i(the)g(actual)e(v)n(alues)0 506 y(stored)g(are)g(on)f(the)h
(order)g(of)e(10)517 491 y Fd(\000)p Fm(15)578 506 y
Fn(.)18 b(A)13 b(second)h(impro)o(v)o(emen)o(t)d(in)h(the)i(to)q(olkit)
e(will)g(b)q(e)i(to)f(drop)g(all)f(results)j(of)d(addition)0
556 y(or)i(subtraction)g(whic)o(h)g(are)g(on)g(the)g(order)h(of)e(mac)o
(hine)g(accuracy)i(and)f(to)f(deallo)q(cate)h(the)h(corresp)q(onding)g
(links.)0 672 y Fe(3.2)56 b(Ev)m(aluation)0 749 y Fn(No)o(w)14
b(w)o(e)g(calculate)g Fh(e)g Fn(using)f(t)o(w)o(o)h(di\013eren)o(t)h(p)
q(o)o(w)o(er)f(series.)0 905 y Fk(#include)20 b(<std.h>)0
955 y(#include)g(<stdio.h>)0 1005 y(#include)g(<stream.h>)0
1054 y(#include)g("mxyzptlk.rsc")0 1154 y(main\(\))h({)0
1254 y(cout)g(<<)g("The)g(correct)g(result)f(is:)h(")h(<<)f(exp\()g
(1.0)g(\))h(<<)f("\\n\\n")0 1353 y(double)g(r[3];)0 1403
y(r[0])g(=)h(0.5;)0 1453 y(r[1])f(=)h(0.4;)0 1503 y(r[2])f(=)h(0.0;)0
1553 y(DASetup\()e(3,)i(7,)f(r)g(\);)262 b(//)21 b(**)g(SEE)h(COMMENT)e
(1)0 1652 y(DA)h(x,)h(y,)f(z;)0 1702 y(DA)g(u,)h(v;)0
1802 y(x.setVariable\(0\);)0 1851 y(y.setVariable\(1\);)0
1901 y(z.setVariable\(2\);)0 2001 y(u)g(=)f(exp\()g(x)h(\);)0
2051 y(v)g(=)f(exp\()g(x)h(+)f(y)h(+)f(z)h(\);)0 2150
y(double)f(s[3];)0 2200 y(r[0])g(=)h(1.0;)435 b(//)21
b(**)g(SEE)h(COMMENT)e(2)0 2250 y(r[1])h(=)h(0.0;)0 2300
y(r[2])f(=)h(0.0;)0 2350 y(s[0])f(=)h(0.33;)0 2399 y(s[1])f(=)h(0.33;)0
2449 y(s[2])f(=)h(1.0)f(-)g(s[0])g(-)h(s[1];)954 2574
y Fn(13)p eop
%%Page: 14 14
14 13 bop 0 357 a Fk(for\()21 b(int)g(w)h(=)f(1;)h(w)f(<=)h(7;)f(w++)g
(\))44 b(//)21 b(**)g(SEE)h(COMMENT)e(3)44 407 y(cout)h(<<)g(w)h(<<)f
(":)65 b(")21 b(<<)h(\(u.filter\()e(0,)h(w)h(\)\)\()f(r)g(\))262
457 y(<<)g(")87 b(")21 b(<<)h(\(v.filter\()e(0,)h(w)h(\)\)\()f(s)g(\))
262 506 y(<<)g("\\n";)0 556 y(})0 639 y Fi(Output:)230
665 y Fk(The)h(correct)e(result)g(is:)i(2.71828)230 764
y(1:)65 b(2.47308)f(2.70556)230 814 y(2:)h(2.67917)f(2.71786)230
864 y(3:)h(2.71352)f(2.71827)230 914 y(4:)h(2.71781)f(2.71828)230
964 y(5:)h(2.71824)f(2.71828)230 1013 y(6:)h(2.71828)f(2.71828)230
1063 y(7:)h(2.71828)f(2.71828)0 1148 y Fi(Commen)o(t)20
b(1:)48 b Fn(W)m(e)19 b(shall)f(expand)i(t)o(w)o(o)e(functions,)i
Fh(u)p Fn(\()p Fh(x;)7 b(y)q(;)g(z)r Fn(\))k(=)h(exp)q(\()p
Fh(x)p Fn(\))19 b(and)g Fh(v)q Fn(\()p Fh(x;)7 b(y)q(;)g(z)r
Fn(\))12 b(=)f(exp)q(\()p Fh(x)e Fn(+)g Fh(y)i Fn(+)f
Fh(z)r Fn(\))p Fh(;)19 b Fn(b)q(oth)0 1198 y(ab)q(out)14
b(the)h(p)q(oin)o(t)f(\()p Fh(x;)7 b(y)q(;)g(z)r Fn(\))k(=)h(\(0)p
Fh(:)p Fn(5)p Fh(;)7 b Fn(0)p Fh(:)p Fn(4)p Fh(;)g Fn(0)p
Fh(:)p Fn(0)o(\))p Fh(:)k Fn(The)k(problem)e(space)j(is)e(therefore)i
(three)f(dimensional.)i(W)m(e)d(shall)g(retain)0 1248
y(terms)g(only)f(up)h(to)f(degree)j(sev)o(en.)0 1323
y Fi(Commen)o(t)f(2:)34 b Fn(In)14 b(setting)h(the)g(p)q(oin)o(ts)g(of)
e(ev)n(aluation,)g Fl(the)j(applic)n(ation)f(pr)n(o)n(gr)n(am)g(ne)n(e)
n(d)h(not)f(r)n(ememb)n(er)g(or)g(explicitly)0 1372 y(r)n(efer)e(to)h
(the)g(r)n(efer)n(enc)n(e)f(p)n(oint)p Fn(:)18 b(the)c(D)o(A)f(v)n
(ariables)f(kno)o(w)h(themselv)o(es)g(where)h(they)g(w)o(ere)g(ev)n
(aluated.)j(\(In)c(fact,)g(w)o(e)g(ev)o(en)0 1422 y(could)h(ha)o(v)o(e)
f(expanded)i Fh(u)f Fn(and)f Fh(v)j Fn(ab)q(out)e(t)o(w)o(o)f
(di\013eren)o(t)i(reference)h(p)q(oin)o(ts.\))0 1497
y Fi(Commen)o(t)g(3:)35 b Fn(In)15 b(this)g(lo)q(op)f(w)o(e)h(\014lter)
g(D)o(A)g(v)n(ariables)f(of)g(v)n(arious)g(w)o(eigh)o(ts)h(up)g(to)g
(the)g(maxim)n(um)c(of)j(sev)o(en.)22 b(In)15 b(this)0
1547 y(w)o(a)o(y)d(w)o(e)i(can)f(follo)o(w)e(the)j(accuracy)g(of)e(the)
i(series)g(as)f(the)h(n)o(um)o(b)q(er)e(of)h(terms)g(increases.)19
b(The)14 b(reader)g(should)f(b)q(e)g(able)g(to)0 1597
y(explain)g(easily)h(the)g(greater)h(accuracy)g(of)e(one)h(series)h(o)o
(v)o(er)f(the)h(other,)f(as)g(sho)o(wn)g(in)f(the)i(output.)0
1713 y Fe(3.3)74 b(Concatenation)0 1789 y Fn(The)11 b(ob)r(ject)g(of)f
(this)g(exercise)j(is)d(to)g(compute)g(a)g(deriv)n(ativ)o(e)g(of)g(t)o
(w)o(o)g(functions)g(whic)o(h)h(ha)o(v)o(e)f(b)q(een)i(concatenated)f
(together.)0 1839 y(The)j(problem)f(space)i(is)f(t)o(w)o(o)f
(dimensional,)e Fh(w)p 718 1846 31 2 v 12 w Fn(=)h(\()p
Fh(x;)7 b(y)q Fn(\))p Fh(:)14 b Fn(Consider)g(the)h(t)o(w)o(o)e
(mappings,)641 1970 y Fh(a)p 641 1977 22 2 v Fn(\()p
Fh(w)p 679 1977 31 2 v 1 w Fn(\))42 b(=)842 1899 y Fb( )895
1930 y Fh(xy)940 1915 y Fm(2)969 1930 y Fn(+)9 b(exp)q(\()p
Fh(x)g Fn(+)g Fh(y)q Fn(\))973 1979 y(cos\()p Fh(y)q(x)1089
1964 y Fm(2)1109 1979 y Fn(\))p 973 1993 153 2 v 1001
2021 a Fh(x)g Fn(+)h(2)1223 1899 y Fb(!)1290 1970 y Fh(;)645
2116 y(b)p 645 2123 18 2 v Fn(\()p Fh(w)p 679 2123 31
2 v 1 w Fn(\))42 b(=)842 2045 y Fb( )895 2076 y Fn(sin)7
b Fh(x)g Fn(cos)g Fh(y)913 2125 y Fn(exp\()p Fh(x)1016
2110 y Fm(3)1035 2125 y Fn(\))p 913 2138 139 2 v 959
2162 a Fh(xy)1089 2045 y Fb(!)1156 2116 y Fh(;)0 2245
y Fn(and)14 b(their)g(concatenation,)827 2295 y Fh(c)p
827 2302 18 2 v -1 w Fn(\()p Fh(w)p 860 2302 31 2 v 1
w Fn(\))e(=)g Fh(b)p 963 2302 18 2 v Fn(\()p Fh(a)p 997
2302 22 2 v Fn(\()p Fh(w)p 1035 2302 31 2 v 1 w Fn(\)\))i
Fh(:)0 2369 y Fn(W)m(e)f(shall)h(calculate)g(b)q(oth)g(comp)q(onen)o
(ts)f(of)g Fh(@)739 2354 y Fm(5)758 2369 y Fh(c)p 758
2376 18 2 v(=@)r(x)845 2354 y Fm(3)864 2369 y Fh(@)r(y)909
2354 y Fm(2)929 2369 y Fg(j)941 2376 y Ff(w)p 941 2383
25 2 v Fm(=\(0)p Ff(;)p Fm(0\))1061 2369 y Fh(:)954 2574
y Fn(14)p eop
%%Page: 15 15
15 14 bop 0 307 a Fk(#include)20 b(<std.h>)0 357 y(#include)g
(<stdio.h>)0 407 y(#include)g("mxyzptlk.rsc")0 506 y(main\(\))h({)0
556 y(DA)g(x,)h(y,)f(u,)h(v,)f(c1,)g(c2;)0 606 y(LieOperator)f(a,)h(b,)
g(c;)0 656 y(int)g(index[2];)0 706 y(double)g(answer[2];)0
805 y(DASetup\()f(2,)i(7,)f(2)g(\);)262 b(//)21 b(**)g(SEE)h(COMMENT)e
(1)0 905 y(x.setVariable\(0\);)0 955 y(y.setVariable\(1\);)0
1054 y(u)i(=)f(x*y*y)g(+)h(exp\()e(x)i(+)g(y)f(\);)0
1104 y(v)h(=)f(cos\()g(y*x*x)g(\))g(/)h(\()g(x)f(+)h(2.0)f(\);)0
1204 y(printf\()f("Standard)g(part)h(of)h(u)f(is)h(\045lf\\n",)e
(u.standardPart\(\))e(\);)0 1254 y(printf\()i("Standard)g(part)h(of)h
(v)f(is)h(\045lf\\n",)e(v.standardPart\(\))e(\);)0 1353
y(a.setVariable\()h(u,)i(0)h(\);)196 b(//)21 b(**)g(SEE)h(COMMENT)e(2)0
1403 y(a.setVariable\()f(v,)i(1)h(\);)0 1503 y(DAFixReferenceAtE)o
(nd\()d(a)i(\);)131 b(//)21 b(**)g(SEE)h(COMMENT)e(3)0
1553 y(b.fixReference\(\);)302 b(//)21 b(**)g(SEE)h(COMMENT)e(4)0
1652 y(x.setVariable\(0\);)302 b(//)21 b(**)g(SEE)h(COMMENT)e(5)0
1702 y(y.setVariable\(1\);)0 1802 y(u)i(=)f(sin\(x\))g(*)g(cos\(y\);)
239 b(//)21 b(**)g(SEE)h(COMMENT)e(6)0 1851 y(v)i(=)f(exp\()g(x*x*x)g
(\))g(/)h(\()g(x*y)f(\);)0 1951 y(b.setVariable\()e(u,)i(0)h(\);)0
2001 y(b.setVariable\()d(v,)i(1)h(\);)0 2100 y(c)g(=)f(b*a;)501
b(//)21 b(**)g(SEE)h(COMMENT)e(7)0 2200 y(index[0])g(=)i(3;)0
2250 y(index[1])e(=)i(2;)0 2300 y(c.derivative\()d(index,)i(answer)f
(\);)0 2399 y(printf\()g("Zero:)h(\045lf\\n",)f(answer[0])g(\);)0
2449 y(printf\()g("One)h(:)h(\045lf\\n",)e(answer[1])g(\);)954
2574 y Fn(15)p eop
%%Page: 16 16
16 15 bop 0 307 a Fk(})0 387 y Fi(Output:)230 412 y Fk(Standard)21
b(part)f(of)i(u)f(is)h(1.000000)230 462 y(Standard)f(part)f(of)i(v)f
(is)h(0.500000)230 511 y(Zero:)f(-25.215473)230 561 y(One)h(:)f
(50880.799265)0 644 y Fi(Commen)o(t)15 b(1:)33 b Fn(F)m(or)14
b(v)n(ariet)o(y)m(,)e(I)i(ha)o(v)o(e)g(here)h(declared)h(the)e(D)o(A)g
(v)n(ariables)f Fl(b)n(efor)n(e)k Fn(in)o(v)o(oking)12
b Fi(D)o(ASetup)p Fn(.)k(As)f(long)e(as)h(it)0 694 y(is)g(in)o(v)o(ok)o
(ed)f(b)q(efore)h(using)g(the)h(v)n(ariables,)d(there)j(is)f(no)g
(problem)e(\(see)k(Section)e(2.1\).)0 769 y Fi(Commen)o(t)g(2:)32
b Fn(This)13 b(is)h(the)g(w)o(a)o(y)f(that)g(LieOp)q(erators)i(get)f
(initialized.)j(First)d(their)f(D)o(A)h(comp)q(onen)o(ts)f(are)h
(calculated)0 818 y(and)j(then)i(inserted)g(in)o(to)e(the)h(LieOp)q
(erator)h(using)e(the)h Fi(.setV)l(ariable)e Fn(metho)q(d.)28
b(The)18 b(in)o(teger)g(argumen)o(t)f(\014xes)h(the)0
868 y(comp)q(onen)o(t)12 b(asso)q(ciated)h(with)e(eac)o(h)i(prolonged)f
(n)o(um)o(b)q(er.)17 b(After)c Fk(u)f Fn(and)g Fk(v)g
Fn(are)h(loaded)e(in)o(to)h Fk(a)p Fn(,)g(the)h(connection)g(b)q(et)o
(w)o(een)0 918 y(them)g(is)h(brok)o(en,)g(and)f(the)i(program)d(is)i
(free)g(to)g(use)h(them)e(again.)62 968 y(In)f(fact,)g(w)o(e)g(do)g
(not)g(need)h(to)e(use)i Fk(u)f Fn(and)g Fk(v)f Fn(at)h(all;)f(lik)o(e)
g Fk(a)p Fn(,)h Fk(b)p Fn(,)f(and)h Fk(pb)f Fn(in)h(Example)e(3.1)h
(these)j(in)o(termediate)d(v)n(ariables)0 1018 y(only)i(serv)o(e)i(to)f
(separate)h(logical)d(steps)j(in)f(the)g(program,)e(making)g(it)h
(easier)i(to)e(read.)19 b(The)14 b(statemen)o(ts,)132
1084 y Fk(a.setVariable\()k(x*y*y)j(+)h(exp\()f(x)g(+)h(y)f(\),)174
b(0)22 b(\);)132 1133 y(a.setVariable\()c(cos\()j(y*x*x)g(\))h(/)f(\()h
(x)f(+)h(2.0)f(\),)43 b(1)22 b(\);)0 1201 y Fn(w)o(ould)13
b(ha)o(v)o(e)h(w)o(ork)o(ed)g(just)g(as)g(w)o(ell.)0
1275 y Fi(Commen)o(t)k(3:)40 b Fn(An)o(ticipating)16
b(concatenation,)h(w)o(e)g(c)o(hange)g(the)g(default)f(reference)j(to)e
(that)g(of)f(the)h(endp)q(oin)o(t)g(of)f Fk(a)p Fn(.)0
1325 y(That)e(is,)f(the)i(default)e(reference)j(here)f(gets)g(set)g(to)
f(\(1)p Fh(;)7 b Fn(0)p Fh(:)p Fn(5\))p Fh(;)k Fn(as)j(indicated)g(b)o
(y)g(the)g(output)h(of)e(the)h Fk(.standardPart)p Fn(.)0
1400 y Fi(Commen)o(t)g(4:)32 b Fn(The)14 b(reference)j(p)q(oin)o(t)c
(of)g Fk(b)g Fn(is)h(set)g(to)g(the)g(default)g(reference,)h(that)f
(is,)f(to)h(the)g(endp)q(oin)o(t)g(of)f Fk(a)p Fn(.)18
b(This)13 b(is)0 1450 y(precisely)i(what)f(is)f(needed)j(to)d
(concatenate)j Fk(b)d Fn(with)h Fk(a)p Fn(.)0 1524 y
Fi(Commen)o(t)h(5:)33 b Fn(The)15 b Fi(.setV)l(ariable)c
Fn(metho)q(d)j(needs)h(to)f(b)q(e)h(in)o(v)o(ok)o(ed)e(b)o(y)h
Fk(x)g Fn(and)g Fk(y)g Fn(again,)e(b)q(ecause)k(w)o(e)f(ha)o(v)o(e)f(c)
o(hanged)0 1574 y(the)g(reference)j(p)q(oin)o(t.)0 1649
y Fi(Commen)o(t)12 b(6:)28 b Fn(Notice)12 b(that)g(w)o(e)f(simply)f
(write)h(these)i(functions)f(as)f(they)h(ha)o(v)o(e)f(b)q(een)i
(de\014ned.)18 b(All)11 b(information)d(ab)q(out)0 1699
y(reference)15 b(p)q(oin)o(ts)d(has)g(b)q(een)h(absorb)q(ed)h(b)o(y)d
(the)i(v)n(ariables)f(themselv)o(es;)g(w)o(e)h(do)f(not)g(need)h(to)f
(use)h(it)f(explicitly)f(in)h(writing)0 1749 y(the)i(rest)h(of)d(the)i
(program.)i(The)e(reference)i(p)q(oin)o(ts)d(of)g Fk(x)g
Fn(and)g Fk(y)h Fn(w)o(ere)g(reset)h(b)o(y)e(the)h Fi(.setV)l(ariable)d
Fn(metho)q(d,)h(and)h(those)0 1798 y(of)g Fk(u)h Fn(and)g
Fk(v)f Fn(are)i Fl(automatic)n(al)r(ly)e Fn(adjusted)i(b)o(y)e(the)i(=)
f(op)q(erator.)0 1873 y Fi(Commen)o(t)i(7:)36 b Fn(And)15
b(here)h(is)f(the)h(concatenation)f(itself.)22 b(All)14
b(that)h(remains)f(is)h(to)g(access)i(and)e(prin)o(t)g(the)g(deriv)n
(ativ)o(e)0 1923 y(w)o(e)f(need.)19 b(Y)m(ou)13 b(are)i(in)o(vited)e
(to)h(con\014rm)f(at)h(y)o(our)f(leisure)i(that)f(the)g(computed)g(v)n
(alues)f(are)i(correct.)0 2059 y Fo(4)67 b(Status)0 2150
y Fn(A)13 b(pre-compiled)e(ob)r(ject)i(library)f(for)g(MXYZPTLK,)i(its)
e(source)i(co)q(de,)f(the)g(necessary)i(header)e(\014le,)g
(mxyzptlk.rsc,)e(and)0 2200 y(the)18 b(L)86 2195 y Fa(a)105
2200 y Fn(T)128 2213 y(E)151 2200 y(X\014le)g(pro)q(ducing)f(this)g(do)
q(cumen)o(t)g(are)h(all)e(con)o(tained)h(in)g(a)g(sub)q(directory)i(of)
d(/home/dip)q(ole/mi)o(c)o(helotti)e(on)0 2250 y(DIPOLE,)j(part)h(of)f
(the)h(BOFF)o(O-MYR)m(TLE-FLIBBER-DIPOLE-QUAD)h(domain)c(of)i(net)o(w)o
(ork)o(ed)h(SUNs)h(used)f(b)o(y)0 2300 y(the)f(Accelerator)h(Division)d
(/)h(Accelerator)i(Ph)o(ysics)f(group.)26 b(These)18
b(\014les)e(are)h(also)f(readable)h(from)d(the)k(V)-5
b(AX)17 b(cluster)0 2350 y(ALMOND,)11 b(but)g(the)g(curren)o(t)h(ob)r
(ject)g(library)e(is)h(for)f(the)i(SUN,)e(not)h(the)h(V)-5
b(AX;)11 b(b)o(y)f(the)i(time)d(this)i(do)q(cumen)o(t)f(is)h(released,)
0 2399 y(a)j(V)-5 b(AX)14 b(ob)r(ject)h(library)e(should)h(b)q(e)g(a)o
(v)n(ailable.)i(Since)e(Macin)o(tosh)g(C)1112 2395 y(++)1190
2399 y(exists,)g(the)h(source)g(co)q(de)g(should)e(b)q(e)i(p)q(ortable)
0 2449 y(without)f(m)o(uc)o(h)e(di\016cult)o(y)h(\(I)h(hop)q(e\))h(to)e
(the)i(Mac)f(I)q(I)g(as)g(w)o(ell.)954 2574 y(16)p eop
%%Page: 17 17
17 16 bop 62 307 a Fn(I)20 b(ha)o(v)o(e)g(tested)h(MXYZPTLK)g(using)f
(a)g(program)e(that)i(mimi)o(cs)e(the)j(b)q(eha)o(vior)e(of)h(a)f
(\(Hewlett-P)o(ac)o(k)n(ard\))i(RPN)0 357 y(calculator,)12
b(but)i(with)f(registers)h(con)o(taining)e(D)o(A)h(v)n(ariables)g
(rather)h(than)f(reals.)18 b(These)c(tests)h(ha)o(v)o(e)e(b)q(een,)h
(of)e(necessit)o(y)m(,)0 407 y(limited,)h(and)j(I)f(w)o(ould)g
(appreciate)h(hearing)f(from)f(an)o(y)o(one)h(in)o(terested)j(in)d
(helping)g(to)g(extend)i(them)d(or)i(who)f(w)o(an)o(t)g(to)0
457 y(use)i(the)g(D)o(A)f(and)g(LieOp)q(erator)h(classes)g(in)f(their)h
(o)o(wn)e(applications.)24 b(Source)18 b(co)q(de)f(is)f(also)f(a)o(v)n
(ailable)f(to)i(those)h(who)0 506 y(w)o(ould)c(lik)o(e)f(to)h(help)h
(expand)f(MXYZPTLK's)i(capabilities;)d(credit)i(will)e(b)q(e)i(giv)o
(en)f(in)f(the)i Fi(D)o(AAb)q(out)e Fn(and)h Fi(D)o(ANews)0
556 y Fn(functions)h(and)g(in)f(subsequen)o(t)j(v)o(ersions)e(of)f
(this)h(do)q(cumen)o(t)g(for)f(upgrades)i(written)f(b)o(y)g(others.)62
606 y(Those)22 b(who)e(w)o(an)o(t)h(to)f(use)i(MXYZPTLK)g(can)f
(request)h(the)g(\014les)f(through)g(MICHELOTTI@FNALAD,)g(AL-)0
656 y(MOND::MICHELOTTI,)15 b(or)h(\(708\))e(840)f(4956.)h(Please)j(let)
f(me)f(kno)o(w)h(of)f(y)o(our)h(exp)q(eriences,)i(esp)q(ecially)e(if)g
(y)o(ou)f(ha)o(v)o(e)0 706 y(problems,)d(disco)o(v)o(er)j(bugs,)e
(upgrade)i(the)f(source)h(co)q(de,)g(or)e(only)g(ha)o(v)o(e)h
(suggestions)h(for)e(impro)o(v)o(emen)o(ts.)62 756 y(W)m(e)h(shall)f
(end)h(this)g(note)g(with)g(a)g(list)f(of)g(upgrades)i(already)e(under)
i(dev)o(elopmen)o(t.)62 837 y Fg(\017)21 b Fn(As)c(already)g(men)o
(tioned,)g(the)h(functions)f Fi(p)q(o)o(w)g Fn(and)g
Fi(log)f Fn(will)g(b)q(e)i(a)o(v)n(ailable)d(in)h(V)m(ersion)i(1.1)e
(of)g(MXYZPTLK,)104 887 y(whic)o(h)e(should)f(b)q(e)i(\014nished)f(b)o
(y)g(the)g(time)f(this)h(note)g(is)g(distributed.)62
970 y Fg(\017)21 b Fn(Links)d(whose)h(computed)f(v)n(alues)h(are)g
(small)d(enough)j(to)f(b)q(e)h(considered)h(zero)g(to)e(mac)o(hine)g
(accuracy)h(will)e(b)q(e)104 1019 y(deallo)q(cated,)d(as)h(will)e
(those)j(whose)f(w)o(eigh)o(ts)g(are)g(higher)g(than)f(the)i(maxim)n
(um)10 b(accurate)16 b(w)o(eigh)o(t)e(after)h(a)g(di\013er-)104
1069 y(en)o(tiation.)62 1152 y Fg(\017)21 b Fn(The)13
b(requiremen)o(t)g(that)f(all)g(D)o(A)g(v)n(ariables)g(p)q(ossess)j
(the)e(same)f(problem)f(space)j(will)d(b)q(e)j(relaxed.)k(Using)12
b(m)o(ultiple)104 1201 y(calls)e(to)g(a)g(new)h Fi(D)o(ASetup)c
Fn(function,)j(w)o(e)h(should)f(b)q(e)h(able)f(to)g(use)h(v)n(ariables)
f(corresp)q(onding)h(to)f(di\013eren)o(t)h(problem)104
