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dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csbx7
%!FontType1-1.0: csbx7 1.1/12-Nov-94
% CSfonts -- pfb ver. Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25269 25774
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csbx7) readonly def
/FamilyName (csbx7) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 444 def
/Ascender 694 def
/Descender -194 def
/CapHeight 686 def
end readonly def
/FontName /csbx7 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 117 /u put
dup 118 /v put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-59 -251 1289 908] readonly def
/UniqueID 4701486 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csr8
%!FontType1-1.0: csr8 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25661 25938
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csr8) readonly def
/FamilyName (csr8) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /csr8 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 67 /C put
dup 68 /D put
dup 83 /S put
dup 84 /T put
dup 86 /V 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 106 /j 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 122 /z put
dup 190 /zcaron put
dup 225 /aacute put
dup 232 /ccaron put
dup 233 /eacute put
dup 236 /ecaron put
dup 237 /iacute put
dup 248 /rcaron put
dup 249 /uring put
dup 253 /yacute put
dup 254 /quotedblbase put
dup 255 /csquotedblright put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-40 -250 1111 864] readonly def
/UniqueID 4701479 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csr6
%!FontType1-1.0: csr6 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25711 25989
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csr6) readonly def
/FamilyName (csr6) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /csr6 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-24 -250 1193 864] readonly def
/UniqueID 4701477 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /square put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{21 -944 1448 791}readonly def
/UniqueID 5000815 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
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94CEDB08E8C92907FE72A0B05AE36A7B9226ACD6E7890A0B528FDDE84A950FC6
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cleartomark
%%EndFont
%%BeginFont: CMMIB10
%!PS-AdobeFont-1.1: CMMIB10 1.100
%%CreationDate: 1996 Jul 23 07:54:00
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMIB10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMIB10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -250 1216 750}readonly def
/UniqueID 5087392 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 75 /K put
dup 81 /Q put
dup 82 /R put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
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7548B34A73DF3723729DDDA5393846A911888F4A87D7DDC3A632460237D26CC5
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7802E7425B3991F84F78802FB1BF6794EB210E41C2C520483130B0E4000D4209
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cleartomark
%%EndFont
%%BeginFont: cssl10
%!FontType1-1.0: cssl10 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 26841 27114
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (cssl10) readonly def
/FamilyName (cssl10) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /cssl10 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 66 /B put
dup 74 /J put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 86 /V 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 106 /j 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 185 /scaron put
dup 187 /tcaron put
dup 190 /zcaron put
dup 225 /aacute put
dup 232 /ccaron put
dup 233 /eacute put
dup 236 /ecaron put
dup 237 /iacute put
dup 239 /dcaron put
dup 242 /ncaron put
dup 248 /rcaron put
dup 249 /uring put
dup 250 /uacute put
dup 253 /yacute put
dup 254 /quotedblbase put
dup 255 /csquotedblright put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-65 -250 1123 857] readonly def
/UniqueID 4701498 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csti10
%!FontType1-1.0: csti10 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 31328 31604
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csti10) readonly def
/FamilyName (csti10) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /csti10 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 50 /two put
dup 58 /colon put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 71 /G put
dup 72 /H put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T 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 106 /j 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 121 /y put
dup 122 /z put
dup 185 /scaron put
dup 190 /zcaron put
dup 225 /aacute put
dup 232 /ccaron put
dup 233 /eacute put
dup 236 /ecaron put
dup 237 /iacute put
dup 243 /oacute put
dup 249 /uring put
dup 253 /yacute put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-35 -250 1125 857] readonly def
/UniqueID 4701494 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csbx10
%!FontType1-1.0: csbx10 1.1/12-Nov-94
% CSfonts -- pfb ver. Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25027 25304
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csbx10) readonly def
/FamilyName (csbx10) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 444 def
/Ascender 694 def
/Descender -194 def
/CapHeight 686 def
