Quelle  manual.ps   Sprache: unbekannt

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%%Title: manual.dvi
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% The idea is to have all the characters normally included in Type 1 fonts
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% 
% Character code assignments were made as follows:
% 
% (1) the Windows ANSI characters are almost all in their Windows ANSI
% positions, because some Windows users cannot easily reencode the
% fonts, and it makes no difference on other systems. The only Windows
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% 
% (2) Remaining characters are assigned arbitrarily to the lower part
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
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% (4) hyphen appears twice for compatibility with both ASCII and Windows.
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% (5) /Euro was assigned to 128, as in Windows ANSI
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%     PostScript      MacRoman        TeXBase1
%     --------------  --------------  --------------
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%     /infinity       176             0x17
%     /lessequal      178             0x18
%     /greaterequal   179             0x19
%     /partialdiff    182             0x1A
%     /summation      183             0x1B
%     /product        184             0x1C
%     /pi             185             0x1D
%     /integral       186             0x81
%     /Omega          189             0x8D
%     /radical        195             0x8E
%     /approxequal    197             0x8F
%     /Delta          198             0x9D
%     /lozenge        215             0x9E
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% 0x00
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% 0x10
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% 0x20
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% 0x30
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% 0x40
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% 0x50
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% 0x70
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 /bar /braceright /asciitilde /.notdef
% 0x80
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% 0x90
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% 0xA0
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% 0xB0
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% 0xC0
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 /Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
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 /Oslash /Ugrave /Uacute /Ucircumflex
 /Udieresis /Yacute /Thorn /germandbls
% 0xE0
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% 0xF0
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%!PS-AdobeFont-1.0: NimbusRomNo9L-Regu 1.05
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% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.0: MSBM10 003.002
%%Title: MSBM10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name MSBM10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/MSBM10 known{/MSBM10 findfont dup/UniqueID known{dup
/UniqueID get 5031982 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /MSBM10 def
/FontBBox {-55 -420 2343 920 }readonly def
/PaintType 0 def