1251 y(spaces,)16 b(with)f(di\013eren)o(t)h(dimensions,)d(in)i(the)g
(same)f(program.)20 b(Of)15 b(course,)h(D)o(A)e(op)q(erations)i(will)d
(automatically)104 1301 y(protect)i(against)e(unallo)o(w)o(ed)g
(mixtures.)62 1384 y Fg(\017)21 b Fn(There)16 b(is)f(no)g(need)h(for)f
(D)o(A)g(v)n(ariables)f(to)h(mo)q(del)f(prolongations)f(of)i(real-v)n
(alued)f(functions)i(only)m(.)k(The)c(concept)104 1433
y(can)e(b)q(e)g(extended)i(naturally)d(to)g(functions)h(of)g(complex)e
(v)n(ariables.)62 1516 y Fg(\017)21 b Fn(A)12 b Fi(.T)l(eX)h
Fn(metho)q(d)e(will)g(write)h(a)g(L)634 1511 y Fa(a)653
1516 y Fn(T)676 1528 y(E)699 1516 y(Xexpression)i(whic)o(h)e(is)g(the)h
(m)o(ultinom)o(ia)o(l)c(represen)o(tation)14 b(of)d(a)h(D)o(A)g(v)n
(ariable)104 1566 y(in)h(terms)h(of)f(user-sp)q(eci\014ed)k(sym)o(b)q
(ols.)62 1648 y Fg(\017)k Fn(When)12 b(the)g(D)o(A)g(v)n(ariable)e(is)i
(supp)q(osed)h(to)f(represen)o(t)i(a)d(symplectic)g(mapping)f(on)h(the)
i(phase)f(space)h(of)e(a)h(Hamilto-)104 1698 y(nian)g(system,)h(the)g
(symplectic)g(condition)f(can)h(b)q(e)h(enforced)g(either)g(at)f(ev)o
(ery)g(stage)h(of)e(a)h(computation)e(or)i(under)104
1748 y(the)h(direct)h(con)o(trol)f(of)f(the)h(application)f(program)f
(using)i(a)f Fi(.symplectify)f Fn(metho)q(d.)62 1830
y Fg(\017)21 b Fn(One)15 b(imp)q(ortan)o(t)d(goal)h(is)h(to)g(compile)f
(a)g(library)h(of)f(user-friendly)i(C)1210 1826 y(++)1289
1830 y(functions,)f(b)q(eginning)f(with)h(those)h(that)104
1880 y(\014nd)10 b(p)q(erio)q(dic)g(orbits)f(of)h(a)f(Hamiltonian)e
(system)i(and)h(reduce)h(it)e(to)h(normal)d(form)h(in)i(their)g
(vicinities,)f(as)h(describ)q(ed)104 1930 y(in)16 b(Reference)i([6)o
(].)25 b(It)17 b(w)o(ould)f(b)q(e)h(w)o(orth)o(while)e(to)i(do)f(this)g
(in)g(the)i(neigh)o(b)q(orho)q(o)q(ds)e(of)g(resonan)o(t)h(orbits)g(as)
f(w)o(ell,)104 1979 y(but)d(\014nding)f(those)i(orbits)f(is)g(a)g(more)
f(di\016cult)g(task,)h(requiring)f(an)h(in)o(terpla)o(y)f(b)q(et)o(w)o
(een)j(mapping,)10 b(analysis,)i(and)104 2029 y(p)q(erhaps)j(ev)o(en)f
(graphics.[8)o(])698 2317 y Fp(A)o(CKNO)o(WLEDGEMENT)62
2399 y Fn(I)h(am)f(indebted)h(to)g(Herb)q(ert)i(Wilf)c(for)i(a)g(stim)o
(ulating)d(discussion)k(of)e(his)h(ranking)f(algorithm)e([14)o(,)j(15)o
(,)g(9])f(whic)o(h)h(is)0 2449 y(at)f(the)g(core)h(of)e(ev)n(aluation)g
(and)g(concatenation.)954 2574 y(17)p eop
%%Page: 18 18
18 17 bop 0 307 a Fo(References)21 398 y Fn([1])19 b(Rob)q(ert)f(L.)e
(Anderson)i(and)f(Nail)f(H.)h(Ibragimo)o(v.)25 b Fl(Lie-B\177)-21
b(acklund)19 b(T)m(r)n(ansformations)d(in)i(Applic)n(ations)p
Fn(.)28 b(So)q(ciet)o(y)85 448 y(for)16 b(Industrial)g(and)g(Applied)g
(Mathematics,)f(Philadelphia,)g(P)o(ennsylv)n(ania,)g(1979.)24
b(SIAM)16 b(Studies)h(in)e(Applied)85 498 y(Mathematics.)21
581 y([2])k(M.)e(Berz.)28 b(Di\013eren)o(tial)16 b(algebra)h({)f(a)h
(new)g(to)q(ol.)26 b(In)17 b(Flo)o(yd)f(Bennett)i(and)f(Jo)o(yce)g
(Kopta,)g(editors,)h Fl(Pr)n(o)n(c)n(e)n(e)n(dings)85
631 y(of)f(the)g(1989)g(IEEE)h(Particle)d(A)n(c)n(c)n(eler)n(ator)h
(Confer)n(enc)n(e)p Fn(.)f(IEEE,)h(Marc)o(h)h(20-23,)d(1989.)23
b(IEEE)17 b(Catalog)d(Num)o(b)q(er)85 680 y(89CH2669-0.)21
763 y([3])19 b(Martin)14 b(Berz.)19 b Fl(Nucle)n(ar)c(Instruments)g
(and)g(Metho)n(ds)p Fn(,)f(A258:431,)e(1987.)21 846 y([4])19
b(Martin)13 b(Berz.)19 b(Di\013eren)o(tial)12 b(algebraic)h
(description)g(of)g(b)q(eam)f(dynamics)g(to)h(v)o(ery)g(high)g(orders.)
18 b Fl(Particle)13 b(A)n(c)n(c)n(eler-)85 896 y(ators)p
Fn(,)g(24\(2\),)g(Marc)o(h)i(1989.)i(to)c(b)q(e)i(published.)21
979 y([5])k(Bruce)d(Ec)o(k)o(el.)i Fl(Using)d(C)479 975
y(++)557 979 y Fn(.)j(Osb)q(orne)d(McGra)o(w-Hill,)d(Berk)o(eley)m(,)i
(1989.)21 1062 y([6])19 b(Etienne)c(F)m(orest,)f(Martin)g(Berz,)g(and)g
(John)g(Irwin.)k(Normal)12 b(form)g(metho)q(ds)h(for)h(complicated)e(p)
q(erio)q(dic)i(systems:)85 1112 y(A)k(complete)f(solution)g(using)g
(di\013eren)o(tial)h(algebra)f(and)g(lie)h(op)q(erators.)30
b Fl(Particle)17 b(A)n(c)n(c)n(eler)n(ators)p Fn(,)g(24\(2\),)h(Marc)o
(h)85 1162 y(1989.)f(T)m(o)c(b)q(e)i(published.)21 1245
y([7])k(Leo)g(Mic)o(helotti.)31 b(Di\013eren)o(tial)18
b(algebras)g(without)h(di\013eren)o(tials:)27 b(an)18
b(easy)h(C)1381 1241 y(++)1464 1245 y(implemen)o(tation.)28
b(In)19 b(Flo)o(yd)85 1295 y(Bennett)13 b(and)d(Jo)o(yce)i(Kopta,)f
(editors,)g Fl(Pr)n(o)n(c)n(e)n(e)n(dings)h(of)g(the)g(1989)g(IEEE)h
(Particle)e(A)n(c)n(c)n(eler)n(ator)g(Confer)n(enc)n(e)p
Fn(.)f(IEEE,)85 1345 y(Marc)o(h)15 b(20-23,)d(1989.)17
b(IEEE)d(Catalog)f(Num)o(b)q(er)g(89CH2669-0.)21 1428
y([8])19 b(Leo)e(Mic)o(helotti.)27 b(Exploratory)17 b(orbit)f
(analysis.)27 b(In)17 b(Flo)o(yd)f(Bennett)j(and)d(Jo)o(yce)i(Kopta,)f
(editors,)h Fl(Pr)n(o)n(c)n(e)n(e)n(dings)85 1477 y(of)f(the)g(1989)g
(IEEE)h(Particle)d(A)n(c)n(c)n(eler)n(ator)h(Confer)n(enc)n(e)p
Fn(.)f(IEEE,)h(Marc)o(h)h(20-23,)d(1989.)23 b(IEEE)17
b(Catalog)d(Num)o(b)q(er)85 1527 y(89CH2669-0.)21 1610
y([9])19 b(Alb)q(ert)c(Nijenh)o(uis)e(and)h(Herb)q(ert)i(S.)d(Wilf.)k
Fl(Combinatorial)d(A)o(lgorithms)p Fn(.)j(Academic)c(Press,)i(New)f(Y)m
(ork,)f(1978.)0 1693 y([10])19 b(L.)f(B.)h(Rall.)30 b(Automatic)17
b(di\013eren)o(tiation:)28 b(T)m(ec)o(hniques)19 b(and)f(applications.)
31 b(In)19 b Fl(L)n(e)n(ctur)n(e)g(Notes)g(in)g(Computer)85
1743 y(Scienc)n(e)d(No.)e(120)p Fn(.)h(Springer-V)m(erlag,)e(1981.)0
1826 y([11])19 b(L.)14 b(B.)f(Rall.)k(The)d(arithmetic)f(of)g
(di\013eren)o(tiation.)18 b Fl(Mathematics)d(Magazine)p
Fn(,)f(59:275{282,)d(1986.)0 1909 y([12])19 b(Bjarne)14
b(Stroustrup.)19 b Fl(The)14 b(C)557 1905 y(++)635 1909
y(Pr)n(o)n(gr)n(amming)g(L)n(anguage)p Fn(.)k(Addison-W)m(esley)m(,)12
b(Reading,)g(Massac)o(h)o(usetts,)j(1986.)0 1992 y([13])k(Ro)o(y)g
(Thatc)o(her.)36 b(Programming)16 b(in)j(C)h(-)f(a)g(w)o(ord)h(of)f
(caution.)35 b(F)m(ermilab)17 b(Computing)h(Division)g(Newsletter,)85
2042 y(V)m(ol.)13 b(XVI)q(I)q(I,)h(No.)f(1,)g(pp.)g(3-4,)g(Jan-F)m(eb)h
(1990.)0 2125 y([14])19 b(Herb)q(ert)f(S.)c(Wilf.)21
b(A)16 b(uni\014ed)f(setting)h(for)f(sequencing,)h(ranking,)f(and)g
(selection)h(algorithms)d(for)i(com)o(binatorial)85 2175
y(ob)r(jects.)k Fl(A)n(dvanc)n(es)d(in)f(Mathematics)p
Fn(,)f(24:281{291,)c(1977.)0 2258 y([15])19 b(Herb)q(ert)c(S.)d(Wilf.)j
(A)d(uni\014ed)h(setting)g(for)g(selection)g(algorithms)e(\(I)q(I\).)16
b Fl(A)o(nnals)e(of)g(Discr)n(ete)f(Mathematics)p Fn(,)g(2:135{)85
2308 y(148,)g(1978.)954 2574 y(18)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
End of mxyzptlk.ps
echo ad.ps 1>&2
cat >ad.ps <<'End of ad.ps'
%!PS-Adobe-2.0
%%Creator: dvips, version 5.392 (C) 1986-90 Radical Eye Software
%%Title: ad.dvi
%%Pages: 4 1
%%BoundingBox: 0 0 612 792
%%EndComments
%%BeginProcSet: tex.pro
/TeXDict 200 dict def TeXDict begin /N /def load def /B{bind def}N /S /exch
load def /X{S N}B /TR /translate load N /isls false N /vsize 10 N /@rigin{
isls{[0 1 -1 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
Resolution VResolution vsize neg mul TR}B /@letter{/vsize 10 N}B /@landscape{
/isls true N /vsize -1 N}B /@a4{/vsize 10.6929133858 N}B /@legal{/vsize 13 N}
B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[
1 0 0 -1 0 0]N /FBB[0 0 0 0]N /df{/sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf
X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /df-tail{/nn 8 dict N nn begin
/FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array
/BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2
array copy cvx N load 0 nn put /ctr 0 N[}B /E{pop nn dup definefont setfont}B
/ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B
/ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub
get}B /ch-xoff{128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup
length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ctr 0 N
/CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get
/ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width
add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub
ch-yoff .1 add]{ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{
]}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1
sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D}B
/bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto}B /eop{
clear SI restore showpage userdict /eop-hook known{eop-hook}if}B /@start{
userdict /start-hook known{start-hook}if /VResolution X /Resolution X 1000 div
/DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for}
B /p /show load N /RMat[1 0 0 -1 -.1 -.1]N /BDot 8 string N /v{/ruley X /rulex
X V}B /V{gsave TR rulex ruley false RMat{BDot}imagemask grestore}B /a{moveto}
B /delta 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p
tail}B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{
3 M}B /k{4 M}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{p 1 w}B /r{
p 2 w}B /s{p 3 w}B /t{p 4 w}B /w{0 rmoveto}B /x{0 S rmoveto}B /y{3 2 roll p a}
B /bos{/SS save N}B /eos{clear SS restore}B end
%%EndProcSet
%%BeginProcSet: special.pro
TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N /vs
792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP false N /BBcalc false N
}B /@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit div
/vsc X}B /@hsize{/hs X /CLIP true N}B /@vsize{/vs X /CLIP true N}B /@hoffset{
/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{10 div /rwi X}B /@llx{/llx X}
B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X /BBcalc true N}B /magscale true
def end /@MacSetUp{userdict /md known{userdict /md get type /dicttype eq{md
begin /letter{}N /note{}N /legal{}N /od{txpose 1 0 mtx defaultmatrix
dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{
transform{itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2
roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
curveto}}{{closepath}}pathforall newpath counttomark array astore /gc xdf pop
ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N
/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}
if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get
neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S
neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip
not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1
scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get
neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop
pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR
pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{
ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale
neg S neg S TR}if}N /cp{pop pop showpage pm restore}N end}if}if}N /normalscale
{Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale}if}
N /psfts{S 65536 div N}N /startTexFig{/psf$SavedState save N userdict
maxlength dict begin /magscale false def normalscale currentpoint TR /psf$ury
psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts /psf$x psfts
currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx psf$llx sub div N
/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div
psf$llx sub psf$cy psf$sy div psf$ury sub TR /showpage{}N /erasepage{}N
/copypage{}N @MacSetUp}N /doclip{psf$llx psf$lly psf$urx psf$ury currentpoint
6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto
closepath clip newpath moveto}N /endTexFig{end psf$SavedState restore}N
/@beginspecial{SDict begin /SpecialSave save N gsave normalscale currentpoint
TR @SpecialDefaults}B /@setspecial{CLIP{newpath 0 0 moveto hs 0 rlineto 0 vs
rlineto hs neg 0 rlineto closepath clip}{initclip}ifelse ho vo TR hsc vsc
scale ang rotate BBcalc{rwi urx llx sub div dup scale llx neg lly neg TR}if
/showpage{}N /erasepage{}N /copypage{}N newpath}B /@endspecial{grestore clear
SpecialSave restore end}B /@defspecial{SDict begin}B /@fedspecial{end}B /li{
lineto}B /rl{rlineto}B /rc{rcurveto}B /np{/SaveX currentpoint /SaveY X N 1
setlinecap newpath}B /st{stroke SaveX SaveY moveto}B /fil{fill SaveX SaveY
moveto}B /ellipse{/endangle X /startangle X /yrad X /xrad X /savematrix matrix
currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix
setmatrix}B end
%%EndProcSet
TeXDict begin 1000 300 300 @start /Fa 2 69 df<70F8F8F87005057D840B>46
D<FFFFC000FFFFF0000F80FC000F803E000F801F000F800F000F8007800F8007800F8007C00F80
07C00F8007C00F8007C00F8007C00F8007C00F8007C00F8007800F8007800F800F800F800F000F
803E000F80FC00FFFFF800FFFFC0001A177E961F>68 D E /Fb 2 69 df<78FCFCFCFC7806067D
850D>46 D<FFFFF800FFFFFF000FC01FC00FC007E00FC001F00FC001F80FC000F80FC000FC0FC0
007C0FC0007C0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0FC0007E0F
C0007C0FC0007C0FC0007C0FC000F80FC000F80FC001F00FC007E00FC01FC0FFFFFF00FFFFF800
1F1C7E9B25>68 D E /Fc 4 121 df<60F0F06004047D830A>58 D<C00000F000003C00000E00
0003800001E000007800001E000007000001C00000F00000F00001C0000700001E0000780001E0
000380000E00003C0000F00000C0000014167D921B>62 D<383C1E0044C6630047028100460301
008E0703000C0603000C0603000C060600180C0600180C0620180C0C20180C0C40301804403018
07801B0E7F8D1F>109 D<0F1F0011A18020C38020C30041800001800001800001800003000003
0200C30200E70400C5080078F000110E7F8D14>120 D E /Fd 65 126 df<C060E0E0E0E0E0E0
E0E0C060C060C060C060C06040400B0B7C9614>34 D<071C00071C00071C00071C00071C007FFF
00FFFF80FFFF800E38000E38000E38000E38000E38000E38000E3800FFFF80FFFF807FFF001C70
001C70001C70001C70001C700011177F9614>I<3806007C0E006C0E00EE1C00EE1C00EE3800EE
38006C38007C700038700000700000E00000E00001C00001C00001C00003800003800007000007
0E00071F000E1B000E3B800E3B801C3B801C3B80381B00381F00180E00111D7F9914>37
D<0700000F800018C00038E00038E00038E00038C00039CF80398F801F1C001E1C001E38001E38
001E38003F7000677000E3F000E3E000E1E380E1E38073F3803F3F001E1E0011177F9614>I<00
C001C0030006000C001C0038003000700070006000E000E000E000E000E000E000E00060007000
7000300038001C000C000600030001C000C00A1D7A9914>40 D<8000C0006000300018001C000E
000600070007000300038003800380038003800380038003000700070006000E001C0018003000
6000C0008000091D7C9914>I<038003800380638CF39EFFFE3FF80FE00FE03FF8FFFEF39E638C
0380038003800F107E9214>I<01C00001C00001C00001C00001C00001C00001C000FFFF80FFFF
80FFFF8001C00001C00001C00001C00001C00001C00001C00011117F9314>I<70F8FCFC7C0C18
30E0C0060A798414>I<FFFEFFFEFFFE0F037E8C14>I<70F8F8F8700505798414>I<0006000E00
0E001C001C003800380070007000E000E001C001C0038003800380070007000E000E001C001C00
3800380070007000E000E000C0000F1D7E9914>I<07C00FE01C7038383018701C701CE00EE00E
E00EE00EE00EE00EE00EE00EE00E701C701C383838381C700FE007C00F177E9614>I<03000300
07000F003F00F7004700070007000700070007000700070007000700070007000700070007007F
F07FF00C177C9614>I<0FC01FF03838701CE00EE00EE00E400E000E001C001C00380030007000
E001C0030006000C00180E300E7FFE7FFE0F177E9614>I<0FC01FF03838701C701C201C001C00