end readonly def
/FontName /csbx10 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 40 /parenleft put
dup 41 /parenright put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 58 /colon put
dup 68 /D put
dup 72 /H put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 90 /Z 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 106 /j 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 185 /scaron put
dup 225 /aacute put
dup 232 /ccaron put
dup 233 /eacute put
dup 236 /ecaron put
dup 237 /iacute put
dup 243 /oacute put
dup 248 /rcaron put
dup 249 /uring put
dup 253 /yacute put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-60 -250 1164 908] readonly def
/UniqueID 4701489 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{37 -250 1349 750}readonly def
/UniqueID 5087380 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csr5
%!FontType1-1.0: csr5 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25158 25424
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csr5) readonly def
/FamilyName (csr5) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/Descender -194 def
/CapHeight 683 def
/XHeight 431 def
/Ascender 694 def
end readonly def
/FontName /csr5 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 61 /equal put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-14 -250 1304 864] readonly def
/UniqueID 4701476 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 12 /vextendsingle put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 26 /braceleftbigg put
dup 32 /parenleftBigg put
dup 33 /parenrightBigg put
dup 34 /bracketleftBigg put
dup 35 /bracketrightBigg put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 80 /summationtext put
dup 81 /producttext put
dup 88 /summationdisplay put
dup 89 /productdisplay put
dup 110 /braceleftBig put
dup 111 /bracerightBig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csr7
%!FontType1-1.0: csr7 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25529 25807
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csr7) readonly def
/FamilyName (csr7) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /csr7 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus 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 55 /seven put
dup 57 /nine put
dup 61 /equal put
dup 76 /L put
dup 80 /P put
dup 112 /p put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-31 -251 1122 864] readonly def
/UniqueID 4701478 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
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cleartomark
%%EndFont
%%BeginFont: cssl9
%!FontType1-1.0: cssl9 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 27303 27578
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (cssl9) readonly def
/FamilyName (cssl9) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /cssl9 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 79 /O put
dup 97 /a put
dup 98 /b put
dup 104 /h put
dup 115 /s put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-64 -251 1150 857] readonly def
/UniqueID 4701497 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csr10
%!FontType1-1.0: csr10 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25429 25707
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csr10) readonly def
/FamilyName (csr10) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /csr10 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 2 /Theta put
dup 6 /Sigma put
dup 12 /fi put
dup 22 /macron put
dup 33 /exclam put
dup 37 /percent put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period 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 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 63 /question 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 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X 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 106 /j 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 174 /Zcaron put
dup 185 /scaron put
dup 187 /tcaron put
dup 190 /zcaron put
dup 200 /Ccaron put
dup 225 /aacute put
dup 232 /ccaron put
dup 233 /eacute put
dup 236 /ecaron put
dup 237 /iacute put
dup 239 /dcaron put
dup 242 /ncaron put
dup 243 /oacute put
dup 248 /rcaron put
dup 249 /uring put
dup 250 /uacute put
dup 253 /yacute put
dup 254 /quotedblbase put
dup 255 /csquotedblright put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-44 -250 1111 864] readonly def
/UniqueID 4701481 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csr12
%!FontType1-1.0: csr12 1.1/12-Nov-94
% CSfonts -- pfb ver.Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25445 25725
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csr12) readonly def
/FamilyName (csr12) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 431 def
/Ascender 694 def
/Descender -194 def
/CapHeight 683 def
end readonly def
/FontName /csr12 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 52 /four put
dup 54 /six put
dup 73 /I put
dup 86 /V put
dup 101 /e put
dup 114 /r put
dup 122 /z put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-38 -251 1111 864] readonly def
/UniqueID 4701482 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: csb10
%!FontType1-1.0: csb10 1.1/12-Nov-94
% CSfonts -- pfb ver. Apr.1998, generated from BaKoMa fonts. NO WARRANTY.
% Accents are added using t1accent program, (c) Petr Olsak, 1998
%%VMusage: 25002 25277
% T1FMT-V2.0, Copyright (c) 1993,1994, Basil K. Malyshev. All rights reserved.