/FontInfo 7 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name MSBM10.) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 81 /Q put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: StandardSymL
%!PS-AdobeFont-1.0: StandardSymL 001.005
%%CreationDate: Thu Oct 21 1999
% Copyright URW Software, Copyright 1997 by URW
% URW Software, Copyright 1997 by URW
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (001.005) readonly def
/Notice (URW Software, Copyright 1997 by URW. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright URW Software, Copyright 1997 by URW) readonly def
/FullName (Standard Symbols L) readonly def
/FamilyName (Standard Symbols L) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -229 def
/UnderlineThickness 46 def
end readonly def
/FontName /StandardSymL def
/PaintType 0 def
/WMode 0 def
/FontBBox {-180 -293 1090 1010} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 70 /Phi put
dup 103 /gamma put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: NimbusRomNo9L-ReguItal
%!PS-AdobeFont-1.0: NimbusRomNo9L-ReguItal 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (Nimbus Roman No9 L Regular Italic) readonly def
/FamilyName (Nimbus Roman No9 L) readonly def
/Weight (Regular) readonly def
/ItalicAngle -15.5 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /NimbusRomNo9L-ReguItal def
/PaintType 0 def
/WMode 0 def
/FontBBox {-169 -270 1010 924} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 59 /comma put
dup 61 /slash put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 61 /equal put
dup 91 /bracketleft put
dup 93 /bracketright put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMTT10
%!PS-AdobeFont-1.0: CMTT10 003.002
%%Title: CMTT10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMTT10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMTT10 known{/CMTT10 findfont dup/UniqueID known{dup
/UniqueID get 5000832 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMTT10 def
/FontBBox {-4 -233 537 696 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMTT10.) readonly def
/FullName (CMTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: MSAM7
%!PS-AdobeFont-1.0: MSAM7 003.002
%%Title: MSAM7
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name MSAM7.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/MSAM7 known{/MSAM7 findfont dup/UniqueID known{dup
/UniqueID get 5032012 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /MSAM7 def
/FontBBox {29 -552 1490 1102 }readonly def
/PaintType 0 def
/FontInfo 7 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name MSAM7.) readonly def
/FullName (MSAM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 73 /trianglerightsld put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.0: CMSY10 003.002
%%Title: CMSY10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup
/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSY10 def
/FontBBox {-29 -960 1116 775 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY10.) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 15 /bullet put
dup 106 /bar put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: NimbusSanL-Regu
%!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a
%%Title: NimbusSanL-Regu
%%CreationDate: Thu Mar 20 10:08:51 2003
%%Creator: Primoz Peterlin
%%DocumentSuppliedResources: font NimbusSanL-Regu
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% Generated by PfaEdit 1.0 (http://pfaedit.sf.net/)