1C0038007007E007F00038001C000E000E400EE00EE00E701C78383FF00FC00F177E9614>I<00
780000F80001B80001B8000338000338000638000E38000C38001C3800383800303800703800E0
3800FFFF80FFFF8000380000380000380000380000380001FF0001FF0011177F9614>I<3FFC7F
FC700070007000700070007000700077C07FF07838201C000C000E000E400EE00EE01C601C7878
3FF00FC00F177E9614>I<01F007F80E1C1C1C381C300070007000E000E7C0EFF0F838F01CF00C
E00EE00E600E700E700C381C1C380FF007C00F177E9614>I<E000FFFEFFFEE01CE03800300070
00E000C001C001800380038007000700070007000E000E000E000E000E000E0004000F187E9714
>I<0FE03FF8783C701CE00EE00EE00EE00E701C1EF003801FF03838701CE00EE00EE00EE00EF0
1E701C38381FF007C00F177E9614>I<07C01FE038307038601CE01CE00CE00EE00E601E701E38
3E1FEE07CE000E001C001C001C7038707070E03FC01F000F177E9614>I<70F8F8F87000000000
000060F0F8F878183070E0800515798F14>59 D<000E003E007C00F003E007C01F003E00F800F0
00F8003E001F0007C003E000F0007C003E000E0F137E9414>I<FFFF80FFFF807FFF8000000000
00000000007FFF80FFFF80FFFF8011097F8F14>I<01C00003E00003E000036000036000077000
0770000770000770000630000E38000E38000E38000E38000E38001FFC001FFC001C1C001C1C00
3C1E00380E00FE3F80FE3F8011177F9614>65 D<03C60FFE1C3E181E381E700E700E600EE000E0
00E000E000E000E000E000600E700E700E380C181C1C380FF003C00F177E9614>67
D<FFE000FFF800383C00381E00380E003807003807003807003803803803803803803803803803
80380380380380380380380700380700380E00381E00383C00FFF800FFE00011177F9614>I<FF
FF00FFFF003807003807003807003807003800003800003870003870003FF0003FF00038700038
7000380000380000380000380380380380380380380380FFFF80FFFF8011177F9614>I<FFFFFF
FF380738073807380738003800387038703FF03FF0387038703800380038003800380038003800
FF00FF0010177E9614>I<03C60FFE1C3E181E381E700E700E600EE000E000E000E000E07FE07F
E00E600E700E700E381E181E1C3E0FFE03CE10177F9614>I<FFF0FFFC381E380E380738073807
38073807380E381E3FFC3FF038003800380038003800380038003800FE00FE0010177F9614>80
D<0FCC1FFC307C603CE01CE01CE01CE00070007E003FE00FF001F8001C001E000E600EE00EE00E
F01CF838FFF0C7E00F177E9614>83 D<FC1F80FC1F807007007007007007007007007007007007
0030060031C6003BEE003BEE003B6E003B6E003B6E003B6E003B6E001B6C001B6C001A2C001E3C
001E3C001E3C0011177F9614>87 D<FFE0FFE0E000E000E000E000E000E000E000E000E000E000
E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000FFE0FFE00B1D799914
>91 D<C000E000E00070007000380038001C001C000E000E000700070003800380038001C001C0
00E000E00070007000380038001C001C000E000E00060F1D7E9914>I<FFE0FFE000E000E000E0
00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000
E000E000E0FFE0FFE00B1D7F9914>I<1FC0007FF000707800201800001C00001C0007FC001FFC
003C1C00701C00E01C00E01C00E01C00707C003FFF800F8F8011107E8F14>97
D<FC0000FC00001C00001C00001C00001C00001C00001CF8001DFE001F07001E03001C03801C01
C01C01C01C01C01C01C01C01C01C01C01C03801E03001F0E001DFC000CF8001217809614>I<03
F80FFC1C1C380870006000E000E000E000E00060007000380E1C1E0FFC03F00F107E8F14>I<00
7E00007E00000E00000E00000E00000E00000E0007CE000FFE001C3E00301E00700E00E00E00E0
0E00E00E00E00E00E00E00E00E00700E00301E00383E001FEFC007CFC012177F9614>I<07E00F
F01C38301C700CE00EE00EFFFEFFFEE00060007000380E1C1E0FFC03F00F107E8F14>I<007C00
FE01CE03840380038003807FFEFFFE038003800380038003800380038003800380038003800380
7FFC7FFC0F177F9614>I<07CF001FFF80383B80301800701C00701C00701C003018003838003F
F00037C0007000007000003FF8001FFC003FFE00700F00E00380E00380E00380E003807007003C
1E001FFC0007F00011197F8F14>I<FC0000FC00001C00001C00001C00001C00001C00001C7800
1DFE001F86001E07001C07001C07001C07001C07001C07001C07001C07001C07001C07001C0700
FF8FE0FF8FE01317809614>I<030007800780030000000000000000007F807F80038003800380
038003800380038003800380038003800380FFFCFFFC0E187D9714>I<006000F000F000600000
0000000000001FF01FF00070007000700070007000700070007000700070007000700070007000
7000700070007040E0E0C07F803F000C207E9714>I<FC0000FC00001C00001C00001C00001C00
001C00001DFF801DFF801C3C001C78001CF0001DE0001FC0001FC0001FE0001EF0001C70001C38
001C38001C1C00FE3F80FE3F8011177F9614>I<FF80FF80038003800380038003800380038003
8003800380038003800380038003800380038003800380FFFEFFFE0F177E9614>I<FB8E00FFDF
003CF3803CF38038E38038E38038E38038E38038E38038E38038E38038E38038E38038E380FEFB
E0FE79E01310808F14>I<FC7800FDFE001F86001E07001C07001C07001C07001C07001C07001C
07001C07001C07001C07001C0700FF8FE0FF8FE01310808F14>I<07C01FF03C78701C701CE00E
E00EE00EE00EE00EE00E701C783C3C781FF007C00F107E8F14>I<FCF800FDFE001F07001E0300
1C03801C01C01C01C01C01C01C01C01C01C01C01C01C03801E03001F0E001DFC001CF8001C0000
1C00001C00001C00001C00001C0000FF8000FF80001218808F14>I<03CE000FFE001C3E00301E
00700E00E00E00E00E00E00E00E00E00E00E00E00E00700E00301E001C3E000FEE0007CE00000E
00000E00000E00000E00000E00000E00007FC0007FC012187F8F14>I<FE1F00FE7F800EE3800F
81000F00000F00000E00000E00000E00000E00000E00000E00000E00000E0000FFF000FFF00011
107F8F14>I<0FD83FF86038C038C038F0007F803FF007F8001C6006E006F006F81CFFF8CFE00F
107E8F14>I<030007000700070007007FFCFFFC07000700070007000700070007000700070E07
0E070E070C03FC00F00F157F9414>I<FC3F00FC3F001C07001C07001C07001C07001C07001C07
001C07001C07001C07001C07001C07001C1F000FFFE003E7E01310808F14>I<FE3F80FE3F801C
1C001C1C001C1C001C1C000E38000E38000E380006300007700007700007700003E00003E00003
E00011107F8F14>I<FF7F80FF7F80380E00380E00380E00380E0039CE0039CE0019CC001B6C00
1B6C001A6C001A6C001E7C000E78000E780011107F8F14>I<7E3F007E3F001E38000E78000770
0007E00003E00001C00003C00003E0000770000E78000E38001C1C00FE3F80FE3F8011107F8F14
>I<FE3F80FE3F801C1C001C1C001C1C000E1C000E38000E380007380007300007300003700003
700001E00001E00001E00001C00001C00001C0000380007380007700007E00003C000011187F8F
14>I<3FFF7FFF700E701C7038007000E001C0038007000E001C0738077007FFFFFFFF10107F8F
14>I<003E00FE01E003800380038003800380038003800380038003807F00FE007F0003800380
0380038003800380038003800380038001E000FE003E0F1D7E9914>I<7800FE000F0003800380
0380038003800380038003800380038001FC00FE01FC0380038003800380038003800380038003
8003800F00FE0078000F1D7E9914>125 D E /Fe 49 123 df<0001FC3C00060E67000C0EC700
1C0DC6001C01C0003801C0003803800038038000380380003803800070038007FFFFF800700700
007007000070070000E0070000E00E0000E00E0000E00E0000E00E0001C00E0001C01C0001C01C
0001C01C0001C01C0003801C000380380003803800038038000300380007003000070070000600
6000C6606000E470C000C8618000703E00002025819C19>11 D<0001FC000703000C03001C0700
1C0300180000380000380000380000380000700007FFFC00701C00701C00701C00E03800E03800
E03800E03800E07001C07001C07001C07001C0E201C0E201C0E20380E403806403803803800003
0000070000060000C60000E40000CC00007000001825819C17>I<000300060008001800300060
00C000C0018003000300060006000C000C001C0018001800380030003000700070006000600060
006000E000E000E000E000E0006000600060006000600020003000100008000800102A7B9E11>
40 D<001000100008000C00040006000600060006000600070007000700070007000600060006
0006000E000E000C000C001C001800180038003000300060006000C000C001800300030006000C
00180010006000C000102A809E11>I<183878380808101020404080050C7D830D>44
D<FFC0FFC0FFC00A037D890F>I<3078F06005047C830D>I<00020006000C001C007C039C003800
3800380038007000700070007000E000E000E000E001C001C001C001C003800380038003800780
FFF00F1C7C9B15>49 D<003E0000C1800101800200C00400C00440C00841C00841C00841C00883
80070380000700000E0001F800003800000C00000C00000E00000E00000E00000E00700E00E01C
00801C0080380080300040600021C0001F0000121D7C9B15>51 D<001E00006100008180018080
0300C00300C006018006018006018007030007860003CC0003F00001F000037800063C00081E00
180E00300E00600600600600600600C00C00C00C00C0180060100060200030C0000F0000121D7C
9B15>56 D<003C0000C6000183000303000603000E03000C03801C03801C03001C030038070038
0700380700380F00380E00181E00181E000C6C00079C00001C00001800003800003000006000E0
C000E0C0008180008600007C0000111D7B9B15>I<060F0F06000000000000000000003078F060
08127C910D>I<0000180000001800000038000000380000007800000078000000B8000001B800
000138000002380000023C0000041C0000041C0000081C0000181C0000101C0000201C0000201C
00007FFC0000401C0000801C0001801C0001001C0002001C0002001C0004000E000C000E001C00
1E00FF00FFC01A1D7E9C1F>65 D<01FFFE00003C0780003803C0003801C0003801C0003801C000
7001C0007003C0007003C00070078000E0070000E00E0000E03C0000FFF80001C01C0001C00E00
01C00F0001C00F0003800F0003800F0003800F0003800F0007001E0007001C0007003C00070078
000E01E000FFFF80001A1C7D9B1D>I<0003F020001E0C60003002E000E003C001C001C0038001
C0070000C00E0000801E0000801C0000803C0000803C000000780000007800000078000000F000
0000F0000000F0000000F0000000F0000400F0000400F0000400F0000800700008007000100038
002000180040000C0180000706000001F800001B1E7A9C1E>I<01FFFE00003C0780003801C000
3801C0003800E0003800E0007000F00070007000700070007000F000E000F000E000F000E000F0
00E000F001C001E001C001E001C001E001C001C0038003C003800380038007800380070007000E
0007001C0007003800070070000E01C000FFFF00001C1C7D9B1F>I<01FFFFE0003C00E0003800
600038004000380040003800400070004000700040007020400070200000E0400000E0400000E0
C00000FFC00001C0800001C0800001C0800001C080000381010003800100038002000380020007
0004000700040007000C00070018000E007800FFFFF0001B1C7D9B1C>I<01FFC0003C00003800
00380000380000380000700000700000700000700000E00000E00000E00000E00001C00001C000
01C00001C0000380000380000380000380000700000700000700000700000F0000FFE000121C7E
9B10>73 D<01FE0007F8003E000780002E000F00002E001700002E001700002E002700004E002E
00004E004E00004E004E00004E008E00008E011C00008E011C00008E021C00008E021C00010704
380001070438000107083800010710380002071070000207207000020720700002074070000407
40E000040780E000040700E0000C0700E0001C0601E000FF861FFC00251C7D9B25>77
D<0007F000001C1C0000700E0000E0070001C0038003800380070003800E0003C01E0003C01C00
03C03C0003C03C0003C0780003C0780003C0780003C0F0000780F0000780F0000780F0000F00F0
000F00F0000E00F0001E00F0003C0070003800700070007800E0003801C0001C0380000E0E0000
03F800001A1E7A9C20>79 D<01FFFC00003C070000380380003801C0003801C0003801C0007003
C0007003C0007003C00070038000E0078000E0070000E00E0000E0380001FFE00001C0000001C0
000001C0000003800000038000000380000003800000070000000700000007000000070000000F
000000FFE000001A1C7D9B1C>I<000F8400304C00403C00801801001803001803001806001006
001006000007000007000003E00003FC0001FF00007F800007C00001C00001C00000C00000C020
00C02000C0600180600180600300600200F00400CC180083E000161E7D9C17>83
D<1FFFFFC01C0701C0300E00C0200E0080600E0080400E0080401C0080801C0080801C0080001C
0000003800000038000000380000003800000070000000700000007000000070000000E0000000
E0000000E0000000E0000001C0000001C0000001C0000001C0000003C000007FFE00001A1C799B
1E>I<FF83FF0FF03C007001C038007001803800F001003800F002003801700200380170040038
0270040038027008001C047008001C047010001C087010001C087020001C107020001C10704000
1C207040001C207080001C407180001C407100001C807200001D807200001D007400001E007400
001E007800001C007800001C00700000180070000018006000001000600000241D779B29>87
D<03CC063C0C3C181C3838303870387038E070E070E070E070E0E2C0E2C0E261E462643C380F12
7B9115>97 D<3F00070007000E000E000E000E001C001C001C001C0039C03E6038303830703870
3870387038E070E070E070E060E0E0C0C0C1C0618063003C000D1D7B9C13>I<01F007080C0818
1C3838300070007000E000E000E000E000E000E008E010602030C01F000E127B9113>I<001F80
000380000380000700000700000700000700000E00000E00000E00000E0003DC00063C000C3C00
181C00383800303800703800703800E07000E07000E07000E07000E0E200C0E200C0E20061E400
6264003C3800111D7B9C15>I<01E007100C1018083810701070607F80E000E000E000E000E000
E0086010602030C01F000D127B9113>I<0003C0000670000C70001C60001C00001C0000380000
380000380000380000380003FF8000700000700000700000700000700000E00000E00000E00000
E00000E00001C00001C00001C00001C00001C000038000038000038000030000030000070000C6
0000E60000CC00007800001425819C0D>I<00F3018F030F06070E0E0C0E1C0E1C0E381C381C38
1C381C383830383038187818F00F700070007000E000E0C0C0E1C0C3007E00101A7D9113>I<0F
C00001C00001C0000380000380000380000380000700000700000700000700000E78000E8C000F
0E000E0E001C0E001C0E001C0E001C0E00381C00381C00381C0038380070388070388070708070
7100E03200601C00111D7D9C15>I<01800380010000000000000000000000000000001C002600
470047008E008E000E001C001C001C0038003800710071007100720072003C00091C7C9B0D>I<
0FC00001C00001C0000380000380000380000380000700000700000700000700000E0F000E1100
0E23800E43801C83001C80001D00001E00003F800039C00038E00038E00070E20070E20070E200
70E400E06400603800111D7D9C13>107 D<1F800380038007000700070007000E000E000E000E
001C001C001C001C0038003800380038007000700070007000E400E400E400E40068003800091D
7C9C0B>I<3C1E0780266318C04683A0E04703C0E08E0380E08E0380E00E0380E00E0380E01C07
01C01C0701C01C0701C01C070380380E0388380E0388380E0708380E0710701C0320300C01C01D
127C9122>I<3C3C002646004687004707008E07008E07000E07000E07001C0E001C0E001C0E00
1C1C00381C40381C40383840383880701900300E0012127C9117>I<01E007180C0C180C380C30
0E700E700EE01CE01CE01CE018E038E030E06060C031801E000F127B9115>I<07870004D98008
E0C008E0C011C0E011C0E001C0E001C0E00381C00381C00381C003818007038007030007070007
06000E8C000E70000E00000E00001C00001C00001C00001C00003C0000FF8000131A7F9115>I<
03C4062C0C3C181C3838303870387038E070E070E070E070E0E0C0E0C0E061E063C03DC001C001
C0038003800380038007803FF00E1A7B9113>I<3C3C26C2468747078E068E000E000E001C001C
001C001C0038003800380038007000300010127C9112>I<01F006080C080C1C18181C001F001F
C00FF007F0007800386030E030C030806060C01F000E127D9111>I<00C001C001C001C0038003
8003800380FFE00700070007000E000E000E000E001C001C001C001C0038403840384038801900
0E000B1A7D990E>I<1E0300270700470700470700870E00870E000E0E000E0E001C1C001C1C00
1C1C001C1C003838803838801838801839001C5900078E0011127C9116>I<1E06270E470E4706
870287020E020E021C041C041C041C0818083808181018200C4007800F127C9113>I<1E018327
03874703874703838707018707010E07010E07011C0E021C0E021C0E021C0E04180C04181C0418
1C081C1C100C263007C3C018127C911C>I<070E0019910010E38020E38041C30041C00001C000
01C000038000038000038000038000070200670200E70400CB04008B080070F00011127D9113>
I<1E03270747074707870E870E0E0E0E0E1C1C1C1C1C1C1C1C38383838183818381C7007F00070
007000E0E0C0E1C0818047003C00101A7C9114>I<038207C20FEC083810080010002000400080
01000200040008081008383067F043E081C00F127D9111>I E /Ff 3 113
df<FEFEC0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
C0C0C0C0C0C0C0C0C0C0FEFE0731788111>2 D<FEFE0606060606060606060606060606060606
06060606060606060606060606060606060606060606060606060606FEFE07317F8111>I<0000
0000020000000006000000000C000000000C000000001800000000180000000030000000003000
00000060000000006000000000C000000000C00000000180000000018000000003000000000300
000000060000000006000000000C000000000C0000000018000000001800000000300000000030
00000000600008000060001C0000C0003C0000C000CE000180000E000180000E00030000070003
00000700060000038006000003800C000001C00C000001C018000001E018000000E030000000E0
300000007060000000706000000038C000000038C00000001D800000001D800000001F00000000