12 dict begin
/FontInfo 13 dict dup begin
/version (1.1/12-Nov-94) readonly def
/Notice (Copyright \(C\) 1994, Basil K. Malyshev. All Rights Reserved.\012BaKoMa Fonts Collection, Level-B.) readonly def
/FullName (csb10) readonly def
/FamilyName (csb10) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -133 def
/UnderlineThickness 20 def
/XHeight 444 def
/Ascender 694 def
/Descender -194 def
/CapHeight 686 def
end readonly def
/FontName /csb10 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
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 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 68 /D put
dup 70 /F put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V 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 106 /j 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 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 121 /y put
dup 122 /z put
dup 169 /Scaron put
dup 185 /scaron put
dup 190 /zcaron put
dup 218 /Uacute put
dup 225 /aacute put
dup 232 /ccaron put
dup 233 /eacute put
dup 236 /ecaron put
dup 237 /iacute put
dup 243 /oacute put
dup 248 /rcaron put
dup 249 /uring put
dup 250 /uacute put
dup 253 /yacute put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox [-66 -250 1111 908] readonly def
/UniqueID 4701500 def
/StrokeWidth 0 def
currentdict end
currentfile eexec
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b(25)-57 4424 y(14)107 b(Konec)26 b(pades\341tn\355k\371)48
b(.)42 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)
h(.)f(.)h(.)f(.)h(.)112 b(26)-57 4524 y(15)107 b(V)-7
b(ektory)26 b(v)i(ohr\341dce)70 b(.)42 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)
f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)112
b(28)-57 4623 y(16)107 b(P)n(erfektn\355)26 b(p\341ro)n(v)n(\341n\355)g
(a)h(determinan)n(t)n(y)69 b(.)42 b(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h
(.)f(.)h(.)112 b(31)p eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 428.031496 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 6 5 bop 1051 1858 a Ft(Obsah)1186 b Fu(6)p
-135 1891 2629 4 v -135 2074 a Fw(1)119 b(Ryc)m(hl\375)41
b(v\375p)s(o)s(\350et)f(Fib)s(onacciho)i(\350\355sel)-135
2256 y Fu(Fib)r(onacciho)31 b(\350\355sla)g Fs(F)578
2268 y Fr(0)615 2256 y Fs(;)14 b(F)705 2268 y Fr(1)743
2256 y Fs(;)g(F)833 2268 y Fr(2)870 2256 y Fs(;)g(:)g(:)g(:)32
b Fu(jsou)f(de\014no)n(v)n(\341na)f(vztah)n(y)g Fs(F)1956
2268 y Fr(0)2024 2256 y Fu(=)f(0,)i Fs(F)2267 2268 y
Fr(1)2334 2256 y Fu(=)e(1,)-135 2356 y(a)j Fs(F)-8 2368