%%EndComments
FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup
/UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /NimbusSanL-Regu def
/FontBBox [-174 -285 1001 953 ]readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (1.05a) readonly def
/Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & Development) readonly def
/FullName (Nimbus Sans L Regular) readonly def
/FamilyName (Nimbus Sans L) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -151 def
/UnderlineThickness 50 def
end readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: NimbusSanL-Bold
%!PS-AdobeFont-1.0: NimbusSanL-Bold 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (Nimbus Sans L Bold) readonly def
/FamilyName (Nimbus Sans L) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -155 def
/UnderlineThickness 69 def
end readonly def
/FontName /NimbusSanL-Bold def
/PaintType 0 def
/WMode 0 def
/FontBBox {-173 -307 1003 949} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: NimbusRomNo9L-Medi
%!PS-AdobeFont-1.0: NimbusRomNo9L-Medi 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (Nimbus Roman No9 L Medium) readonly def
/FamilyName (Nimbus Roman No9 L) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /NimbusRomNo9L-Medi def
/PaintType 0 def
/WMode 0 def
/FontBBox {-168 -341 1000 960} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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%%Page: 2 2
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Fq(1)49 b(Intr)o(oduction)1548 b(3)79 684 y(2)49 b(Methods)11
b(and)g(functions)1366 b(4)48 759 y Fr(2.1)49 b(Functions)10
b(for)f(\002nite)h Fp(p)p Fr(-groups)40 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)99
b(4)48 833 y(2.2)49 b(Functions)10 b(to)f(generate)i(groups)f(and)g
(trees)78 b(.)39 b(.)h(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)f(.)h(.)g(.)99 b(4)48 908 y(2.3)49 b(Example)72
b(.)40 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)f(.)
h(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)99
b(5)149 983 y Fq(Bibliograph)o(y)1539 b(7)p eop end
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TeXDict begin 3 2 bop -30 285 a Fo(1)882 b Ft(Intr)m(oduction)0
519 y Fr(This)10 b(package)i(pro)o(vides)d Fn(GAP)p Fr(-functions)g(to)
g(reproduce)i(the)f(e)o(xperimental)g(results)g(described)g(in)g(our)g
(paper)g([ER09].)0 587 y(More)g(precisely)m(,)h(it)f(pro)o(vides)42
667 y Fm(\017)20 b Fr(functions)9 b(to)h(determine)g(the)g(rank,)h
(width)e(and)h(obliquity)d(of)j(a)h(\002nite)f Fp(p)p
Fr(-group,)42 735 y Fm(\017)20 b Fr(functions)10 b(to)h(in)n(v)o
(estigate)g(the)h(graph)f(of)h(all)f(\002nite)g Fp(p)p
Fr(-groups)f(of)i(a)g(gi)o(v)o(en)f(rank,)h(width)e(and)i(obliquity)d
(using)h(the)i(ANUPQ-)83 784 y(package)f([ONG06],)f(and)42
852 y Fm(\017)20 b Fr(a)11 b(library)e(of)h(\002nite)g(quotients)e(of)i
(certain)g(in\002nite)f(pro-)p Fp(p)p Fr(-groups)g(of)h(\002nite)f
(rank,)i(width)e(and)h(obliquity)m(.)p eop end
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TeXDict begin 4 3 bop -30 290 a Fo(2)1011 107 y Ft(Methods)53
b(and)1270 290 y(functions)0 523 y Fr(This)10 b(chapter)h(describes)g
(all)e(the)i(main)f(methods)g(and)g(functions)f(of)h(this)g(package.)0
641 y Fs(2.1)27 b(Functions)15 b(f)o(or)g(\002nite)g
Fp(p)p Fs(-gr)o(oups)0 733 y Fr(Let)c Fp(G)f Fr(be)h(a)f(\002nite)g
Fp(p)p Fr(-group)f(gi)o(v)o(en)h(by)g(a)h(consistent)e(polyc)o(yclic)h