0F000000000E000000000600000027327C812A>112 D E /Fg 2 111 df<3E0006000C000C000C
000C001800187018B819383230340038003E006300631063106310C320C1C00D147E9312>107
D<30F8590C4E0C9C0C980C180C180C30183019303130316032601C100D7F8C15>110
D E /Fh 5 50 df<FFFFC0FFFFC012027D871A>0 D<040004000400C460E4E03F800E003F80E4
E0C4600400040004000B0D7E8D11>3 D<00000400000004000000020000000100FFFFFFE0FFFF
FFE0000001000000020000000400000004001B0A7E8B21>33 D<040E0E1C1C1C38383070706060
C0C0070F7F8F0A>48 D<0F001E003BC061806060804040310040801A0020800E0020800E002080
0E0020800B0020401180404020C0C030C07B800F001E001B0D7E8C21>I
E /Fi 6 107 df<FFFFFF80FFFFFF8019027D8A20>0 D<60F0F06004047C8B0C>I<07C000201F
E000203FF80020783C0060E01F00E0C00783C08003FF808000FF0080007C000000000007C00020
1FE000203FF80020783C0060E01F00E0C00783C08003FF808000FF0080007C001B137E9320>25
D<000000040000000002000000000200000000010000000000800000000040FFFFFFFFF8FFFFFF
FFF8000000004000000000800000000100000000020000000002000000000400250E7E902A>33
D<007FF801FFF80780000E0000180000300000300000600000600000C00000C00000C00000FFFF
F8FFFFF8C00000C00000C000006000006000003000003000001800000E000007800001FFF8007F
F8151A7D961C>50 D<C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
C0C0C0C0C0C0C0C0C0C0C002297B9E0C>106 D E /Fj 12 123 df<60F0F06004047C830C>58
D<60F0F0701010101020204080040C7C830C>I<0000038000000F0000003C000000F0000003C0
00000F0000003C000000F0000003C000000F0000003C000000F0000000F00000003C0000000F00
000003C0000000F00000003C0000000F00000003C0000000F00000003C0000000F000000038019
187D9520>I<003E0000C3000100800200C0030060078060078070030030000030000030000030
00FC700382700601700C01701800F03800E03000E07000E07001C0E001C0E001C0E00180E00380
E00300E00600E00600600C003018001860000F8000141F7E9D16>64 D<01FFFFF0003C00F00038
00300038002000380020003800200070002000700020007010200070100000E0200000E0200000
E0600000FFE00001C0400001C0400001C0400001C0400003808000038000000380000003800000
070000000700000007000000070000000F000000FFF000001C1C7E9B1B>70
D<01FFFE00003C03C0003800E0003800F00038007000380070007000F0007000F0007000F00070
01E000E001C000E0078000E01E0000FFF00001C0300001C0180001C01C0001C01C0003801C0003
801C0003801C0003801C0007003C0007003C0807003C0807003C100F001E10FFE00E20000007C0
1D1D7E9B20>82 D<0001E0000630000E78000CF0001C60001C00001C00001C00003C0000380000
380003FFC000380000380000700000700000700000700000700000E00000E00000E00000E00000
E00001C00001C00001C00001C00001C000018000038000038000630000F30000F60000E4000078
000015257E9C14>102 D<0FC00001C00001C00003800003800003800003800007000007000007
00000700000E07000E18800E21C00E23C01C47801C83001D00001E00003F800039C00038E00038
E00070E10070E10070E10070E200E06200603C00121D7E9C16>107 D<381F81F04E20C6184640
E81C4680F01C8F00F01C8E00E01C0E00E01C0E00E01C1C01C0381C01C0381C01C0381C01C07038
03807138038071380380E1380380E2700700643003003820127E9124>109
D<07878008C84010F0C020F1E020E3C040E18000E00000E00001C00001C00001C00001C0006380
80F38080F38100E5810084C60078780013127E9118>120 D<1C00C02701C04701C04701C08703
808703800E03800E03801C07001C07001C07001C0700180E00180E00180E001C1E000C3C0007DC
00001C00001800603800F03000F06000E0C0004180003E0000121A7E9114>I<038107C10FE608
1C10080010002000400080010002000400080410042C1877F843F081C010127E9113>I
E /Fk 5 111 df<60F0F0600404798312>46 D<038007C007C006C006C00EE00EE00EE00EE00C
601C701C701C701FF01FF0383838383838FC7EFC7E0F147F9312>65 D<FFC0FFF038783838381C
381C381E380E380E380E380E380E380E380E381C381C38383878FFF0FFC00F147F9312>68
D<FFFEFFFE380E380E380E3800380038E038E03FE03FE038E038E038003800380038003800FF00
FF000F147F9312>70 D<F9E0FFF03E383C3838383838383838383838383838383838FE3EFE3E0F
0E7F8D12>110 D E /Fl 7 55 df<1F00318060C04040C060C060C060C060C060C060C060C060
404060C031801F000B107F8F0F>48 D<0C003C00CC000C000C000C000C000C000C000C000C000C
000C000C000C00FF8009107E8F0F>I<1F00618040C08060C0600060006000C00180030006000C
00102020207FC0FFC00B107F8F0F>I<1F00218060C060C000C0008001800F00008000400060C0
60C060804060801F000B107F8F0F>I<0300030007000F000B001300330023004300C300FFE003
000300030003001FE00B107F8F0F>I<20803F002C002000200020002F00308020400060006000
60C06080C061801F000B107F8F0F>I<0780184030C060C06000C000CF00F080E040C060C060C0
60406060C030801F000B107F8F0F>I E /Fm 47 122 df<00FC000782000E07001C07001C0200
1C00001C00001C00001C0000FFFF001C07001C07001C07001C07001C07001C07001C07001C0700
1C07001C07001C07001C0700FF1FE01317809614>12 D<00FC7E000703C1000E0783801C070380
1C0701001C0700001C0700001C0700001C070000FFFFFF801C0703801C0703801C0703801C0703
801C0703801C0703801C0703801C0703801C0703801C0703801C0703801C070380FF1FCFF01C17
80961D>14 D<60C0F1E0F1E070E01020102020402040408040800B0A7F9612>34
D<0102040C1818303070606060E0E0E0E0E0E0E0E0E0E060606070303018180C04020108227D98
0E>40 D<8040203018180C0C0E060606070707070707070707070606060E0C0C18183020408008
227E980E>I<60F0F070101020204040040A7D830A>44 D<FF80FF80090280870C>I<60F0F06004
047D830A>I<03000700FF00070007000700070007000700070007000700070007000700070007
000700070007007FF00C157E9412>49 D<00300030007000F001F0017002700470087018701070
20704070C070FFFE0070007000700070007003FE0F157F9412>52 D<07E018302018600C600C70
0C78183E101F600FC00FF018F8607C601EC00EC006C006C004600C38300FE00F157F9412>56
D<60F0F06000000000000060F0F07010102020404004147D8D0A>59 D<FFFFFCFFFFFC00000000
0000000000000000000000000000FFFFFCFFFFFC160A7E8C1B>61 D<0010000038000038000038
00005C00005C00005C00008E00008E00008E0001070001070003078002038002038007FFC00401
C00401C00800E00800E01800E03800F0FE03FE17177F961A>65 D<FFFF001C01C01C00E01C0030
1C00381C00181C001C1C000C1C000E1C000E1C000E1C000E1C000E1C000E1C000E1C000C1C001C
1C001C1C00381C00301C00601C01C0FFFF0017177F961B>68 D<FFFFE01C00E01C00601C00201C
00101C00101C00101C04001C04001C04001C0C001FFC001C0C001C04001C04081C04081C00081C
00181C00101C00101C00301C00F0FFFFF015177F9618>I<FFE00E000E000E000E000E000E000E
000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE00B177F960D>73
D<00FC000303000E01C01C00E0380070300030700038600018E0001CE0001CE0001CE0001CE000
1CE0001CE0001C7000387000383000303800701C00E00E01C003030000FC0016177E961B>79
D<FFFC001C03801C00C01C00E01C00701C00701C00701C00701C00E01C00C01C03801FFE001C07
801C01C01C00E01C00E01C00E01C00E01C00E01C00E11C00E11C0072FF803C18177F961A>82
D<0FC4302C601C400CC004C004C004E00070007F003FE00FF801FC001C000E0006800680068006
C004E008D81087E00F177E9614>I<7FFFF8603818403808403808803804803804803804003800
003800003800003800003800003800003800003800003800003800003800003800003800003800
00380007FFC016177F9619>I<FF80FE1C00381C00101C00101C00101C00101C00101C00101C00
101C00101C00101C00101C00101C00101C00101C00101C00101C00100E00200600200300400181
80007E0017177F961A>I<FCFCC0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
C0C0C0FCFC06217D980A>91 D<204020404080408081008100E1C0F1E0F1E060C00B0A7B9612>
I<FCFC0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0CFCFC062180980A
>I<1FC0386038301038003803F81E3830387038E039E039E07970FF1F1E100E7F8D12>97
D<FC00001C00001C00001C00001C00001C00001C00001C00001C00001CF8001F06001C03001C03
801C01801C01C01C01C01C01C01C01C01C01801C03801C03001B0E0010F8001217809614>I<07
F01838303870106000E000E000E000E000600070083008183007C00D0E7F8D10>I<007E00000E
00000E00000E00000E00000E00000E00000E00000E0007CE001C3E00300E00700E00600E00E00E
00E00E00E00E00E00E00600E00700E00301E00182E0007CFC012177F9614>I<0FC01860303070
38E018FFF8E000E000E000600070083010183007C00D0E7F8D10>I<03E006700E701C201C001C
001C001C001C00FF801C001C001C001C001C001C001C001C001C001C001C001C00FF800C178096
0B>I<0F9E18E33060707070707070306018C02F80200060003FE03FF83FFC600EC006C006C006
600C38380FE010157F8D12>I<FC00001C00001C00001C00001C00001C00001C00001C00001C00
001C7C001D8E001E07001C07001C07001C07001C07001C07001C07001C07001C07001C07001C07
00FF9FE01317809614>I<183C3C1800000000007C1C1C1C1C1C1C1C1C1C1C1C1CFF081780960A>
I<0300078007800300000000000000000000001F80038003800380038003800380038003800380
0380038003800380038003804380E300E7007C00091D82960B>I<FC001C001C001C001C001C00
1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00FF80091780960A
>108 D<FC7C1F001D8E63801E0781C01C0701C01C0701C01C0701C01C0701C01C0701C01C0701
C01C0701C01C0701C01C0701C01C0701C0FF9FE7F81D0E808D1E>I<FC7C001D8E001E07001C07
001C07001C07001C07001C07001C07001C07001C07001C07001C0700FF9FE0130E808D14>I<07
C018303018600C600CE00EE00EE00EE00EE00E701C3018183007C00F0E7F8D12>I<FCF8001F0E
001C03001C03801C01801C01C01C01C01C01C01C01C01C01801C03801C07001F0E001CF8001C00
001C00001C00001C00001C0000FF80001214808D14>I<FCF01D381E381C101C001C001C001C00
1C001C001C001C001C00FF800D0E808D0E>114 D<1F4060C0C040C040E000FF007F801FC001E0
80608060C060E0C09F000B0E7F8D0E>I<080008000800180018003800FF803800380038003800
38003800380038403840384038401C800F000A147F930E>I<FC3F001C07001C07001C07001C07
001C07001C07001C07001C07001C07001C07001C0F000E170003E7E0130E808D14>I<FE1F3C0E
3C0C1C081C080E100E100720072003C003C003C001800180100E7F8D13>I<FCFE7C3838383838
101C3C201C3C201C4C200E4E400E4E400E8640078780078780070380030300030300160E7F8D19
>I<FE1F3C0E3C0C1C081C080E100E100720072003C003C003C00180018001000100E200E200A4
00780010147F8D13>121 D E /Fn 1 4 df<0C000C008C40EDC07F800C007F80EDC08C400C000C
000A0B7D8B10>3 D E /Fo 9 121 df<00E00001F00001F00001B00001B00003B80003B80003B8
00031800071C00071C00071C00071C00071C000E0E000E0E000FFE000FFE001FFF001C07001C07
001C07007F1FC0FF1FE07F1FC013197F9816>65 D<7FF800FFFE007FFF001C0F001C07801C03C0
1C01C01C01C01C01E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C01C01C01C0
1C03C01C07801C0F807FFF00FFFE007FF8001319809816>68 D<FFFFE0FFFFE0FFFFE01C00E01C
00E01C00E01C00E01C00001C00001C1C001C1C001FFC001FFC001FFC001C1C001C1C001C00001C
00001C00001C00001C00001C0000FF8000FFC000FF800013197F9816>70
D<03E30007FF000FFF001E1F003C0F00380700700700700700F00000E00000E00000E00000E000
00E03F80E07FC0E03F80F00700700700700700380F003C0F001E1F000FFF0007F70003E7001219
7E9816>I<03F80FFC1FFE3C1E780C7000E000E000E000E000E000F000700778073E0E1FFC0FF8
03F010127D9116>99 D<003F00007F00003F0000070000070000070000070003C7000FF7001FFF
003C1F00780F00700700E00700E00700E00700E00700E00700E00700700F00700F003C1F001FFF
E00FE7F007C7E014197F9816>I<03E0000FF8001FFC003C1E00780F00700700E00380E00380E0
0380E00380E00380F00780700700780F003C1E001FFC000FF80003E00011127E9116>111
D<FF0FC0FF3FE0FF7FE007F04007C0000780000780000700000700000700000700000700000700
00070000070000FFFC00FFFC00FFFC0013127F9116>114 D<7F1FC07F3FC07F1FC00F1C00073C
0003B80003F00001F00000E00001E00001F00003B800073C00071C000E0E007F1FC0FF3FE07F1F
C013127F9116>120 D E /Fp 23 119 df<78FCFCFCFC7806067A8513>46
D<00000C00000000000C00000000000C00000000001E00000000001E00000000003F0000000000
3F00000000003F00000000004F80000000004F80000000004F800000000087C00000000087C000
00000107E00000000103E00000000103E00000000201F00000000201F00000000201F000000004
00F80000000400F80000000800FC00000008007C00000008007C00000010003E00000010003E00
00003FFFFF0000003FFFFF00000020001F00000040001F80000040000F80000040000F80000080
0007C00000800007C00001800007E00001000003E00001000003E00003000003F00007000001F0
000F800003F800FFF0003FFFC0FFF0003FFFC02A2A7DA931>65 D<FFFF81FFFFFFFF81FFFF07F0
000FE003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003
E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C0
03E00007C003FFFFFFC003FFFFFFC003E00007C003E00007C003E00007C003E00007C003E00007
C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E000
07C003E00007C003E00007C003E00007C003E00007C007F0000FE0FFFF81FFFFFFFF81FFFF2829
7CA831>72 D<FFFF80FFFF8007F00003E00003E00003E00003E00003E00003E00003E00003E000
03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000
03E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E000
03E00007F000FFFF80FFFF8011297DA818>I<FFFFFE000000FFFFFFC0000007E003F0000003E0
00FC000003E0003E000003E0001F000003E0001F800003E0000F800003E0000FC00003E0000FC0
0003E0000FC00003E0000FC00003E0000FC00003E0000FC00003E0000F800003E0001F000003E0
001E000003E0003C000003E000F8000003E003E0000003FFFE00000003E00780000003E001E000
0003E000F0000003E00078000003E0007C000003E0003C000003E0003E000003E0003E000003E0
003E000003E0003E000003E0003F000003E0003F000003E0003F000003E0003F000003E0003F00
4003E0003F804003E0001F804007F0000F8080FFFF8007C080FFFF8003E10000000000FE002A2A
7CA830>82 D<FFFF0000FFF0FFFF0000FFF007F000001F0003E000000E0003F000000C0001F000
00080001F00000080000F80000100000F80000100000FC00001000007C00002000007C00002000
003E00004000003E00004000003F00004000001F00008000001F00008000000F80010000000F80
010000000FC00100000007C00200000007C00200000003E00400000003E00400000003F0040000
0001F00800000001F00800000000F81000000000F81000000000FC10000000007C20000000007C
20000000003E40000000003E40000000003FC0000000001F80000000001F80000000000F000000
00000F00000000000F0000000000060000000000060000002C2A7EA831>86
D<000100000003800000038000000380000007C0000007C000000BE0000009E0000009E0000010
F0000010F0000030F800002078000020780000403C0000403C0000C03E0000801E0000801E0001
FFFF0001FFFF0001000F000200078002000780040003C0040003C00C0003C00C0001E03E0003F0
FF000FFEFF000FFE1F1F7E9E25>97 D<000FE020007FF86001F80CE003E002E0078001E00F0000
E01E0000E03E0000603C0000607C0000207C00002078000020F8000000F8000000F8000000F800
0000F8000000F8000000F8000000780000007C0000207C0000203C0000203E0000601E0000400F
0000C00780008003E0030001F80E00007FF800000FE0001B1F7D9E23>99
D<FFFFE000FFFFF8000F007E000F000F000F0007800F0003C00F0003C00F0001E00F0001F00F00
00F00F0000F00F0000F80F0000F80F0000F80F0000F80F0000F80F0000F80F0000F80F0000F80F
0000F80F0000F00F0000F00F0001F00F0001E00F0001E00F0003C00F0007800F000F000F003E00
FFFFF800FFFFE0001D1F7D9E25>I<FFFFFF00FFFFFF000F000F000F0003000F0003000F000100
0F0001800F0000800F0000800F0080800F0080800F0080000F0080000F0180000FFF80000FFF80
000F0180000F0080000F0080000F0080200F0080200F0000200F0000400F0000400F0000400F00
00C00F0000C00F0001C00F000F80FFFFFF80FFFFFF801B1F7D9E21>I<FFFFFF00FFFFFF000F00
0F000F0003000F0003000F0001000F0001800F0000800F0000800F0080800F0080800F0080000F
0080000F0180000FFF80000FFF80000F0180000F0080000F0080000F0080000F0080000F000000
0F0000000F0000000F0000000F0000000F0000000F0000000F800000FFF80000FFF80000191F7D
9E20>I<000FE010007FFC3000FC0E7003E00370078000F00F0000701E0000703E0000303C0000
307C0000107C00001078000010F8000000F8000000F8000000F8000000F8000000F8000000F800
3FFE78003FFE7C0001F07C0000F03C0000F03E0000F01E0000F00F0000F0078000F003E001F000
FC0770007FFE30000FF0101F1F7D9E26>I<FFFCFFFC0780078007800780078007800780078007
80078007800780078007800780078007800780078007800780078007800780078007800780FFFC
FFFC0E1F7F9E12>105 D<FFF800FFF8000F80000F00000F00000F00000F00000F00000F00000F
00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00010F00010F00010F