y Fq(n)p Fr(+2)153 2356 y Fu(=)e Fs(F)301 2368 y Fq(n)p
Fr(+1)452 2356 y Fu(+)22 b Fs(F)592 2368 y Fq(n)670 2356
y Fu(pro)31 b(v\271ec)n(hna)h Fs(n)f Fu(=)f(0)p Fs(;)14
b Fu(1)p Fs(;)g Fu(2)p Fs(;)g(:)g(:)g(:)n Fu(.)33 b(\310\355slo)f
Fs(F)1967 2368 y Fq(n)2045 2356 y Fu(se)g(zjevn\354)g(d\341)-135
2455 y(sp)r(o)r(\350\355tat)c(\370\341do)n(v)n(\354)d
Fs(n)j Fu(aritmetic)n(k\375mi)e(op)r(eracemi.)-11 2555
y(N\341sleduj\355c\355m)39 b(trik)n(em)f(jej)h(m)n(\371\276eme)g(sp)r
(o)r(\350\355tat)f(mnohem)h(ryc)n(hleji,)f(p)r(omo)r(c\355)-135
2655 y(\370\341do)n(v)n(\354)25 b(log)14 b Fs(n)28 b
Fu(aritmetic)n(k\375c)n(h)e(op)r(erac\355.)h(Ozna\350me)875
2874 y Fs(M)k Fu(=)1075 2757 y Fp(\022)1178 2823 y Fu(1)82
b(1)1178 2923 y(1)g(0)1385 2757 y Fp(\023)1460 2874 y
Fs(:)-135 3093 y Fu(P)n(otom)26 b(plat\355)665 3120 y
Fp(\022)768 3187 y Fs(F)821 3199 y Fq(n)p Fr(+2)768 3287
y Fs(F)821 3299 y Fq(n)p Fr(+1)992 3120 y Fp(\023)1076
3238 y Fu(=)d Fs(M)1268 3120 y Fp(\022)1370 3187 y Fs(F)1423
3199 y Fq(n)p Fr(+1)1412 3287 y Fs(F)1465 3299 y Fq(n)1594
3120 y Fp(\023)1669 3238 y Fs(;)-135 3427 y Fu(a)k(tud\355\276)732
3439 y Fp(\022)835 3505 y Fs(F)888 3517 y Fq(n)p Fr(+1)877
3605 y Fs(F)930 3617 y Fq(n)1059 3439 y Fp(\023)1143
3556 y Fu(=)c Fs(M)1321 3521 y Fq(n)1379 3439 y Fp(\022)1482
3505 y Fu(1)1482 3605 y(0)1565 3439 y Fp(\023)-135 3758
y Fu(\(vyu\276\355v)n(\341me)32 b(aso)r(ciativit)n(y)f(n\341sob)r
(en\355)i(matic\).)g(Pro)e Fs(n)h Fu(=)f(2)1785 3728
y Fq(k)1858 3758 y Fu(m)n(\371\276eme)i(mo)r(cnin)n(u)-135
3857 y Fs(M)-45 3827 y Fq(n)39 3857 y Fu(sp)r(o)r(\350\355tat)38
b(opak)n(o)n(v)n(an)n(\375m)e(umo)r(c\362o)n(v)n(\341n\355m)i(na)g
(druhou,)h(p)r(omo)r(c\355)f Fs(k)k Fu(op)r(erac\355)-135
3957 y(n\341sob)r(en\355)23 b(matic)h(t)n(ypu)g(2)p Fo(\002)o
Fu(2.)g(Ob)r(ecn\351)g Fs(n)g Fu(zap\355\271eme)f(v)n(e)g(dv)n(o)5
b(jk)n(o)n(v)n(\351)22 b(sousta)n(v)n(\354,)g(\350\355m\276)-135
4057 y(ho)31 b(vyj\341d\370\355me)g(v)n(e)g(tv)n(aru)g
Fs(n)e Fu(=)h(2)930 4026 y Fq(k)965 4034 y Fn(1)1022
4057 y Fu(+)21 b(2)1150 4026 y Fq(k)1185 4034 y Fn(2)1242
4057 y Fu(+)g Fo(\001)14 b(\001)g(\001)21 b Fu(+)f(2)1573
4026 y Fq(k)1608 4034 y Fm(t)1640 4057 y Fu(,)32 b Fs(k)1738
4069 y Fr(1)1805 4057 y Fs(<)d(k)1942 4069 y Fr(2)2009
4057 y Fs(<)g Fo(\001)14 b(\001)g(\001)30 b Fs(<)f(k)2367
4069 y Fq(t)2397 4057 y Fu(,)i(a)-135 4165 y(mo)r(cnin)n(u)26
b Fs(M)290 4135 y Fq(n)362 4165 y Fu(pak)g(vyp)r(o)r(\350teme)h(v)n(e)e
(tv)n(aru)h Fs(M)1354 4135 y Fq(n)1422 4165 y Fu(=)c
Fs(M)1599 4135 y Fr(2)1632 4110 y Fm(k)1663 4122 y Fn(1)1704