(presentation)f(as)i(Pc)g(group.)-71 808 y Fk(1)-47 802
y Fj(I)0 808 y Fi(LCSFactorTypes\()19 b(G)i(\))0 888
y Fr(returns)10 b(the)g(abelian)g(in)n(v)o(ariants)f(of)h(the)g(lo)o
(wer)g(central)h(series)g(factors)e(of)h Fp(G)p Fr(.)-71
963 y Fk(2)-47 957 y Fj(I)0 963 y Fi(LCSFactorSizes\()19
b(G)i(\))0 1043 y Fr(returns)10 b(the)g(orders)g(of)g(the)g(lo)o(wer)g
(central)g(series)h(factors)f(of)g Fp(G)p Fr(.)-71 1118
y Fk(3)-47 1112 y Fj(I)0 1118 y Fi(WidthPGroup\()19 b(G)j(\))0
1198 y Fr(returns)10 b(the)g(width)f(of)h Fp(G)p Fr(.)-71
1273 y Fk(4)-47 1267 y Fj(I)0 1273 y Fi(SubgroupRank\()19
b(G)j(\))0 1353 y Fr(returns)10 b(the)g(\(subgroup-\)rank)e(of)i
Fp(G)p Fr(.)-71 1428 y Fk(5)-47 1422 y Fj(I)0 1428 y
Fi(Obliquity\()20 b(G)h(\))0 1508 y Fr(returns)10 b(the)g(obliquity)d
(of)j Fp(G)p Fr(.)-71 1582 y Fk(6)-47 1576 y Fj(I)0 1582
y Fi(HasObliquityZero\()18 b(G)k(\))0 1663 y Fr(checks)11
b(whether)f Fp(G)h Fr(has)f(obliquity)e(0)i(and)g(returns)g(true)g(or)g
(false.)0 1780 y Fs(2.2)27 b(Functions)15 b(to)g(g)q(enerate)f(gr)o
(oups)h(and)g(trees)0 1873 y Fr(Let)g Fp(G)p Fh(\()p
Fp(p)p Ff(;)7 b Fp(rwo)p Fh(\))13 b Fr(denote)h(the)g(full)f(tree)i(of)
f(all)g(\002nite)g Fp(p)p Fr(-groups)f(with)g(rank)h
Fp(rwo)p Fh([)p Fr(1)p Fh(])p Fr(,)f(width)g Fp(rwo)p
Fh([)p Fr(2)p Fh(])g Fr(and)h(obliquity)e Fp(rwo)p Fh([)p
Fr(3)p Fh(])p Fr(.)h(This)0 1923 y(tree)e(can)h(be)f(\002nite)f(or)h
(in\002nite;)e(if)i(it)f(is)g(in\002nite,)g(then)h(the)g(in\002nite)e
(pro-)p Fp(p)p Fr(-groups)g(of)i(the)f(considered)h(rank,)g(width)f
(and)h(obliquity)0 1972 y(specify)f(in\002nite)f(subtrees)i(of)f(the)g
(full)f(tree.)i(The)g(groups)e(not)g(contained)h(in)g(such)g(an)h
(in\002nite)e(subtree)h(are)h(called)g(sporadic.)-71
2047 y Fk(1)-47 2041 y Fj(I)0 2047 y Fi(GroupsByRankWidth)o(Obliq)o
(uity\()18 b(p,)k(d,)f(rwo,)g(roots,)f(limit)h(\))0 2127
y Fr(determines)13 b(all)f Fp(p)p Fr(-groups)f Fp(G)h
Fr(with)f Fp(G)p Ff(=)p Fl(F)p Fh(\()p Fp(G)p Fh(\))h
Fr(of)g(order)g Fp(p)862 2112 y Fe(d)892 2127 y Fr(and)g(rank,)h(width)
e(and)h(obliquity)d(as)k(prescribed)g(in)e Fp(rwo)h Fr(up)g(to)g(order)
0 2177 y Fp(limit)q Fr(.)d(Here)i Fp(p)f Fr(and)g Fp(d)h
Fr(are)g(inte)o(gers,)g Fp(rwo)f Fr(is)g(a)h(list)e(of)h(three)g(inte)o
(gers)g(and)h Fp(limit)e Fr(is)h(an)h(inte)o(ger)n(.)0
2245 y(The)f(parameter)g Fp(r)n(oots)f Fr(is)g(a)h(list)e(of)h(groups)f
(described)i(by)e(their)h(id')n(s)f(with)g(respect)i(to)f(the)g(small)g
(groups)g(library)m(.)f(The)i(descendants)0 2295 y(of)i(the)g(groups)f
(described)i(in)e Fp(r)n(oots)h Fr(are)h(e)o(xcluded)g(from)f(the)g
(output)e(of)i(this)f(function.)g(This)h(option)f(can)i(be)f(used)h(to)
e(prune)h(the)0 2344 y(tree)f(of)f(groups)f(determined)h(by)g(this)f
(function.)0 2412 y(If)i(there)f(are)i(only)e(\002nitely)f(man)o(y)j
(sporadic)e Fp(p)p Fr(-groups)g(with)f(gi)o(v)o(en)i(rank,)g(width)e
(and)i(obliquity)m(,)e(then)h(this)g(function)f(can)j(be)f(used)0
2462 y(to)e(generate)i(them;)e(in)g(this)g(case)j Fp(r)n(oots)d
Fr(must)h(contain)f(a)h(complete)g(list)f(of)h(all)f(id')n(s)g(of)g
(roots)g(of)h(in\002nite)e(subtrees)i(and)g Fp(limit)f
Fr(can)i(be)0 2512 y(set)f(to)g(in\002nity)m(.)p eop
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TeXDict begin 5 4 bop 0 -58 a Fp(Section)10 b(3.)g(Example)1603
b Fr(5)-71 42 y Fk(2)-47 36 y Fj(I)0 42 y Fi(BranchRWO\()20