00010F00030F00030F00020F00060F000E0F003EFFFFFEFFFFFE181F7D9E1F>108
D<FF00000FF8FF00000FF80F00000F800B800017800B8000178009C000278009C000278009C000
278008E000478008E000478008700087800870008780087000878008380107800838010780081C
020780081C020780081C020780080E040780080E040780080E0407800807080780080708078008
03900780080390078008039007800801E007801C01E007803E00C00780FF80C07FF8FF80C07FF8
251F7D9E2D>I<FF000FF8FF800FF80F8003E00BC001C009E0008009E0008008F0008008780080
08780080083C0080081E0080081E0080080F008008078080080780800803C0800801E0800801E0
800800F080080078800800788008003C8008001E8008001E8008000F8008000780080007801C00
03803E000180FF800180FF8000801D1F7D9E25>I<001FE0000070380001C00E00038007000F00
03C00E0001C01E0001E03C0000F03C0000F07C0000F87800007878000078F800007CF800007CF8
00007CF800007CF800007CF800007CF800007CF800007C7C0000F87C0000F83C0000F03C0000F0
1E0001E01F0003E00F0003C00780078001C00E0000703800001FE0001E1F7D9E26>I<FFFFC000
FFFFF8000F007C000F001E000F001F000F000F000F000F800F000F800F000F800F000F800F000F
800F000F000F001F000F001E000F007C000FFFF0000F0000000F0000000F0000000F0000000F00
00000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F000000FFF00000FF
F00000191F7D9E21>I<FFFF8000FFFFF0000F00FC000F003E000F001F000F000F000F000F800F
000F800F000F800F000F800F000F800F000F000F001E000F003C000F00F0000FFF80000F01C000
0F0060000F0070000F0038000F003C000F003C000F003C000F003E000F003E000F003E000F003E
020F003F020F001F02FFF00F8CFFF003F01F1F7D9E24>114 D<07F0400FFCC01C0FC03003C070
01C06000C0E00040E00040E00040F00000F000007800007F80003FF8001FFE000FFF0001FF8000
1FC00003C00001E00001E00000E08000E08000E08000E0C000C0C001C0F00380FC0700CFFE0081
F800131F7D9E1B>I<7FFFFFF07FFFFFF0780780F0600780304007801040078010C00780188007
800880078008800780088007800800078000000780000007800000078000000780000007800000
078000000780000007800000078000000780000007800000078000000780000007800000078000
00078000000FC00001FFFE0001FFFE001D1F7E9E23>I<FFF00FF8FFF00FF80F0003E00F0001C0
0F0000800F0000800F0000800F0000800F0000800F0000800F0000800F0000800F0000800F0000
800F0000800F0000800F0000800F0000800F0000800F0000800F0000800F0000800F0000800F00
008007800100078001000380020001C0040000F03800003FF000000FC0001D1F7D9E25>I<FFF0
007F80FFF0007F800F80003C000F800018000780001000078000100003C000200003C000200003
E000600001E000400001E000400000F000800000F000800000780100000078010000007C030000
003C020000003C020000001E040000001E040000000F080000000F080000000F88000000079000
0000079000000003E000000003E000000003E000000001C000000001C000000000800000211F7F
9E25>I E /Fq 7 117 df<0000001C000000001C000000003C000000003C000000007C00000000
FC00000000FC00000001FC00000001FC000000037C000000037C000000067C0000000E7C000000
0C7C000000187C000000187C000000307C000000307E000000603E000000603E000000C03E0000
01C03E000001803E000003003E000003003E000006003E000006003E00000FFFFE00000FFFFE00
0018003E000038003E000030003E000060003E000060003E0000C0003F0000C0001F000180001F
000380001F000380001F000FC0003F00FFF007FFF8FFF007FFF0252A7CA92C>65
D<003E000000E1180001C0BC000380FC00070078000F0078001E0078001E0078003E00F0007C00
F0007C00F0007C00F000F801E000F801E000F801E000F801E000F003C000F003C180F003C180F0
03C180F0078300700F8300700B82003833860018618C000F80F800191A79991F>97
D<01E0003FE0003FE00003E00003C00003C00003C00003C0000780000780000780000780000F00
000F00000F00000F00001E3C001EC3001F83801F03C03E01C03C01C03C01E03C03E07803E07803
E07803E07803E0F007C0F007C0F007C0F00780E00F80E00F80E00F00E01E00E01E00E03C006038
0070700030C0000F0000132A78A91B>I<001F8000706001E0300380700780F00F01F01E01F01E
00E03E00003C00007C00007C0000F80000F80000F80000F80000F00000F00000F00000F00020F0
00607000C03801803807000C1C0007F000141A79991B>I<0781F808C30C10E40E30FC1E30F83E
60F03E60F01C60F000C1E00001E00001E00001E00003C00003C00003C00003C000078000078000
0780000780000F00000F00000F00000F00001E00000C0000171A7B9919>114
D<003F0000E0C001C0600380600300E00701E00701E00700C007800007E00007FC0007FE0003FF
0001FF80001F800007800007803803807C03807C0380F80700700600600E00600C003830000FC0
00131A7B9918>I<00300078007800F000F000F000F001E001E001E001E0FFFFFFFF03C003C007
800780078007800F000F000F000F001E001E001E001E003C003C063C063C0C780C781838103830
18400F8010257AA414>I E /Fr 3 107 df<020002000200C218F2783AE00F800F803AE0F278C2
180200020002000D0E7E8E12>3 D<0000300000F00001C0000700001E0000780001E000038000
0E00003C0000F00000F000003800000E000007800001E000007800001C000007000003C00000F0
0000300000000000000000000000000000000000007FFFE0FFFFF0141E7D951B>20
D<C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C002217C980A
>106 D E /Fs 26 121 df<70F8FCFC7404040404080810102040060F7C840E>44
D<70F8F8F87005057C840E>46 D<01F000071C000C06001803003803803803807001C07001C070
01C07001C0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F001E0F0
01E0F001E0F001E07001C07001C07001C07803C03803803803801C07000C0600071C0001F00013
227EA018>48 D<008003800F80F380038003800380038003800380038003800380038003800380
03800380038003800380038003800380038003800380038003800380038007C0FFFE0F217CA018
>I<1000801E07001FFF001FFE001FF80013E00010000010000010000010000010000010000010
F800130E001407001803801003800001C00001C00001E00001E00001E00001E07001E0F001E0F0
01E0E001C08001C04003C04003802007001006000C1C0003F00013227EA018>53
D<007E0001C1000300800601C00E03C01C03C0180180380000380000780000700000700000F0F8
00F30C00F40600F40300F80380F801C0F001C0F001E0F001E0F001E0F001E0F001E07001E07001
E07001E03801C03801C01803801C03000C0600070C0001F00013227EA018>I<FFFFF8000F800E
0007800780078003C0078003E0078001E0078001F0078001F0078001F0078001F0078001F00780
01E0078003E0078007C007800F8007803E0007FFFE0007800780078003C0078001E0078001F007
8000F0078000F8078000F8078000F8078000F8078000F8078000F8078001F0078001F0078003E0
078007C00F800F00FFFFFC001D227EA123>66 D<FFFFFFC00F8007C0078001C0078000C0078000
400780004007800060078000200780002007800020078020200780200007802000078020000780
60000780E00007FFE0000780E00007806000078020000780200007802000078020000780000007
800000078000000780000007800000078000000780000007800000078000000FC00000FFFE0000
1B227EA120>70 D<FFFC0FC0078007800780078007800780078007800780078007800780078007
8007800780078007800780078007800780078007800780078007800780078007800FC0FFFC0E22
7EA112>73 D<FFFE00000FC0000007800000078000000780000007800000078000000780000007
800000078000000780000007800000078000000780000007800000078000000780000007800000
078000000780000007800000078000000780008007800080078000800780008007800180078001
8007800100078003000780030007800F000F803F00FFFFFF0019227EA11E>76
D<FFC00003FF0FC00003F007C00003E005E00005E005E00005E004F00009E004F00009E004F000
09E004780011E004780011E004780011E0043C0021E0043C0021E0043C0021E0041E0041E0041E
0041E0040F0081E0040F0081E0040F0081E004078101E004078101E004078101E00403C201E004
03C201E00401E401E00401E401E00401E401E00400F801E00400F801E00400F801E004007001E0
0E007001E01F007003F0FFE0203FFF28227EA12D>I<000FE00000783C0000E00E0003C0078007
8003C00F0001E00E0000E01E0000F03C0000783C0000787C00007C7C00007C7800003C7800003C
F800003EF800003EF800003EF800003EF800003EF800003EF800003EF800003EF800003E780000
3C7C00007C7C00007C3C0000783E0000F81E0000F00F0001E00F0001E0078003C003C0078000E0
0E0000783C00000FE0001F247DA226>79 D<FFFFF0000F803C0007800F0007800780078007C007
8003C0078003E0078003E0078003E0078003E0078003E0078003E0078003C0078007C007800780
07800F0007803C0007FFF000078000000780000007800000078000000780000007800000078000
00078000000780000007800000078000000780000007800000078000000FC00000FFFC00001B22
7EA121>I<0FE0001838003C0C003C0E0018070000070000070000070000FF0007C7001E07003C
0700780700700700F00708F00708F00708F00F087817083C23900FC1E015157E9418>97
D<0E0000FE00001E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00
000E00000E1F000E61C00E80600F00300E00380E003C0E001C0E001E0E001E0E001E0E001E0E00
1E0E001E0E001E0E001C0E003C0E00380F00700C80600C41C0083F0017237FA21B>I<01FE0007
03000C07801C0780380300780000700000F00000F00000F00000F00000F00000F00000F0000070
00007800403800401C00800C010007060001F80012157E9416>I<01FC000707000C03801C01C0
3801C07801E07000E0F000E0FFFFE0F00000F00000F00000F00000F00000700000780020380020
1C00400E008007030000FC0013157F9416>101 D<0E0000FE00001E00000E00000E00000E0000
0E00000E00000E00000E00000E00000E00000E00000E00000E1F800E60C00E80E00F00700F0070
0E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E00700E0070
0E00700E0070FFE7FF18237FA21B>104 D<1C003E003E003E001C000000000000000000000000
00000000000E00FE001E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00
0E000E000E00FFC00A227FA10E>I<0E00FE001E000E000E000E000E000E000E000E000E000E00
0E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E
000E000E00FFE00B237FA20E>108 D<0E1FC07F00FE60E183801E807201C00F003C00E00F003C
00E00E003800E00E003800E00E003800E00E003800E00E003800E00E003800E00E003800E00E00
3800E00E003800E00E003800E00E003800E00E003800E00E003800E00E003800E00E003800E0FF
E3FF8FFE27157F942A>I<01FC000707000C01801800C03800E0700070700070F00078F00078F0
0078F00078F00078F00078F000787000707800F03800E01C01C00E038007070001FC0015157F94
18>111 D<0E3CFE461E8F0F0F0F060F000E000E000E000E000E000E000E000E000E000E000E00
0E000E000F00FFF010157F9413>114 D<02000200020002000600060006000E001E003E00FFF8
0E000E000E000E000E000E000E000E000E000E000E000E040E040E040E040E040E040708030801
F00E1F7F9E13>116 D<FFC1FE1E00780E00300E00200E00200700400700400380800380800380
8001C10001C10000E20000E20000E20000740000740000380000380000380000100017157F941A
>118 D<FF83FE1F01F00E00C007008003810003830001C20000E400007800007800003800003C
00004E00008E000187000103800201C00401E00C00E03E01F0FF03FE17157F941A>120
D E /Ft 17 118 df<0001FE01F8000701C704001C002E0E007800FC1F00F001F81F00E001F81F
01E001F00E03C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F0
0003C000F00003C000F00003C000F00003C000F00003C000F000FFFFFFFFF0FFFFFFFFF003C000
F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C0
00F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003
C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F00003C000F000
03C000F00003C000F00007E001F8007FFE1FFFC07FFE1FFFC028327FB126>11
D<00000300000000000300000000000300000000000780000000000780000000000FC000000000
0FC0000000000FC00000000017E00000000013E00000000013E00000000023F00000000021F000
00000021F00000000040F80000000040F80000000040F800000000807C00000000807C00000001
807E00000001003E00000001003E00000002003F00000002001F00000002001F00000004000F80
000004000F80000004000F800000080007C00000080007C00000180007E000001FFFFFE000001F
FFFFE00000200003F00000200001F00000200001F00000400001F80000400000F80000400000F8
00008000007C00008000007C00008000007C00010000003E00010000003E00030000003F000300
00001F00070000001F001F8000003F80FFE00003FFFCFFE00003FFFC2E327EB132>65
D<FFFFFFE00000FFFFFFFC000007E0007F000003E0000F800003E00003C00003E00001E00003E0
0000F00003E00000780003E000003C0003E000001E0003E000001E0003E000000F0003E000000F
0003E000000F8003E00000078003E0000007C003E0000007C003E0000003C003E0000003C003E0
000003E003E0000003E003E0000003E003E0000003E003E0000003E003E0000003E003E0000003
E003E0000003E003E0000003E003E0000003E003E0000003E003E0000003C003E0000003C003E0
000007C003E0000007C003E00000078003E00000078003E000000F8003E000000F0003E000001F
0003E000001E0003E000003C0003E00000780003E00000F80003E00001F00003E00003E00003E0
000F800007E0003F0000FFFFFFFC0000FFFFFFE000002B317CB033>68 D<FFFFFFFFC0FFFFFFFF
C007E0001FC003E00003C003E00001E003E00000E003E000006003E000006003E000002003E000
002003E000002003E000002003E000001003E000001003E000001003E000801003E000800003E0
00800003E000800003E000800003E001800003E001800003E007800003FFFF800003FFFF800003
E007800003E001800003E001800003E000800003E000800003E000800003E000800003E0008000
03E000000003E000000003E000000003E000000003E000000003E000000003E000000003E00000
0003E000000003E000000003E000000003E000000003E000000007F0000000FFFFC00000FFFFC0
000024317CB02B>70 D<FFFFC00000FFFFC0000007F000000003E000000003E000000003E00000
0003E000000003E000000003E000000003E000000003E000000003E000000003E000000003E000
000003E000000003E000000003E000000003E000000003E000000003E000000003E000000003E0
00000003E000000003E000000003E000000003E000000003E000000003E000000003E000000003
E000000003E000000003E000004003E000004003E000004003E000004003E000008003E0000080
03E000008003E000008003E000018003E000018003E000038003E000038003E000078003E0000F
0003E0003F0007E000FF00FFFFFFFF00FFFFFFFF0022317CB029>76 D<00FE00000303C0000C00
E00010007000100038003C003C003E001C003E001E003E001E0008001E0000001E0000001E0000
001E00000FFE0000FC1E0003E01E000F801E001F001E003E001E003C001E007C001E00F8001E04
F8001E04F8001E04F8003E04F8003E0478003E047C005E043E008F080F0307F003FC03E01E1F7D
9E21>97 D<003F8000E0600380180700040F00041E001E1C003E3C003E7C003E7C0008780000F8
0000F80000F80000F80000F80000F80000F80000F80000F800007800007C00007C00003C00011E
00011E00020F000207000403801800E060003F80181F7D9E1D>99 D<003F800000E0E000038038
0007003C000E001E001E001E001C000F003C000F007C000F0078000F8078000780F8000780F800
0780FFFFFF80F8000000F8000000F8000000F8000000F8000000F8000000780000007C0000003C
0000003C0000801E0000800E0001000F0002000780020001C00C0000F03000001FC000191F7E9E
1D>101 D<0007E0001C1000383800707C00E07C01E07C01C03803C00003C00003C00003C00003
C00003C00003C00003C00003C00003C00003C00003C000FFFFC0FFFFC003C00003C00003C00003
C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003
C00003C00003C00003C00003C00003C00003C00003C00003C00003C00007E0007FFF007FFF0016
327FB114>I<0F001F801F801F801F800F00000000000000000000000000000000000000000000
000780FF80FF800F80078007800780078007800780078007800780078007800780078007800780
0780078007800780078007800780078007800FC0FFF8FFF80D307EAF12>105
D<0780FE001FC000FF83078060F000FF8C03C18078000F9001E2003C0007A001E4003C0007A000
F4001E0007C000F8001E0007C000F8001E00078000F0001E00078000F0001E00078000F0001E00
078000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0
001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E0007
8000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F0001E00078000F000
1E000FC001F8003F00FFFC1FFF83FFF0FFFC1FFF83FFF0341F7E9E38>109
D<0780FE0000FF83078000FF8C03C0000F9001E00007A001E00007A000F00007C000F00007C000
F000078000F000078000F000078000F000078000F000078000F000078000F000078000F0000780
00F000078000F000078000F000078000F000078000F000078000F000078000F000078000F00007
8000F000078000F000078000F000078000F000078000F0000FC001F800FFFC1FFF80FFFC1FFF80
211F7E9E25>I<001FC00000F0780001C01C00070007000F0007801E0003C01C0001C03C0001E0
3C0001E0780000F0780000F0780000F0F80000F8F80000F8F80000F8F80000F8F80000F8F80000
F8F80000F8F80000F8780000F07C0001F03C0001E03C0001E01E0003C01E0003C00F0007800780
0F0001C01C0000F07800001FC0001D1F7E9E21>I<0783E0FF8C18FF907C0F907C07A07C07C038
07C00007C00007C000078000078000078000078000078000078000078000078000078000078000
0780000780000780000780000780000780000780000780000780000FC000FFFE00FFFE00161F7E
9E19>114 D<01FC100E03301800F0300070600030E00030E00010E00010E00010F00010F80000
7E00003FF0001FFF000FFFC003FFE0003FF00001F80000F880003C80003C80001CC0001CC0001C
E0001CE00018F00038F00030CC0060C301C080FE00161F7E9E1A>I<0040000040000040000040
0000400000C00000C00000C00001C00001C00003C00007C0000FC0001FFFE0FFFFE003C00003C0
0003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C0
0003C00003C01003C01003C01003C01003C01003C01003C01003C01001C02001E02000E0400078
C0001F00142C7FAB19>I<078000F000FF801FF000FF801FF0000F8001F000078000F000078000
F000078000F000078000F000078000F000078000F000078000F000078000F000078000F0000780
00F000078000F000078000F000078000F000078000F000078000F000078000F000078000F00007
8000F000078000F000078001F000078001F000078001F000038002F00003C004F00001C008F800
007030FF80001FC0FF80211F7E9E25>I E /Fu 81 125 df<000C0000000C0000000C0000001E
0000001E0000001E0000003F0000002F0000002F0000004F8000004780000047800000C7C00000
83C0000083C0000183E0000101E0000101E0000101E0000200F0000200F0000200F00004007800
040078000400780008003C000C003C001E007E00FF83FFC01A1D7F9C1D>3
D<007E1F0001C1B1800303E3C00703C3C00E03C1800E01C0000E01C0000E01C0000E01C0000E01
C0000E01C000FFFFFC000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E
01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0007F87FC00
1A1D809C18>11 D<007E0001C1800301800703C00E03C00E01800E00000E00000E00000E00000E
0000FFFFC00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E
01C00E01C00E01C00E01C00E01C07F87F8151D809C17>I<003F07E00001C09C18000380F01800
0701F03C000E01E03C000E00E018000E00E000000E00E000000E00E000000E00E000000E00E000
00FFFFFFFC000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E0
1C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00E01C000E00
E01C000E00E01C007FC7FCFF80211D809C23>14 D<6060F0F0F8F8686808080808080810101010
2020404080800D0C7F9C15>34 D<60F0F8680808081010204080050C7C9C0C>39
D<004000800100020006000C000C0018001800300030007000600060006000E000E000E000E000
E000E000E000E000E000E000E000E000600060006000700030003000180018000C000C00060002
000100008000400A2A7D9E10>I<800040002000100018000C000C000600060003000300038001
800180018001C001C001C001C001C001C001C001C001C001C001C001C001800180018003800300
0300060006000C000C00180010002000400080000A2A7E9E10>I<000600000006000000060000
000600000006000000060000000600000006000000060000000600000006000000060000000600
00FFFFFFE0FFFFFFE0000600000006000000060000000600000006000000060000000600000006
000000060000000600000006000000060000000600001B1C7E9720>43 D<60F0F0701010101020
204080040C7C830C>I<FFE0FFE00B0280890E>I<60F0F06004047C830C>I<0001000300060006
0006000C000C000C0018001800180030003000300060006000C000C000C0018001800180030003
000300060006000C000C000C00180018001800300030003000600060006000C000C00010297E9E
15>I<03C00C301818300C300C700E60066006E007E007E007E007E007E007E007E007E007E007
E007E007E00760066006700E300C300C18180C3007E0101D7E9B15>I<030007003F00C7000700
070007000700070007000700070007000700070007000700070007000700070007000700070007
0007000F80FFF80D1C7C9B15>I<07C01830201C400C400EF00FF80FF807F8077007000F000E00
0E001C001C00380070006000C00180030006010C01180110023FFE7FFEFFFE101C7E9B15>I<07
E01830201C201C781E780E781E381E001C001C00180030006007E00030001C001C000E000F000F
700FF80FF80FF80FF00E401C201C183007E0101D7E9B15>I<000C00000C00001C00003C00003C
00005C0000DC00009C00011C00031C00021C00041C000C1C00081C00101C00301C00201C00401C
00C01C00FFFFC0001C00001C00001C00001C00001C00001C00001C0001FFC0121C7F9B15>I<30
0C3FF83FF03FC020002000200020002000200023E024302818301C200E000E000F000F000F600F
F00FF00FF00F800E401E401C2038187007C0101D7E9B15>I<00F0030C06040C0E181E301E300C
700070006000E3E0E430E818F00CF00EE006E007E007E007E007E007600760077006300E300C18
180C3003E0101D7E9B15>I<4000007FFF807FFF007FFF00400200800400800400800800001000
00100000200000600000400000C00000C00001C000018000018000038000038000038000038000
078000078000078000078000078000078000030000111D7E9B15>I<03E00C301008200C200660
06600660067006780C3E083FB01FE007F007F818FC307E601E600FC007C003C003C003C0036002
6004300C1C1007E0101D7E9B15>I<03C00C301818300C700C600EE006E006E007E007E007E007
E0076007700F300F18170C2707C700060006000E300C780C78187010203030C00F80101D7E9B15
>I<60F0F0600000000000000000000060F0F06004127C910C>I<60F0F060000000000000000000
0060F0F0701010101020204080041A7C910C>I<7FFFFFC0FFFFFFE00000000000000000000000
000000000000000000000000000000000000000000FFFFFFE07FFFFFC01B0C7E8F20>61
D<000600000006000000060000000F0000000F0000000F00000017800000178000001780000023
C0000023C0000023C0000041E0000041E0000041E0000080F0000080F0000180F8000100780001
FFF80003007C0002003C0002003C0006003E0004001E0004001E000C001F001E001F00FF80FFF0
1C1D7F9C1F>65 D<FFFFC00F00F00F00380F003C0F001C0F001E0F001E0F001E0F001E0F001C0F
003C0F00780F01F00FFFE00F00780F003C0F001E0F000E0F000F0F000F0F000F0F000F0F000F0F
001E0F001E0F003C0F0078FFFFE0181C7E9B1D>I<001F808000E0618001801980070007800E00
03801C0003801C00018038000180780000807800008070000080F0000000F0000000F0000000F0
000000F0000000F0000000F0000000F0000000700000807800008078000080380000801C000100
1C0001000E000200070004000180080000E03000001FC000191E7E9C1E>I<FFFFC0000F00F000
0F003C000F000E000F0007000F0007000F0003800F0003C00F0001C00F0001C00F0001E00F0001
E00F0001E00F0001E00F0001E00F0001E00F0001E00F0001E00F0001C00F0001C00F0003C00F00
03800F0007800F0007000F000E000F001C000F007000FFFFC0001B1C7E9B20>I<FFFFFC0F003C
0F000C0F00040F00040F00060F00020F00020F02020F02000F02000F02000F06000FFE000F0600
0F02000F02000F02000F02010F00010F00020F00020F00020F00060F00060F000C0F003CFFFFFC
181C7E9B1C>I<FFFFF80F00780F00180F00080F00080F000C0F00040F00040F02040F02000F02
000F02000F06000FFE000F06000F02000F02000F02000F02000F00000F00000F00000F00000F00
000F00000F00000F8000FFF800161C7E9B1B>I<001F808000E0618001801980070007800E0003
801C0003801C00018038000180780000807800008070000080F0000000F0000000F0000000F000
0000F0000000F0000000F000FFF0F0000F80700007807800078078000780380007801C0007801C
0007800E00078007000B800180118000E06080001F80001C1E7E9C21>I<FFF3FFC00F003C000F
003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C00
0F003C000FFFFC000F003C000F003C000F003C000F003C000F003C000F003C000F003C000F003C
000F003C000F003C000F003C000F003C000F003C00FFF3FFC01A1C7E9B1F>I<FFF00F000F000F
000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F00
0F000F000F000F00FFF00C1C7F9B0F>I<1FFF00F8007800780078007800780078007800780078
00780078007800780078007800780078007800787078F878F878F878F0F040E021C01F00101D7F
9B15>I<FFF03FE00F000F000F000C000F0008000F0010000F0020000F0040000F0080000F0100
000F0200000F0400000F0E00000F1F00000F2F00000F2780000F4780000F83C0000F01E0000F01
E0000F00F0000F00F8000F0078000F003C000F003C000F001E000F001F000F001F80FFF07FF01C
1C7E9B20>I<FFF8000F80000F00000F00000F00000F00000F00000F00000F00000F00000F0000
0F00000F00000F00000F00000F00000F00000F00000F00080F00080F00080F00180F00180F0010
0F00300F00700F01F0FFFFF0151C7E9B1A>I<FF8000FF800F8000F8000F8000F8000BC0017800
0BC00178000BC001780009E002780009E002780008F004780008F004780008F004780008780878
0008780878000878087800083C107800083C107800083C107800081E207800081E207800081E20
7800080F407800080F40780008078078000807807800080780780008030078001C03007800FF83
07FF80211C7E9B26>I<FF007FC00F800E000F8004000BC0040009E0040009E0040008F0040008
F8040008780400083C0400083C0400081E0400080F0400080F0400080784000807C4000803C400
0801E4000801E4000800F40008007C0008007C0008003C0008003C0008001C0008000C001C000C
00FF8004001A1C7E9B1F>I<003F800000E0E0000380380007001C000E000E001C0007003C0007
8038000380780003C0780003C0700001C0F00001E0F00001E0F00001E0F00001E0F00001E0F000
01E0F00001E0F00001E0700001C0780003C0780003C0380003803C0007801C0007000E000E0007
001C000380380000E0E000003F80001B1E7E9C20>I<FFFF800F00E00F00780F003C0F001C0F00
1E0F001E0F001E0F001E0F001E0F001C0F003C0F00780F00E00FFF800F00000F00000F00000F00
000F00000F00000F00000F00000F00000F00000F00000F0000FFF000171C7E9B1C>I<FFFF0000
0F01E0000F0078000F003C000F001C000F001E000F001E000F001E000F001E000F001C000F003C
000F0078000F01E0000FFF00000F03C0000F00E0000F00F0000F0078000F0078000F0078000F00
78000F0078000F0078000F0078100F0078100F0038100F003C20FFF01C20000007C01C1D7E9B1F
>82 D<07E0801C1980300580700380600180E00180E00080E00080E00080F00000F800007C0000
7FC0003FF8001FFE0007FF0000FF80000F800007C00003C00001C08001C08001C08001C0C00180
C00180E00300D00200CC0C0083F800121E7E9C17>I<7FFFFFC0700F01C0600F00C0400F004040
0F0040C00F0020800F0020800F0020800F0020000F0000000F0000000F0000000F0000000F0000
000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00
00000F0000000F0000001F800003FFFC001B1C7F9B1E>I<FFF07FC00F000E000F0004000F0004
000F0004000F0004000F0004000F0004000F0004000F0004000F0004000F0004000F0004000F00
04000F0004000F0004000F0004000F0004000F0004000F0004000F0004000F0004000700080007
800800038010000180100000C020000070C000001F00001A1D7E9B1F>I<FFE0FFE0FF1F001F00
3C1E001E00180F001F00100F001F00100F001F001007801F00200780278020078027802003C027
804003C043C04003C043C04003E043C04001E081E08001E081E08001E081E08000F100F10000F1
00F10000F100F100007900FA00007A007A00007A007A00003E007C00003C003C00003C003C0000
3C003C00001800180000180018000018001800281D7F9B2B>87 D<7FF0FFC00FC03E0007801800
03C0180003E0100001E0200001F0600000F0400000788000007D8000003D0000001E0000001F00
00000F0000000F8000000F80000013C0000023E0000021E0000041F00000C0F800008078000100
7C0003003C0002001E0006001F001F003F80FFC0FFF01C1C7F9B1F>I<FFF007FC0F8001E00780
008007C0018003C0010003E0020001F0020000F0040000F8040000780800007C1800003C100000
1E2000001F2000000F4000000FC000000780000007800000078000000780000007800000078000
0007800000078000000780000007800000078000007FF8001E1C809B1F>I<7FFFF07C01F07001
E06003C06003C0400780400F80400F00401E00001E00003C00007C0000780000F00000F00001E0
0003E00003C0100780100780100F00101F00301E00203C00203C00607800E0F803E0FFFFE0141C
7E9B19>I<FEFEC0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
C0C0C0C0C0FEFE07297C9E0C>I<08081010202040404040808080808080B0B0F8F8787830300D
0C7A9C15>I<FEFE06060606060606060606060606060606060606060606060606060606060606
060606060606FEFE0729809E0C>I<1FC000307000783800781C00301C00001C00001C0001FC00
0F1C00381C00701C00601C00E01C40E01C40E01C40603C40304E801F870012127E9115>97
D<FC00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C7C001D86
001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C00C01C01C01C01
801E030019060010F800131D7F9C17>I<07E00C301878307870306000E000E000E000E000E000
E00060007004300418080C3007C00E127E9112>I<003F00000700000700000700000700000700
00070000070000070000070000070003E7000C1700180F00300700700700600700E00700E00700
E00700E00700E00700E00700600700700700300700180F000C370007C7E0131D7E9C17>I<03E0
0C301818300C700E6006E006FFFEE000E000E000E00060007002300218040C1803E00F127F9112
>I<00F8018C071E061E0E0C0E000E000E000E000E000E00FFE00E000E000E000E000E000E000E
000E000E000E000E000E000E000E000E000E007FE00F1D809C0D>I<00038003C4C00C38C01C38
80181800381C00381C00381C00381C001818001C38000C300013C0001000003000001800001FF8
001FFF001FFF803003806001C0C000C0C000C0C000C06001803003001C0E0007F800121C7F9215
>I<FC00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C7C001C
87001D03001E03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C
03801C03801C0380FF9FF0141D7F9C17>I<18003C003C00180000000000000000000000000000
00FC001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00FF80091D
7F9C0C>I<00C001E001E000C000000000000000000000000000000FE000E000E000E000E000E0
00E000E000E000E000E000E000E000E000E000E000E000E000E000E000E060E0F0C0F1C061803E
000B25839C0D>I<FC00001C00001C00001C00001C00001C00001C00001C00001C00001C00001C
00001C3FC01C0F001C0C001C08001C10001C20001C40001CE0001DE0001E70001C78001C38001C
3C001C1C001C0E001C0F001C0F80FF9FE0131D7F9C16>I<FC001C001C001C001C001C001C001C
001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00
1C00FF80091D7F9C0C>I<FC7E07E0001C838838001D019018001E01E01C001C01C01C001C01C0
1C001C01C01C001C01C01C001C01C01C001C01C01C001C01C01C001C01C01C001C01C01C001C01
C01C001C01C01C001C01C01C001C01C01C00FF8FF8FF8021127F9124>I<FC7C001C87001D0300
1E03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C0380
1C0380FF9FF014127F9117>I<03F0000E1C00180600300300700380600180E001C0E001C0E001
C0E001C0E001C0E001C06001807003803003001806000E1C0003F00012127F9115>I<FC7C001D
86001E03001C01801C01C01C00C01C00E01C00E01C00E01C00E01C00E01C00E01C01C01C01C01C
01801E03001D06001CF8001C00001C00001C00001C00001C00001C00001C0000FF8000131A7F91
17>I<03C1000C3300180B00300F00700700700700E00700E00700E00700E00700E00700E00700
600700700700300F00180F000C370007C700000700000700000700000700000700000700000700
003FE0131A7E9116>I<FCE01D301E781E781C301C001C001C001C001C001C001C001C001C001C
001C001C00FFC00D127F9110>I<1F9030704030C010C010E010F8007F803FE00FF000F8803880
18C018C018E010D0608FC00D127F9110>I<04000400040004000C000C001C003C00FFE01C001C
001C001C001C001C001C001C001C001C101C101C101C101C100C100E2003C00C1A7F9910>I<FC
1F801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C03801C
03801C07800C07800E1B8003E3F014127F9117>I<FF07E03C03801C01001C01000E02000E0200
07040007040007040003880003880003D80001D00001D00000E00000E00000E00000400013127F
9116>I<FF3FCFE03C0F03801C0701801C0701001C0B01000E0B82000E0B82000E1182000711C4
000711C4000720C40003A0E80003A0E80003C0680001C0700001C0700001803000008020001B12
7F911E>I<7F8FF00F03800F030007020003840001C80001D80000F00000700000780000F80000
9C00010E00020E000607000403801E07C0FF0FF81512809116>I<FF07E03C03801C01001C0100
0E02000E020007040007040007040003880003880003D80001D00001D00000E00000E00000E000
004000004000008000008000F08000F10000F300006600003C0000131A7F9116>I<7FFC703860
38407040F040E041C003C0038007000F040E041C043C0C380870087038FFF80E127F9112>I<FF
FFF01401808B15>I<FFFFFFFFFF802901808B2A>I E /Fv 11 117 df<00600000600000600000
6000006000006000006000006000006000006000FFFFF0FFFFF000600000600000600000600000
600000600000600000600000600000600014167E9119>43 D<0C001C00EC000C000C000C000C00
0C000C000C000C000C000C000C000C000C000C000C00FFC00A137D9211>49
D<1F0060C06060F070F030603000700070006000C001C00180020004000810101020207FE0FFE0
0C137E9211>I<0FC030707038703870380038003000E00FC0007000380018001C601CF01CF018
E03860701FC00E137F9211>I<006000E000E00160026006600C600860106020606060C060FFFC
0060006000600060006003FC0E137F9211>I<60607FC07F8044004000400040004F0070C040E0
006000700070E070E070E06040E021C01F000C137E9211>I<07C00C201070207060006000C000
CF00D0C0E060C020C030C030C03040306020206010C00F000C137E9211>I<FCFCC0C0C0C0C0C0
C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0FCFC061D7E9509>91 D<FCFC0C0C0C0C0C0C0C0C