b(G,)h(i,)g(rwo)h(\))0 122 y Fr(for)9 b(a)h(stable)f(quotient)e(\(see)k
([ER09]\))d Fp(G)i Fr(of)e(a)i(pro-)p Fp(p)p Fr(-group)d(of)i(rank)h
Fp(rwo)p Fh([)p Fr(1)p Fh(])p Fr(,)e Fp(rwo)p Fh([)p
Fr(2)p Fh(])f Fr(and)j(obliquity)c Fp(rwo)p Fh([)p Fr(3)p
Fh(])p Fr(,)i(this)h(function)e(returns)0 171 y(the)k
Fp(i)p Fr(-th)f(branch)h(of)f(its)g(corresponding)g(tree.)i(The)f
(structure)g(of)f(the)h(tree)g(is)g(encoded)h(in)e(a)h(list.)g(If)f
(one)h(of)g(the)g(global)f(parameters)0 221 y Fi(CHECK)p
113 221 14 2 v 15 w(RANK)h Fr(or)h Fi(CHECK)p 384 221
V 15 w(OBLIQUITY)e Fr(is)i(set)h(to)e(false,)i(then)f(checking)g(the)g
(corresponding)f(in)n(v)o(ariant)g(is)h(omitted)f(and)h(hence)h(a)0
271 y(potentially)8 b(lar)o(ger)i(tree)h(is)f(returned.)0
339 y(The)i(user)g(is)g(advised)f(not)g(to)g(perform)h(an)o(y)g(other)f
(computations)f(using)h(ANUPQ)h(or)f(the)g Fi(pq)p Fr(-program)g(while)
g(using)g(this)g(or)g(the)0 389 y(follo)o(wing)d(function,)h(because)j
(such)e(computations)f(will)g(be)i(terminated.)-71 463
y Fk(3)-47 457 y Fj(I)0 463 y Fi(BoundedDescendant)o(sRWO\()18
b(G,)k(i,)f(c,)g(rwo\))0 543 y Fr(returns)10 b(the)g(tree)g(of)g(all)g
(descendants)h(of)f Fp(G)p Ff(=)p Fg(g)680 549 y Fe(i)690
543 y Fh(\()p Fp(G)p Fh(\))h Fr(of)f(rank)g Fp(rwo)p
Fh([)p Fr(1)p Fh(])p Fr(,)f(width)g Fp(rwo)p Fh([)p Fr(2)p
Fh(])p Fr(,)g(obliquity)e Fp(rwo)p Fh([)p Fr(3)p Fh(])i
Fr(and)h(class)h(at)g(most)f Fp(c)p Fr(.)-71 618 y Fk(4)-47
612 y Fj(I)0 618 y Fi(DrawBranch\()20 b(branch)g(\))0
698 y Fr(if)8 b(the)h(package)h(is)f(run)f(under)h(XGap,)g(then)g(this)
f(function)f(can)j(be)f(used)g(to)g(dra)o(w)g(a)g(branch)g(as)h(output)
d(by)i(the)f(abo)o(v)o(e)i(two)e(functions)0 748 y(in)g(the)h(case)h
(of)e(width)f(2.)i(The)h(user)e(may)i(wish)e(to)g(impro)o(v)o(e)h(the)f
(quality)f(of)i(the)f(output)f(by)h(modifying)f(the)h(\002le)h
Fi(gap/xbranch.gi)p Fr(.)0 816 y(V)-5 b(ertices)11 b(dra)o(wn)e(on)h
(the)f(same)i(le)o(v)o(el)f(correspond)f(to)h(groups)e(of)i(the)f(same)
i(class.)g(If)f Fp(G)f Fr(is)h(a)g(descendant)g(of)g
Fp(H)h Fr(in)f(the)f(branch,)h(then)0 866 y Fp(G)g Fr(is)g(dra)o(wn)h
(as)g(a)g(\002lled)e(circle)i(if)f Fm(j)p Fp(G)p Fm(j)g
Fh(=)i Fm(j)p Fp(H)r Fm(j)p Fp(p)d Fr(and)h(as)h(a)g(solid)e(box)h(if)g
Fm(j)p Fp(G)p Fm(j)g Fh(=)i Fm(j)p Fp(H)r Fm(j)p Fp(p)1223
851 y Fc(2)1238 866 y Fr(.)0 933 y(The)g(package)g(also)f(pro)o(vides)g
(\002nite)f(quotients)g(of)h(a)g(number)g(of)g(in\002nite)f(pro-)p
Fp(p)p Fr(-groups)f(with)h(\002nite)h(rank,)g(width)f(and)h(obliquity)m
(.)0 983 y(Throughout)d(the)i(section,)h Fp(p)f Fr(is)g(an)h(odd)e
(prime.)-71 1058 y Fk(5)-47 1052 y Fj(I)0 1058 y Fi(ProPSylowGroupOfP)o
(SL\(d,)18 b(p,)k(n\))0 1138 y Fr(returns)8 b(the)g(quotient)e(of)i
(the)g(Sylo)o(w)f(pro-)p Fp(p)p Fr(-subgroup)f(of)i(PSL)923
1144 y Fe(d)941 1138 y Fh(\()p Fb(Q)989 1144 y Fe(p)1006
1138 y Fh(\))g Fr(modulo)f(the)h(matrices)h(which)f(are)h(congruent)e
(to)h(the)g(identity)0 1188 y(modulo)h Fp(p)158 1173
y Fe(n)175 1188 y Fr(.)-71 1263 y Fk(6)-47 1257 y Fj(I)0
1263 y Fi(ProPSylowGroupOfP)o(SF\(p,)18 b(n\))0 1343
y Fr(Let)c Fp(L)g Fr(be)g(the)f(simple)g(Lie)h(algebra)g(of)f
(dimension)g(3)g(o)o(v)o(er)h Fb(Q)939 1349 y Fe(p)969
1343 y Fr(which)g(is)f(not)f(isomorphic)h(to)g Fp(sl)1467
1349 y Fc(2)1483 1343 y Fh(\()p Fb(Q)1531 1349 y Fe(p)1548
1343 y Fh(\))p Fr(.)h(This)f(function)f(returns)0 1392
y(a)i(\002nite)e(quotient)g(of)h(the)g(Sylo)o(w)f(pro-)p
Fp(p)p Fr(-subgroup)f(of)i(its)f(automorphism)g(group.)h(The)h
(parameter)g Fp(n)f Fr(speci\002es)h(ho)o(w)f(lar)o(ge)h(this)0
1442 y(quotient)8 b(is.)0 1510 y(In)j([KLGP97],)g(a)g(library)f(of)g
(maximal)i(pro-)p Fp(p)p Fr(-groups)d(with)g(\002nite)i(rank,)g(width)f
(and)h(obliquity)d(corresponding)h(to)i(the)f(Lie)i(alge-)0
1560 y(bras)f(of)e(small)i(dimension)e(is)h(pro)o(vided.)g(Here,)h(we)g
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(groups)g(for)f(some)i(of)f(the)g(Lie)0 1610 y(algebras)i(of)e(type)h
Fp(sl)306 1616 y Fe(d)323 1610 y Fh(\()p Fp(K)r Fh(\))p
Fr(,)h(where)g Fp(K)h Fr(is)e(a)h(\002nite)e(e)o(xtension)h(of)g
Fb(Q)974 1616 y Fe(p)991 1610 y Fr(.)g(These)i(groups)d(ha)o(v)o(e)i
(been)g(determined)f(using)f(the)h(programs)0 1659 y(described)g(in)f
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(one)h(of)0 1709 y(the)f(last)g(non-tri)o(vial)e(terms)i(of)g(the)g(lo)
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(of)i(the)g(respecti)o(v)o(e)h(pro-)p Fp(p)p Fr(-group.)-71
1784 y Fk(7)-47 1778 y Fj(I)0 1784 y Fi(ProPQuotient\(p,)19
b(dim,)i(deg,)g(no\))0 1864 y Fr(returns)12 b(a)i(\002nite)e(group)g
(corresponding)f(to)i(the)g(maximal)g(pro-)p Fp(p)p Fr(-group)d
Fp(G)j Fr(with)f(Lie)i(algebra)f Fp(sl)1461 1870 y Fe(dim)1506
1864 y Fh(\()p Fp(K)r Fh(\))p Fr(,)h(where)f Fp(K)i Fr(is)e(a)g
(\002eld)g(of)0 1914 y(de)o(gree)e Fp(de)n(g)g Fr(o)o(v)o(er)g
Fb(Q)304 1920 y Fe(p)321 1914 y Fr(.)g(The)g(parameter)g
Fp(no)f Fr(speci\002es)h(the)f(number)g(of)g(the)g(group)g(in)f(our)h
(database.)0 2037 y Fs(2.3)27 b(Example)0 2129 y Fr(When)12
b(run)f(under)g(XGap,)h(the)f(follo)o(wing)e(code)j(constructs)f(and)g
(dra)o(ws)h(the)g(branch)f(with)f(root)h Fp(G)p Ff(=)p
Fg(g)1509 2135 y Fc(5)1525 2129 y Fh(\()p Fp(G)p Fh(\))h
Fr(in)f(the)g(graph)g(of)g(\002nite)0 2179 y(5-groups)e(of)h(rank)g(3,)
h(width)d(2)j(and)f(obliquity)d(0,)k(where)g Fp(G)f Fr(is)g(the)g(Sylo)
o(w)g(pro-)p Fp(p)p Fr(-subgroup)d(of)j(Aut)o Fh(\()p
Fp(sl)1523 2185 y Fc(2)1540 2179 y Fh(\()p Fb(Q)1588
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%%Page: 6 6
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b(2.)i(Methods)e(and)g(functions)59 42 y Fi(gap>)21 b(g)h(:=)f
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(2,0]\))o(;;)59 191 y(ConstructBranch:)e(root-p-class:)g(4)59
241 y(Constructed)h(3)h(1-step)g(descendants.)59 291
y(ConstructBranch:)e(root-p-class:)g(5)59 340 y(Constructed)h(0)h
(1-step)g(descendants.)59 390 y(Constructed)f(0)h(2-step)g
(descendants.)59 440 y(ConstructBranch:)e(root-p-class:)g(5)59
490 y(Constructed)h(0)h(1-step)g(descendants.)59 540
y(Constructed)f(0)h(2-step)g(descendants.)59 589 y(ConstructBranch:)e
(root-p-class:)g(5)59 639 y(Constructed)h(0)h(1-step)g(descendants.)59
689 y(Constructed)f(0)h(2-step)g(descendants.)59 739
y(Constructed)f(3)h(2-step)g(descendants.)59 789 y(ConstructBranch:)e
(root-p-class:)g(5)59 839 y(Constructed)h(0)h(1-step)g(descendants.)59
888 y(Constructed)f(0)h(2-step)g(descendants.)59 938
y(ConstructBranch:)e(root-p-class:)g(5)59 988 y(Constructed)h(0)h
(1-step)g(descendants.)59 1038 y(Constructed)f(0)h(2-step)g
(descendants.)59 1088 y(time:)43 b(0:00:16.525)59 1137
y(gap>)21 b(DrawBranch\(branch\))o(;)0 1230 y Fr(A)10
b(windo)o(w)f(with)h(the)g(follo)o(wing)d(graph)j(should)f(appear)n(.)0
1834 y @beginspecial 0 @llx 0 @lly 600 @urx 364 @ury
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