0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0CFCFC061D809509>93 D<F00030003000300030003000
300033E034303818301830183018301830183018301830183018FC7E0F147F9312>104
D<10001000100030007000FF80300030003000300030003000300030803080308011000E000912
7F910D>116 D E end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin @letter
%%EndSetup
%%Page: 1 1
bop -72 -30 a Fv(1)1885 3075 y Fu(P)o(age)14 b(1)p eop
%%Page: 1 2
bop 299 198 a Ft(Automatic)21 b(Di\013eren)n(tiation)g(of)h(Limit)f(F)-6
b(unctions)792 339 y Fs(Leo)17 b(Mic)o(helotti)489 397 y(F)l(ermilab)677
375 y Fr(\003)697 397 y Fs(,)e(P)l(.O.Bo)o(x)g(500,)i(Bata)o(via,)f(IL)g
(60510)-114 775 y Fq(A)n(bstr)m(act)-114 869 y Fu(Automatic)21
b(di\013eren)o(tiation)i(can)g(b)q(e)g(used)h(to)f(ev)n(aluate)f(the)-114
919 y(deriv)n(ativ)o(es)17 b(of)g(and)f(set)j(up)e(T)m(a)o(ylor)e(series)k
(for)e(implicitly)d(de-)-114 969 y(\014ned)k(functions)f(and)g(maps.)26
b(W)m(e)16 b(pro)o(vide)h(sev)o(eral)h(examples)-114 1019 y(of)11
b(ho)o(w)h(this)f(w)o(orks,)h(within)f(the)i(con)o(text)f(of)f(the)i
(MXYZPTLK)-114 1068 y(class)d(library)m(,)f(and)h(discuss)h(its)f(extension)g
(to)g(in)o(v)o(erse)g(functions.)136 1215 y Fp(I.)67 b(Intr)o(oduction.)-114
1309 y Fu(The)13 b(tec)o(hniques)h(of)d(automatic)g(di\013eren)o(tiation)h
([2)o(])g(and)h(di\013er-)-114 1359 y(en)o(tial)k(algebra)g([1,)g(3)o(,)h(9)o
(])g(are)g(rapidly)f(b)q(ecoming)f(a)i(standard)-114 1409 y(part)g(of)f
(accelerator)h(ph)o(ysicists')g(arsenals.)29 b(That)18 b(automatic)-114
1459 y(di\013eren)o(tiation)j(can)h(b)q(e)f(used)i(to)e(calculate)g(the)h
(deriv)n(ativ)o(es)-114 1508 y(of)c(recursiv)o(ely)i(or)f(iterativ)o(ely)390
1493 y Fv(1)427 1508 y Fu(de\014ned)h(functions)e(is)h(not)g(as)-114
1558 y(w)o(ell)12 b(appreciated)h(as)g(it)f(should)g(b)q(e.)18
b(Applying)11 b(recursiv)o(e)j(algo-)-114 1608 y(rithms)f(directly)i(to)f
Fo(DA)g Fu(v)n(ariables)438 1593 y Fv(2)470 1608 y Fu(pro)o(vides)g(an)g
(easy)h(metho)q(d)-114 1658 y(for)20 b(obtaining)e(deriv)n(ativ)o(es)i(of)g
(suc)o(h)h(functions.)36 b(In)20 b(the)h(fol-)-114 1708 y(lo)o(wing)11
b(sections)j(w)o(e)f(shall)e(\(a\))i(sk)o(etc)o(h)h(the)f(essen)o(tial)g
(argumen)o(t)-114 1758 y(needed)k(to)f(pro)o(v)o(e)g(this)g(assertion,)g
(\(b\))g(discuss)i(t)o(w)o(o)d(examples)-114 1807 y(written)d(using)g(the)g
(C)235 1803 y(++)312 1807 y(classes)h(in)e(MXYZPTLK)i([5,)e(6],)g(and)-114
1857 y(\(c\))17 b(pro)o(vide)g(C)134 1853 y(++)215 1857 y(co)q(de)g(fragmen)o
(ts)f(for)g(a)g(general)h(program.)-114 1907 y(This)k(pap)q(er)g(builds)f(on)
h(w)o(ork)f(done)h(previously)g([7)o(])f(but)h(re-)-114 1957
y(mains)c(necessarily)i(short.)32 b(Applications)18 b(of)g(the)h(tec)o
(hniques)-114 2007 y(describ)q(ed)i(are)f(to)q(o)e(n)o(umerous)h(to)g(men)o
(tion)f(and)g(so)i(ob)o(vious)-114 2056 y(that)14 b(there)h(is)f(no)g(need)g
(to)g(do)g(so.)-15 2203 y Fp(I)r(I.)67 b(Heuristics)23 b(f)o(or)g(a)f(pr)o
(oof)-114 2297 y Fu(F)m(ollo)o(wing)12 b([7],)i(a)g(mathematically)d(correct)
17 b(pro)q(of)e(that)g(recur-)-114 2347 y(sions)j(can)f(b)q(e)i(extended)g
(to)e Fo(DA)g Fu(v)n(ariables)g(w)o(as)g(published)h(b)o(y)-114
2397 y(Gilb)q(ert)f([4)o(])g(for)g(single)g(deriv)n(ativ)o(es;)i(its)e
(extension)i(to)e(higher)-114 2447 y(deriv)n(ativ)o(es)g(is)h(implied.)26
b(The)18 b(pro)q(of)s('s)f(correctness)k(mak)o(es)16 b(it)p
-114 2488 414 2 v -68 2515 a Fn(\003)-50 2527 y Fm(Op)q(erated)11
b(b)o(y)h(the)g(Univ)o(ersities)f(Researc)o(h)g(Asso)q(ciation,)g(Inc.)h
(under)-114 2566 y(con)o(tract)d(with)j(the)e(U.S.)i(Departmen)o(t)c(of)j
(Energy)m(.)-68 2594 y Fl(1)-50 2606 y Fm(I)i(confess)e(to)i(b)q(eing)e
(confused)g(ab)q(out)h(the)g(distinction)e(b)q(et)o(w)o(een)i(\\re-)-114
2645 y(cursiv)o(e")d(and)i(\\iterativ)o(e.")-68 2673 y Fl(2)-50
2685 y Fm(A)g Fk(DA)f Fm(v)n(ariable)f(carries)g(information)e(ab)q(out)i
(deriv)n(ativ)o(es)f(of)j(functions)-114 2724 y(as)g(w)o(ell)h(the)f(v)n
(alue)f(of)h(the)g(functions.)j(It)d(is)g(a)h(computer)d(implemen)o(ta)o(tio)
o(n)-114 2764 y(of)i(a)h(\\jet")e(structure)f([8)o(].)972 660
y Fu(formal,)g(and)i(ho)o(w)f(it)h(w)o(orks)g(is)g(not)g(ob)o(vious)f(to)h
(naiv)o(e)f(in)o(tuition-)972 710 y(ists.)18 b(It)11 b(is)g(hop)q(ed)h(that)f
(the)h(follo)o(wing)d(heuristic)j(argumen)o(t)e(will)972 760
y(b)q(e)j(easier)g(to)f(understand)i(while)e(retaining)g(essen)o(tial)g(p)q
(oin)o(ts)h(of)972 810 y(the)h(pro)q(of.)1014 859 y(Let)g Fj(f)j
Fu(:)11 b Fj(R)g Fi(!)g Fj(R)j Fu(p)q(ossess)i(a)e(\014xed)h(p)q(oin)o(t,)e
Fj(x)1713 844 y Fh(\003)1732 859 y Fu(.)19 b(The)c(sequence)972
909 y Fj(x)996 915 y Fg(n)p Fv(+1)1072 909 y Fu(=)d Fj(f)t
Fu(\()p Fj(x)1180 915 y Fg(n)1203 909 y Fu(\))p Fj(;)h Fu(started)h(\\close)g
(enough")f(to)g Fj(x)1741 894 y Fh(\003)1760 909 y Fu(,)g(con)o(v)o(erges)h
(to)972 959 y Fj(x)996 944 y Fh(\003)1033 959 y Fu(pro)o(vided)19
b(that)g Fi(j)7 b Fj(f)1347 944 y Fh(0)1359 959 y Fu(\()p Fj(x)1399
944 y Fh(\003)1418 959 y Fu(\))g Fi(j)k Fj(<)h Fu(1)p Fj(:)17
b Fu(No)o(w)i(consider)g(the)h(recur-)972 1009 y(sion,)1243
1059 y Fj(x)1267 1065 y Fg(n)p Fv(+1)1331 1059 y Fu(\()p Fj(m)p
Fu(\))12 b(=)g Fj(F)6 b Fu(\()p Fj(x)1528 1065 y Fg(n)1550
1059 y Fu(\()p Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\))29 b Fj(;)224
b Fu(\(1\))972 1132 y(and)14 b(assume)f(that)h(it)g(con)o(v)o(erges)h(to)f(a)
g(\014xed)g(p)q(oin)o(t,)f Fj(x)1844 1117 y Fh(\003)1863 1132
y Fu(\()p Fj(m)p Fu(\))p Fj(;)h Fu(for)972 1182 y(a)g(giv)o(en)f
Fj(m)p Fu(.)18 b(This)c(requires)h(that)1005 1270 y Fj(x)1029
1253 y Fh(\003)1047 1270 y Fu(\()p Fj(m)p Fu(\))e(=)f Fj(F)6
b Fu(\()p Fj(x)1245 1253 y Fh(\003)1263 1270 y Fu(\()p Fj(m)p
Fu(\))p Fj(;)h(m)p Fu(\))28 b(and)g Fi(j)7 b Fj(@)1566 1276
y Fv(1)1584 1270 y Fj(F)f Fu(\()p Fj(x)1657 1253 y Fh(\003)1675
1270 y Fu(\()p Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\))g Fi(j)12 b
Fj(<)g Fu(1)p Fj(:)32 b Fu(\(2\))972 1359 y(Di\013eren)o(tiating)12
b(b)q(oth)i(Eqs.\(1\))f(and)g(\(2\),)f(w)o(e)i(get)f(the)h(follo)o(wing)972
1409 y(result.)1076 1501 y Fj(x)1100 1486 y Fh(\003)1119 1482
y(0)1131 1501 y Fu(\()p Fj(m)p Fu(\)\(1)c Fi(\000)f Fj(@)1309
1507 y Fv(1)1328 1501 y Fj(F)d Fu(\()p Fj(x)1401 1486 y Fh(\003)1419
1501 y Fu(\()p Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\)\))13 b(=)f Fj(@)1653
1507 y Fv(2)1671 1501 y Fj(F)6 b Fu(\()p Fj(x)1744 1486 y Fh(\003)1763
1501 y Fu(\()p Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\))1076 1570 y
Fj(x)1100 1555 y Fh(0)1100 1581 y Fg(n)p Fv(+1)1176 1570 y
Fu(=)12 b Fj(x)1244 1555 y Fh(0)1244 1581 y Fg(n)1267 1570
y Fj(@)1289 1576 y Fv(1)1307 1570 y Fj(F)6 b Fu(\()p Fj(x)1380
1576 y Fg(n)1402 1570 y Fj(;)h(m)p Fu(\))i(+)h Fj(@)1546 1576
y Fv(2)1565 1570 y Fj(F)c Fu(\()p Fj(x)1638 1576 y Fg(n)1659
1570 y Fj(;)h(m)p Fu(\))28 b Fj(;)990 1663 y Fu(where)18 b(primes)f(denote)i
(di\013eren)o(tiation)e(with)h(resp)q(ect)i(to)d Fj(m)p Fu(,)972
1713 y(and)11 b Fj(@)1072 1719 y Fg(k)1104 1713 y Fu(means)g(di\013eren)o
(tiation)h(with)f(resp)q(ect)j(to)d(the)h Fj(k)1867 1698 y
Fv(th)1912 1713 y Fu(argu-)972 1763 y(men)o(t.)17 b(The)c(defect)h(b)q(et)o
(w)o(een)g Fj(x)1480 1748 y Fh(0)1480 1773 y Fg(n)p Fv(+1)1556
1763 y Fu(and)f Fj(x)1660 1748 y Fh(\003)1679 1744 y(0)1690
1763 y Fu(\()p Fj(m)p Fu(\))h(can)e(therefore)972 1813 y(b)q(e)i(estimated)g
(as)g(follo)o(ws.)972 1901 y Fj(x)996 1884 y Fh(0)996 1911
y Fg(n)p Fv(+1)1070 1901 y Fi(\000)9 b Fj(x)1135 1884 y Fh(\003)1154
1881 y(0)1166 1901 y Fu(\()p Fj(m)p Fu(\))j(=)g(\()7 b Fj(x)1337
1884 y Fh(0)1337 1911 y Fg(n)1368 1901 y Fi(\000)j Fj(x)1434
1884 y Fh(\003)1453 1881 y(0)1464 1901 y Fu(\()p Fj(m)p Fu(\))d(\))g
Fj(@)1584 1907 y Fv(1)1604 1901 y Fj(F)f Fu(\()p Fj(x)1677
1907 y Fg(n)1698 1901 y Fj(;)h(m)p Fu(\))1110 1968 y Fi(\000)1152
1934 y Ff(\002)1176 1968 y Fj(x)1200 1951 y Fh(\003)1219 1948
y(0)1231 1968 y Fu(\()p Fj(m)p Fu(\)\(1)i Fi(\000)h Fj(@)1409
1974 y Fv(1)1428 1968 y Fj(F)c Fu(\()p Fj(x)1501 1974 y Fg(n)1522
1968 y Fj(;)h(m)p Fu(\)\))j Fi(\000)f Fj(@)1682 1974 y Fv(2)1701
1968 y Fj(F)d Fu(\()p Fj(x)1774 1974 y Fg(n)1796 1968 y Fj(;)h(m)p
Fu(\))1874 1934 y Ff(\003)1014 2036 y Fi(\031)41 b Fu(\()7
b Fj(x)1134 2019 y Fh(0)1134 2046 y Fg(n)1166 2036 y Fi(\000)i
Fj(x)1231 2019 y Fh(\003)1250 2015 y(0)1262 2036 y Fu(\()p
Fj(m)p Fu(\))e(\))g Fj(@)1382 2042 y Fv(1)1401 2036 y Fj(F)f
Fu(\()p Fj(x)1474 2019 y Fh(\003)1493 2036 y Fu(\()p Fj(m)p
Fu(\))p Fj(;)h(m)p Fu(\))1110 2098 y Fi(\000)1152 2064 y Ff(\002)1176
2098 y Fj(x)1200 2081 y Fh(\003)1219 2078 y(0)1231 2098 y Fu(\()p
Fj(m)p Fu(\)\(1)i Fi(\000)h Fj(@)1409 2104 y Fv(1)1428 2098
y Fj(F)c Fu(\()p Fj(x)1501 2081 y Fh(\003)1519 2098 y Fu(\()p
Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\)\))j Fi(\000)g Fj(@)1748 2104
y Fv(2)1766 2098 y Fj(F)c Fu(\()p Fj(x)1839 2081 y Fh(\003)1858
2098 y Fu(\()p Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\))2004 2064 y
Ff(\003)1014 2166 y Fu(=)41 b(\()7 b Fj(x)1134 2149 y Fh(0)1134
2176 y Fg(n)1166 2166 y Fi(\000)i Fj(x)1231 2149 y Fh(\003)1250
2145 y(0)1262 2166 y Fu(\()p Fj(m)p Fu(\))e(\))g Fj(@)1382
2172 y Fv(1)1401 2166 y Fj(F)f Fu(\()p Fj(x)1474 2149 y Fh(\003)1493
2166 y Fu(\()p Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\))972 2254 y(As)15
b(long)f(as)h(Eq.\(2\))g(is)f(satis\014ed,)i(i.e.,)d(as)i(long)f(as)h(the)h
Fe(original)972 2304 y(se)n(quenc)n(e)i(c)n(onver)n(ges)g(to)g(a)g(\014xe)n
(d)g(p)n(oint,)g Fu(the)f(defect)h(decreases)972 2354 y(and)9
b(lim)1106 2360 y Fg(n)p Fh(!1)1202 2354 y Fj(x)1226 2339 y
Fh(0)1226 2364 y Fg(n)1260 2354 y Fu(=)i Fj(x)1327 2339 y Fh(\003)1346
2336 y(0)1358 2354 y Fu(\()p Fj(m)p Fu(\))p Fj(:)f Fu(Higher)g(deriv)n(ativ)o
(es)f(w)o(ork)g(as)h(w)o(ell.)972 2404 y(The)k(imp)q(ortan)o(t)e(thing)i(is)g
(to)f(recognize)i(that)f(sim)o(ultaneously)m(,)1002 2492 y
Fj(x)1026 2475 y Fh(\003)p Fv([)p Fg(k)q Fv(])1082 2492 y Fu(\()p
Fj(m)p Fu(\)\(1)c Fi(\000)g Fj(@)1261 2498 y Fv(1)1279 2492
y Fj(F)c Fu(\()p Fj(x)1352 2475 y Fh(\003)1371 2492 y Fu(\()p
Fj(m)p Fu(\))p Fj(;)h(m)p Fu(\)\))1085 2555 y(=)12 b(\003\()p
Fj(x)1198 2538 y Fh(\003)p Fv([)p Fg(k)q Fh(\000)p Fv(1])1297
2555 y Fu(\()p Fj(m)p Fu(\))p Fj(;)7 b(x)1408 2538 y Fh(\003)p
Fv([)p Fg(k)q Fh(\000)p Fv(2])1506 2555 y Fu(\()p Fj(m)p Fu(\))p
Fj(;)g(:)g(:)g(:)f(;)h(x)1692 2538 y Fh(\003)1710 2555 y Fu(\()p
Fj(m)p Fu(\))p Fj(;)g(m)p Fu(\))28 b Fj(;)21 b Fu(and)1002
2625 y Fj(x)1026 2604 y Fv([)p Fg(k)q Fv(])1026 2636 y Fg(n)p
Fv(+1)1102 2625 y Fu(=)12 b Fj(x)1170 2608 y Fv([)p Fg(k)q
Fv(])1170 2635 y Fg(n)1209 2625 y Fj(@)1231 2631 y Fv(1)1250
2625 y Fj(F)6 b Fu(\()p Fj(x)1323 2631 y Fg(n)1345 2625 y Fj(;)h(m)p
Fu(\))i(+)g(\003\()p Fj(x)1535 2608 y Fv([)p Fg(k)q Fh(\000)p
Fv(1])1535 2635 y Fg(n)1617 2625 y Fj(;)e(x)1660 2608 y Fv([)p
Fg(k)q Fh(\000)p Fv(2])1660 2635 y Fg(n)1741 2625 y Fj(;)g(:)g(:)g(:)t(;)g(x)
1857 2631 y Fg(n)1879 2625 y Fj(;)g(m)p Fu(\))28 b Fj(:)972
2714 y Fu(The)20 b(demonstration)f(of)g(a)h(con)o(v)o(ergen)o(t)g(sequence)i
(then)f(go)q(es)972 2764 y(through)f(exactly)h(as)f(with)h(the)g(\014rst)g
(deriv)n(ativ)o(e.)37 b(The)21 b Fe(only)1885 3075 y Fu(P)o(age)14
b(1)p eop
%%Page: 2 3
bop -114 -15 a Fe(c)n(ondition)16 b Fu(that)c(en)o(ters)i(in)o(to)d(pla)o(y)h
(is)g(Eq.\(2\),)f(whic)o(h)i(is)f(nothing)-114 35 y(more)e(than)h(the)h
(original)d(requiremen)o(t)i(of)g(con)o(v)o(ergence.)19 b(These)-114
85 y(argumen)o(ts)d(still)f(go)h(through)h(for)f(a)g(dimension)f(greater)j
(than)-114 135 y(one,)13 b(but)g(the)g(condition)f(Eq.\(2\))h(b)q(ecomes)g(a)
f(statemen)o(t)h(ab)q(out)-114 184 y(the)h(sp)q(ectral)i(radius)d(of)h(the)g
(Jacobian,)f Fj(@)r(F)p 542 191 57 2 v 542 199 V 6 w Fu(\()p
Fj(x)p 615 191 24 2 v -15 x Fh(\003)658 184 y Fu(\()p Fj(m)p
674 191 37 2 v 1 w Fu(\))p Fj(;)7 b(m)p 746 191 V Fu(\))p Fj(:)44
322 y Fp(I)r(I)r(I.)66 b(Implicit)23 b(functions)-114 412 y
Fu(Consider)10 b(the)g(function)f Fj(x)p Fu(\()p Fj(m)p Fu(\))h(de\014ned)h
(implicitly)6 b(b)o(y)k(the)g(equa-)-114 462 y(tion)180 512
y Fj(x)p Fu(\()p Fj(m)p Fu(\))i(=)g(cos\()7 b Fj(m)j Fi(\001)f
Fj(x)p Fu(\()p Fj(m)p Fu(\))e(\))28 b Fj(:)240 b Fu(\(3\))-114
587 y(Simple)18 b(recursion)j(can)f(b)q(e)h(used)f(to)g(construct)i
Fj(x)p Fu(\()p Fj(m)p Fu(\))e(for)g Fj(m)-114 636 y Fu(in)11
b(the)i(appro)o(ximate)d(range,)h Fj(m)h Fi(2)g Fu(\()p Fi(\000)p
Fu(1)p Fj(:)p Fu(2)p Fj(;)7 b Fu(1)p Fj(:)p Fu(2\))n(,)k(determined)h(b)o(y)
-114 686 y(the)f(condition)e Fi(j)p Fj(m)e Fu(sin\()g Fj(m)i
Fi(\001)g Fj(x)p Fu(\()p Fj(m)p Fu(\))e(\))p Fi(j)12 b Fj(<)g
Fu(1)p Fj(:)d Fu(A)h(fragmen)o(t)e(of)i(source)-114 736 y(co)q(de)16
b(that)f(uses)h(the)g(MXYZPTLK)g Fo(DA)f Fu(ob)r(ject)g(\(class\))h(to)f(im-)
-114 786 y(plemen)o(t)e(this)h(is)g(sho)o(wn)g(b)q(elo)o(w.)-114
891 y Fd(coord)k(m)h(\()g(0.5)g(\);)-114 936 y(DA)g(x;)-114
982 y(x)g(=)g(cos\()g(m)g(\);)-114 1028 y(for\()f(i)h(=)h(0;)e(i)i(<)f(15;)f
(i++)h(\))g(x)g(=)g(cos\()f(m)i(*)f(x)g(\);)-114 1112 y Fu(This)12
b(example)e(used)j(a)f Fo(coord)e Fu(v)n(ariable)h(for)h Fj(m)p
Fu(,)g(set)h(to)e(ev)n(aluate)-114 1162 y(deriv)n(ativ)o(es)i(of)g
Fj(x)p Fu(\()p Fj(m)p Fu(\))g(at)g Fj(m)f Fu(=)g(0)p Fj(:)p
Fu(5)p Fj(:)g Fo(coord)p Fu(s)h(are)g(the)h(atomic)d Fo(DA)-114
1211 y Fu(v)n(ariables)17 b(used)h(to)f(start)h(calculations,)g(basically)e
(the)i(imple-)-114 1261 y(men)o(tation)d(of)h(a)g(pro)r(jector.)28
b(The)17 b(b)q(eha)o(vior)g(of)f(the)h(w)o(eigh)o(ted)-114
1311 y(deriv)n(ativ)o(es)d(|)g(whic)o(h)g(w)o(ould)g(b)q(e)h(the)g(co)q
(e\016cien)o(ts)h(in)e(a)g(p)q(o)o(w)o(er)-114 1361 y(series)g(represen)o
(tation)h(of)e Fj(x)p Fu(\()p Fj(m)p Fu(\))g(|)g(is)g(sho)o(wn)g(in)g(Figure)
g(1;)f(the)-114 1411 y(\014rst)19 b(\014v)o(e)g(are)g(plotted)g(v)o(ersus)h
(lo)q(op)e(index.)32 b(Con)o(v)o(ergence)20 b(is)-114 1460
y(seen)d(to)g(b)q(e)f(rapid,)g(although,)g(as)g(suggested)i(b)o(y)e(the)g
(pro)q(of,)g(a)-114 1510 y(deriv)n(ativ)o(e)i(do)q(es)i(not)f(b)q(egin)g(to)g
(con)o(v)o(erge)h(un)o(til)e(the)h(ones)h(at)-114 1560 y(lo)o(w)o(er)14
b(order)g(ha)o(v)o(e)g(already)f(done)i(so.)51 1697 y Fp(IV.)66
b(Inverse)24 b(functions)-114 1788 y Fu(One)c(of)e(the)i(most)d(frequen)o(t)j
(application)e(of)g(recursion)i(is)f(to)-114 1838 y(compute)11
b(the)h(in)o(v)o(erse)h(of)e(a)g(giv)o(en)h(function.)17 b(F)m(or)11
b(example,)f(ap-)-114 1888 y(plying)k(Newton's)i(metho)q(d)e(to)i(the)g
(equation)e(tan\()p Fj(x)p Fu(\()p Fj(m)p Fu(\)\))f(=)f Fj(m)-114
1938 y Fu(pro)o(vides)i(the)h(recursion)36 2029 y Fj(x)60 2035
y Fg(n)p Fv(+1)136 2029 y Fu(=)d Fj(x)204 2035 y Fg(n)235 2029
y Fi(\000)e Fu(cos)d Fj(x)363 2035 y Fg(n)392 2029 y Fu(\(sin)g
Fj(x)490 2035 y Fg(n)522 2029 y Fi(\000)j Fj(m)d Fu(cos)g Fj(x)693
2035 y Fg(n)716 2029 y Fu(\))28 b Fj(;)-114 2116 y Fu(whic)o(h)18
b(con)o(v)o(erges)h(to)e(the)i(function)e Fj(x)p Fu(\()p Fj(m)p
Fu(\))12 b(=)g(arctan)7 b Fj(m:)813 2101 y Fv(3)850 2116 y
Fu(The)-114 2161 y(recursion)22 b(can)g(b)q(e)g(applied)e Fe(dir)n(e)n(ctly)k
Fu(to)d Fo(DA)g Fu(v)n(ariables.)40 b(Us-)-114 2207 y(ing)16
b(MXYZPTLK,)i(the)f(follo)o(wing)e(short,)i(simple)f(C)766
2203 y(++)847 2207 y(pro-)-114 2253 y(gram)9 b(follo)o(ws)f(the)j(recursion)h
(explicitly)d(through)h(six)g(steps)i(and)-114 2298 y(prin)o(ts)h(out)g(the)h
(v)n(alue)e(and)h(deriv)n(ativ)o(es)g(of)g Fj(x)f Fu(for)h(a)g(giv)o(en)g(v)n
(alue)-114 2344 y(of)g Fj(m)p Fu(.)-114 2423 y Fd(#include)k("mxyzptl)o(k.r)o
(sc")-114 2468 y(main\()h(int)g(argc,)g(char**)f(argv)h(\))h({)-94
2514 y(const)e(int)38 b(dim)137 b(=)19 b(1;)-94 2560 y(const)e(int)38
b(maxWeight)17 b(=)i(5;)-94 2605 y(DASetup\()d(dim,)i(maxWeight,)e(dim)i(\);)
-94 2651 y(double)f(a)i(=)g(atof\()f(argv[1])f(\);)p -114 2686
414 2 v -68 2712 a Fl(3)-50 2724 y Fm(As)10 b(an)g(acceptable)e(seed,)h(w)o
(e)i(could)e(set)h Fc(x)523 2729 y Fl(0)540 2724 y Fm(\()p
Fc(m)p Fm(\))f(=)h Fc(m)h Fm(when)f Fr(j)p Fc(m)p Fr(j)g(\024)g
Fm(1)p Fc(:)p Fm(4)-114 2764 y(and)h Fc(x)-25 2769 y Fl(0)-8
2764 y Fm(\()p Fc(m)p Fm(\))e(=)h(1)p Fc(:)p Fm(4)h(when)g
Fr(j)p Fc(m)p Fr(j)f Fc(>)g Fm(1)p Fc(:)p Fm(4)p Fc(:)992 -15
y Fd(coord)17 b(m)j(\()f(a)g(\);)992 31 y(DA)f(x,)h(s,)g(c;)992
76 y(int)f(i,)h(j,)g(d[1];)992 122 y(x)g(=)g(m;)992 168 y(for\()f(i)h(=)g(0;)
g(i)g(<)g(6;)g(i++)g(\){)1011 213 y(s)g(=)h(sin\()e(x)h(\);)1011
259 y(c)g(=)h(cos\()e(x)h(\);)1011 305 y(x)g(=)h(x)f(-)g(c*\()g(s)g(-)g(m*c)f
(\);)1011 350 y(printf\()f("\045-7.4lf)36 b(",)19 b(x.standard)o(Pa)o(rt\()o
(\))e(\);)1011 396 y(for\()h(j)i(=)f(1;)g(j)g(<)g(6;)g(j++)f(\))i({)1031
442 y(d[0])e(=)h(j;)1031 487 y(printf\()e("\045-7.4lf)36 b(",)19
b(x.derivat)o(iv)o(e\(d)o(\))e(\);)1011 533 y(})1011 579 y(printf\()g("\\n")h
(\);)992 624 y(})972 670 y(})1014 740 y Fu(When)10 b(compiled)f(and)h(run)h
(with)f(a)g(command)d(line)j(argumen)o(t)972 785 y(of)j(1.2)g(it)h(pro)q
(duced)h(the)f(output)g(lines:)972 855 y Fd(1.0198)57 b(1.0581)f(1.7697)h
(4.7170)f(-1.6753)37 b(-30.666)972 901 y(0.9027)57 b(0.6776)f(1.9990)h
(19.1460)36 b(119.009)h(531.937)972 946 y(0.8769)57 b(0.4280)f(-0.0384)37
b(7.3912)56 b(124.051)37 b(2092.93)972 992 y(0.8761)57 b(0.4099)f(-0.4015)37
b(0.5231)56 b(2.2807)h(101.790)972 1038 y(0.8761)g(0.4098)f(-0.4031)37
b(0.4571)56 b(-0.3575)37 b(-0.8372)972 1083 y(0.8761)57 b(0.4098)f(-0.4031)37
b(0.4571)56 b(-0.3575)37 b(-0.8414)972 1157 y Fu(Notice)19
b(the)h(rep)q(etition)f(of)g(the)g(earlier)g(pattern:)29 b(deriv)n(ativ)o(es)
972 1207 y(settle)19 b(do)o(wn)e(to)g(their)h(limiting)c(v)n(alue)j(in)g
(sequence.)32 b(In)17 b(par-)972 1257 y(ticular,)f(the)g(highest)h(order)g
(deriv)n(ativ)o(es)e(can)i(undergo)f(unset-)972 1306 y(tlingly)10
b(large)i(excursions)h(b)q(efore)f(con)o(v)o(ergence)i(kic)o(ks)e(in.)k(Ho)o
(w-)972 1356 y(ev)o(er,)j(this)e(is)h(not)f(a)g(danger,)h(as)g(ev)n(aluation)
e(of)h(higher)g(order)972 1406 y(deriv)n(ativ)o(es)12 b(could)h(b)q(e)g
(suppressed,)h(if)e(needed,)i(un)o(til)d(the)i(lo)o(w)o(er)972
1456 y(order)i(ones)f(ha)o(v)o(e)g(con)o(v)o(erged.)1014 1501
y(The)c(w)o(onderful)h(thing)f(is)g(that)h(w)o(e)f(could)h(start)g(the)g
(recursion)972 1547 y(using)16 b(an)o(y)g Fo(DA)g Fu(v)n(ariable)g(for)g
Fj(m)p Fu(,)h(not)g(just)f(atomic)f(pro)r(jectors.)972 1593
y(W)m(e)g(could,)h(for)f(example,)g(use)h(a)g(co)q(de)h(fragmen)o(t)d(lik)o
(e)h(the)h(fol-)972 1638 y(lo)o(wing)992 1708 y Fd(coord)h(y)j(\()f(ay)g(\),)
f(z)i(\()f(az)g(\);)992 1754 y(DA)f(m,)h(x,)g(s,)g(c;)992 1799
y(m)g(=)g(sqrt\()f(y*y)g(+)h(z*z)g(\);)992 1845 y(x)g(=)g(m;)992
1891 y(while\()e(x.isChang)o(ing)o(\(\))f(\){)1011 1936 y(s)j(=)h(sin\()e(x)h
(\);)1011 1982 y(c)g(=)h(cos\()e(x)h(\);)1011 2028 y(x)g(=)h(x)f(-)g(c*\()g
(s)g(-)g(m*c)f(\);)992 2073 y(})972 2147 y Fu(to)33 b(\014nd)g(deriv)n(ativ)o
(es)h(of)e(arctan)1559 2111 y Ff(p)p 1601 2111 131 2 v 36 x
Fj(y)1622 2135 y Fv(2)1651 2147 y Fu(+)9 b Fj(z)1713 2135 y
Fv(2)1765 2147 y Fu(ev)n(aluated)33 b(at)972 2197 y(\()p Fj(y)q(;)7
b(z)r Fu(\))12 b(=)g(\(a)o(y)p Fj(;)7 b Fu(az\))p Fj(:)17 b
Fu(This)h(little)f(lo)q(op)g(th)o(us)i(b)q(ecomes)f(the)g(com-)972
2247 y(putational)c(core)i(of)e(a)h Fo(DA)f Fu(-v)n(alued)g(function)h(that)g
(returns)h(the)972 2297 y(arctangen)o(t)f(of)e(an)o(y)g Fo(DA)h
Fu(argumen)o(t.)1122 2432 y Fp(V.)66 b(A)22 b(general)h(pr)o(ogram)972
2519 y Fu(Because)c Fo(DA)d Fu(v)n(ariables)g(p)q(ossess)j(a)e(di\013eren)o
(tiation)g(op)q(eration,)972 2564 y(Newton's)e(metho)q(d)e(can)i(b)q(e)f
(used)i(to)e(write)g(a)g(general)h(metho)q(d)972 2610 y(that)e(w)o(orks)g
(with)f(\\arbitrary")g Fo(DA)h Fu(functions)f Fj(F)6 b Fu(.)17
b(The)d(k)o(ey)e(line)972 2656 y(that)i(sets)h(up)f(the)h(solution)1419
2641 y Fv(4)p 972 2686 414 2 v 1018 2712 a Fl(4)1036 2724 y
Fm(This)e(is)f(written)g(ine\016cien)o(tly;)g(it)g(w)o(ould)h(b)q(e)f(b)q
(etter)g(to)g(a)o(v)o(oid)g(ev)n(alu-)972 2764 y(ating)e Fk(F)i
Fm(t)o(wice.)1885 3075 y Fu(P)o(age)i(2)p eop
%%Page: 3 4
bop 197 994 a @beginspecial 0 @llx 0 @lly 360 @urx 252 @ury
3600 @rwi @setspecial
%%BeginDocument: theFigure.ps
40 dict begin
/gnulinewidth 2.500 def
/vshift -23 def
/dl {10 mul} def
/hpt 15.5 def
/vpt 15.5 def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke moveto
  0 vshift rmoveto show } def
/Rshow { currentpoint stroke moveto
  dup stringwidth pop neg vshift rmoveto show } def
/Cshow { currentpoint stroke moveto
  dup stringwidth pop -2 div vshift rmoveto show } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 setdash } def
/LTa { AL [1 dl 2 dl] 0 setdash } def
/LT0 { PL [] 0 setdash } def
/LT1 { PL [4 dl 2 dl] 0 setdash } def
/LT2 { PL [2 dl 3 dl] 0 setdash } def
/LT3 { PL [1 dl 1.5 dl] 0 setdash } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 setdash } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 0 setdash } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 setdash } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0 setdash } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0 setdash } def
/M {moveto} def
/L {lineto} def
/P {  LT0
  currentlinewidth 2 div sub moveto
  0 currentlinewidth rlineto  stroke } def
/D {  LT0  2 copy  vpt add moveto
  hpt neg vpt neg rlineto  hpt vpt neg rlineto
  hpt vpt rlineto  hpt neg vpt rlineto  closepath  stroke
  P  } def
/A {  LT0  vpt sub moveto  0 vpt2 rlineto
  currentpoint stroke moveto
  hpt neg vpt neg rmoveto  hpt2 0 rlineto stroke
  } def
/B {  LT0  2 copy  exch hpt sub exch vpt add moveto
  0 vpt2 neg rlineto  hpt2 0 rlineto  0 vpt2 rlineto
  hpt2 neg 0 rlineto  closepath  stroke
  P  } def
/C {  LT0  exch hpt sub exch vpt add moveto
  hpt2 vpt2 neg rlineto  currentpoint  stroke  moveto
  hpt2 neg 0 rmoveto  hpt2 vpt2 rlineto stroke  } def
/T {  LT0  2 copy  vpt 1.12 mul add moveto
  hpt neg vpt -1.62 mul rlineto
  hpt 2 mul 0 rlineto
  hpt neg vpt 1.62 mul rlineto  closepath  stroke
  P  } def
/S {  LT0  2 copy A C} def
/Gnu_save save def
0.100 0.100 scale
0 setgray
/Courier findfont 70 scalefont setfont
newpath
LTa
504 1015 M
3485 1015 L
504 176 M
504 2414 L
LTb
LTa
504 176 M
3485 176 L
LTb
504 176 M
535 176 L
3485 176 M
3454 176 L
462 176 M
(-0.6) Rshow
LTa
504 456 M
3485 456 L
LTb
504 456 M
535 456 L
3485 456 M
3454 456 L
462 456 M
(-0.4) Rshow
LTa
504 736 M
3485 736 L
LTb
504 736 M
535 736 L
3485 736 M
3454 736 L
462 736 M
(-0.2) Rshow
LTa
504 1015 M
3485 1015 L
LTb
504 1015 M
535 1015 L
3485 1015 M
3454 1015 L
462 1015 M
(0) Rshow
LTa
504 1295 M
3485 1295 L
LTb
504 1295 M
535 1295 L
3485 1295 M
3454 1295 L
462 1295 M
(0.2) Rshow
LTa
504 1575 M
3485 1575 L
LTb
504 1575 M
535 1575 L
3485 1575 M
3454 1575 L
462 1575 M
(0.4) Rshow
LTa
504 1855 M
3485 1855 L
LTb
504 1855 M
535 1855 L
3485 1855 M
3454 1855 L
462 1855 M
(0.6) Rshow
LTa
504 2134 M
3485 2134 L
LTb
504 2134 M
535 2134 L
3485 2134 M
3454 2134 L
462 2134 M
(0.8) Rshow
LTa
504 2414 M
3485 2414 L
LTb
504 2414 M
535 2414 L
3485 2414 M
3454 2414 L
462 2414 M
(1) Rshow
LTa
504 176 M
504 2414 L
LTb
504 176 M
504 207 L
504 2414 M
504 2383 L
504 106 M
(0) Cshow
LTa
1100 176 M
1100 2414 L
LTb
1100 176 M
1100 207 L
1100 2414 M
1100 2383 L
1100 106 M
(2) Cshow
LTa
1696 176 M
1696 2414 L
LTb
1696 176 M
1696 207 L
1696 2414 M
1696 2383 L
1696 106 M
(4) Cshow
LTa
2293 176 M
2293 2414 L
LTb
2293 176 M
2293 207 L
2293 2414 M
2293 2383 L
2293 106 M
(6) Cshow
LTa
2889 176 M
2889 2414 L
LTb
2889 176 M
2889 207 L
2889 2414 M
2889 2383 L
2889 106 M
(8) Cshow
LTa
3485 176 M
3485 2414 L
LTb
3485 176 M
3485 207 L
3485 2414 M
3485 2383 L
3485 106 M
(10) Cshow
LTb
504 176 M
3485 176 L
3485 2414 L
504 2414 L
504 176 L
2889 1057 M
(5th coefficient) Lshow
2889 791 M
(4th coefficient) Lshow
2889 1435 M
(3rd coefficient) Lshow
2889 945 M
(2nd coefficient) Lshow
2889 610 M
(1st coefficient) Lshow
LT0
LT0
504 2275 M
504 2275 L
802 2275 L
1100 2275 L
1398 2275 L
1696 2275 L
1995 2275 L
2293 2275 L
2591 2275 L
2889 2275 L
3187 2275 L
3485 2275 L
3485 2275 L
LT1
504 586 M
504 586 L
802 561 L
1100 566 L
1398 565 L
1696 565 L
1995 565 L
2293 565 L
2591 565 L
2889 565 L
3187 565 L
3485 565 L
3485 565 L
LT2
504 1052 M
504 1052 L
802 842 L
1100 908 L
1398 889 L
1696 894 L
1995 893 L
2293 893 L
2591 893 L
2889 893 L
3187 893 L
3485 893 L
3485 893 L
LT3
504 1766 M
504 1766 L
802 1154 L
1100 1461 L
1398 1341 L
1696 1382 L
1995 1369 L
2293 1373 L
2591 1372 L
2889 1372 L
3187 1372 L
3485 1372 L
3485 1372 L
LT4
504 994 M
504 994 L
802 328 L
1100 1030 L
1398 616 L
1696 806 L
1995 731 L
2293 758 L
2591 749 L
2889 751 L
3187 751 L
3485 751 L
3485 751 L
LT5
504 675 M
504 675 L
802 752 L
1100 1459 L
1398 659 L
1696 1197 L
1995 918 L
2293 1042 L
2591 993 L
2889 1011 L
3187 1004 L
3485 1006 L
3485 1006 L
stroke
Gnu_save restore
showpage
end
%%EndDocument
 @endspecial 389 1085 a Fu(Figure)14 b(1:)j(Beha)o(vior)d(of)f(the)i(co)q
(e\016cien)o(ts)g(with)f(iteration)f(n)o(um)o(b)q(er.)-114
1218 y Fd(G)19 b(=)g(x)h(-)f(\()g(F\(x\))f(/)h(F\(x\).D\(n\))e(\);)-114
1289 y Fu(where)d Fo(G)f Fu(and)g Fo(x)g Fu(are)g Fo(DA)g Fu(v)n(ariables,)f
Fo(F)h Fu(is)g(a)f Fo(DA)h Fu(-v)n(alued)f(function)-114 1335
y(of)g(a)g Fo(DA)h Fu(argumen)o(t,)e(and)i Fb(.D)f Fu(is)h(the)g(di\013eren)o
(tiation)f(op)q(erator.)902 1319 y Fv(5)-114 1380 y Fo(G)j
Fu(will)e(b)q(e)i(a)g Fo(DA)f Fu(v)n(ariable)g(corresp)q(onding)i(to)e(a)h
(single)f(Newton)-114 1426 y(step.)19 b(Once)c(it)f(is)f(constructed,)j
(iterating)d(the)i(line)-114 1497 y Fd(x)k(=)g(G.multiEval)o(\()d(x)k(\);)
-114 1569 y Fu(will)12 b(mak)o(e)g Fo(x)p Fu(,)h(with)g(all)g(its)g(deriv)n
(ativ)o(es,)g(con)o(v)o(erge)h(to)g(a)f(zero)i(of)-114 1614
y Fo(F)p Fu(.)e(T)m(o)g(rep)q(eat)i(the)g(example)d(of)i(Eq.\(3\),)f(w)o(e)h
(then)g(de\014ne)-114 1686 y Fd(DA)19 b(F\()g(DA&)f(x)h(\))h({)f(return)e(\()
i(x)h(-)f(cos\()f(m*x)g(\))i(\);)e(})-114 1761 y Fu(b)q(efore)j(en)o(tering)h
(the)f(main)e(function.)38 b(The)21 b(complete)f(pro-)-114
1811 y(gram,)25 b(although)e(short)i(\(ab)q(out)f(60)g(lines\))g(is)g(to)q(o)
g(long)f(to)-114 1861 y(b)q(e)30 b(included)f(here.)64 b(F)m(or)29
b(those)g(w)o(ould)f(lik)o(e)h(to)f(exp)q(eri-)-114 1911 y(men)o(t)c(with)h
(the)h(program)e(and)h(who)g(ha)o(v)o(e)g(a)h(C)744 1907 y(++)833
1911 y(com-)-114 1961 y(piler,)34 b(it)29 b(and)h(the)h(MXYZPTLK)g(pac)o(k)n
(age)f(can)h(b)q(e)f(ob-)-114 2010 y(tained)e Fe(as)g(is)j
Fu(via)d(anon)o(ymous)e(ftp)i(from)e(calvin.fnal.go)o(v)-114
2060 y(in)20 b(the)i(directory)g(/pub/outgoing/m)o(ic)o(helotti/m)n(xyzptlk)c
(or)-114 2110 y(/pub/outgoing/mi)o(c)o(helotti/b)q(eam)o(li)o(ne.)553
2095 y Fv(6)229 2246 y Fp(References)-114 2337 y Fu([1])i(Martin)25
b(Berz.)54 b(Di\013eren)o(tial)25 b(algebraic)f(description)j(of)-49
2386 y(b)q(eam)16 b(dynamics)h(to)h(v)o(ery)g(high)f(orders.)31
b Fe(Particle)18 b(A)n(c)n(c)n(el-)-49 2436 y(er)n(ators)p
Fu(,)12 b(24\(2\):109,)g(Marc)o(h)i(1989.)-114 2515 y([2])20
b(G.)14 b(Corliss)h(and)g(A.)g(Griew)o(ank,)f(editors,)23 b
Fe(A)o(utomatic)16 b(Dif-)-49 2565 y(fer)n(entiation)i(of)g(A)o(lgorithms:)25
b(The)n(ory,)19 b(Implementation,)-49 2615 y(and)c(Applic)n(ation.)f
Fu(SIAM,)f(1991.)k(Philadelphia,)12 b(P)m(A.)p -114 2646 414
2 v -68 2673 a Fl(5)-50 2685 y Fk(n)f Fm(is)h(an)f(in)o(teger)f(arra)o(y)g
(needed)g(b)o(y)h Fa(.D)p Fm(;)h(essen)o(tially)m(,)d Fk(n)j
Fm(tells)f Fk(.D)g Fm(whic)o(h)-114 2724 y(deriv)n(ativ)o(e)e(is)i(desired.)
-68 2752 y Fl(6)-50 2764 y Fm(These)g(\014les)f(ma)o(y)h(b)q(e)g(mo)o(v)o(ed)
f(ev)o(en)o(tually)l(.)972 1218 y Fu([3])20 b(Etienne)f(F)m(orest,)g(Martin)g
(Berz,)h(and)e(John)h(Irwin.)31 b(Nor-)1037 1267 y(mal)14 b(form)i(metho)q
(ds)g(for)h(complicated)f(p)q(erio)q(dic)h(systems:)1037 1317
y(A)e(complete)f(solution)h(using)g(di\013eren)o(tial)g(algebra)f(and)h(lie)
1037 1367 y(op)q(erators.)j Fe(Particle)d(A)n(c)n(c)n(eler)n(ators)p
Fu(,)c(24:91,)h(1989.)972 1450 y([4])20 b(Jean)d(Charles)g(Gilb)q(ert.)27
b(Automatic)15 b(di\013eren)o(tiation)i(and)1037 1500 y(iterativ)o(e)e(pro)q
(cesses.)26 b Fe(Optimization:)c(Metho)n(ds)17 b(and)g(Soft-)1037
1550 y(war)n(e)p Fu(,)12 b(1\(1\):13{21,)g(1992.)972 1633 y([5])20
b(Leo)12 b(Mic)o(helotti.)k(MXYZPTLK)e(and)e(BEAMLINE:)h(C)1942
1629 y(++)1037 1682 y(ob)r(jects)23 b(for)f(b)q(eam)g(ph)o(ysics.)44
b(In)22 b Fe(A)n(dvanc)n(e)n(d)i(Be)n(am)f(Dy-)1037 1732 y(namics)e(Workshop)
h(on)g(E\013e)n(cts)g(of)f(Err)n(ors)f(in)h(A)n(c)n(c)n(eler)n(a-)1037
1782 y(tors,)12 b(their)g(Diagnosis)h(and)g(Corr)n(e)n(ction.)e(\(Corpus)i
(Christi,)1037 1832 y(T)m(exas.)27 b(Octob)n(er)g(3-8,)j(1991\))p
Fu(.)e(American)f(Institute)i(of)1037 1882 y(Ph)o(ysics,)14
b(1992.)j(Conference)e(Pro)q(ceedings)h(No.255.)972 1965 y([6])k(|)-14
b(|)g(|)g(|)15 b(MXYZPTLK:)f(A)g(practical,)f(user-friendly)h(C)1942
1961 y(++)1037 2015 y(implem)o(en)o(tation)h(of)j(di\013eren)o(tial)f
(algebra:)26 b(User's)20 b(guide.)1037 2064 y(F)m(ermi)12 b(Note)i(FN-535,)f
(F)m(ermilab,)e(Jan)o(uary)j(31,)f(1990.)972 2147 y([7])20
b(|)-7 b(|)g(|)g(|)27 b(A)17 b(note)h(on)f(the)h(automated)e(di\013eren)o
(tiation)i(of)1037 2197 y(implicit)d(functions.)32 b(T)m(ec)o(hnical)18
b(Memo)g(1742,)g(F)m(ermilab,)1037 2247 y(June,)c(1991.)972
2330 y([8])20 b(Gordon)13 b(Pusc)o(h.)19 b(Priv)n(ate)14 b(comm)o(unicati)o
(on.)972 2413 y([9])20 b(Joseph)k(F)m(els)g(Ritt.)47 b Fe(Di\013er)n(ential)
23 b(A)o(lgebr)n(a)p Fu(.)47 b(American)1037 2463 y(Mathematical)12
b(So)q(ciet)o(y)m(,)h(New)h(Y)m(ork,)f(1950.)1885 3075 y(P)o(age)h(3)p
eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
End of ad.ps