4165 y Fs(M)1794 4135 y Fr(2)1827 4110 y Fm(k)1858 4122
y Fn(2)1913 4165 y Fo(\001)14 b(\001)g(\001)g Fs(M)2114
4135 y Fr(2)2147 4110 y Fm(k)2178 4121 y(t)2214 4165
y Fu(,)26 b(na)h(co\276)-135 4265 y(sta\350\355)g(nejv\375\271)h(2)p
Fs(k)401 4277 y Fq(t)453 4265 y Fo(\024)22 b Fu(2)14
b(log)703 4285 y Fr(2)754 4265 y Fs(n)27 b Fu(n\341sob)r(en\355)g
(matic)h(2)p Fo(\002)o Fu(2.)-135 4387 y Fl(P)m(ozn\341mky)-8
b(.)151 b Fu(P)n(o)r(dobn\351ho)69 b(triku)h(m)n(\371\276eme)f(p)r
(ou\276\355t)i(pro)e(p)r(osloupnosti)-135 4487 y(\()p
Fs(y)-62 4499 y Fr(0)-25 4487 y Fs(;)14 b(y)53 4499 y
Fr(1)90 4487 y Fs(;)g(y)168 4499 y Fr(2)205 4487 y Fs(;)g(:)g(:)g(:)p
Fu(\))28 b(dan\351)g(rekurencemi)f(tv)n(aru)f Fs(y)1329
4499 y Fq(n)p Fr(+)p Fq(k)1486 4487 y Fu(=)d Fs(a)1618
4499 y Fq(k)q Fk(\000)p Fr(1)1744 4487 y Fs(y)1785 4499
y Fq(n)p Fr(+)p Fq(k)q Fk(\000)p Fr(1)2021 4487 y Fu(+)18
b Fo(\001)c(\001)g(\001)19 b Fu(+)f Fs(a)2347 4499 y
Fr(0)2384 4487 y Fs(y)2425 4499 y Fq(n)2470 4487 y Fu(,)-135
4587 y(kde)27 b Fs(k)k Fu(a)c Fs(a)206 4599 y Fr(0)243
4587 y Fs(;)14 b(a)324 4599 y Fr(1)361 4587 y Fs(;)g(:)g(:)g(:)g(;)g(a)
590 4599 y Fq(k)q Fk(\000)p Fr(1)743 4587 y Fu(jsou)28
b(k)n(onstan)n(t)n(y)-7 b(.)-11 4686 y(P\370i)41 b(v\375p)r(o)r(\350tu)
g(se)h(m)n(us\355)f(d\341t)g(p)r(ozor)f(na)h(to,)h(\276e)f(Fib)r
(onacciho)g(\350\355sla)f(rostou)-135 4786 y(v)n(elmi)24
b(ryc)n(hle.)g(Uk)n(azuje)g(se,)h(\276e)f(des\355tk)n(o)n(v\375)f
(z\341pis)h Fs(F)1501 4798 y Fq(n)1572 4786 y Fu(m\341)g(\370\341do)n
(v)n(\354)f Fs(n)h Fu(\350\355slic,)h(a)f(tedy)-135 4886
y(m)n(us\355me)33 b(p)r(ou\276\355t)h(vho)r(dnou)f(n\341sobnou)g
(aritmetiku.)g(Aritmetic)n(k)n(\351)g(op)r(erace)f(pak)-135
4985 y(budou)c(p)r(om\354rn\354)f(p)r(omal\351.)-135
5258 y Fw(2)119 b(Vzorec)40 b(pro)h(Fib)s(onacciho)g(\350\355sla)-135
5440 y Fu(Na)5 b(jdeme)21 b(vzorec)e(pro)h Fs(n)p Fu(-t\351)h(Fib)r
(onacciho)f(\350\355slo)h Fs(F)1459 5452 y Fq(n)1504
5440 y Fu(.)g(Uv)n(a\276me)f(v)n(ektoro)n(v\375)f(prostor)-135
5540 y(v\271ec)n(h)h(nek)n(one\350n)n(\375c)n(h)f(p)r(osloupnost\355)h
(\()p Fs(u)1111 5552 y Fr(0)1148 5540 y Fs(;)14 b(u)1233
5552 y Fr(1)1270 5540 y Fs(;)g(u)1355 5552 y Fr(2)1391
5540 y Fs(;)g(:)g(:)g(:)p Fu(\))21 b(re\341ln)n(\375c)n(h)e
(\350\355sel,)i(se)f(s\350\355t\341n\355m)-135 5639 y(a)30
b(n\341sob)r(en\355m)h(re\341ln)n(\375m)e(\350\355slem)i(p)r(o)g
(slo\276k)n(\341c)n(h.)e(V)i(n\354m)g(de\014n)n(ujeme)g(p)r(o)r
(dprostor)-135 5739 y Fs(W)44 b Fu(v\271ec)n(h)31 b(p)r(osloupnost\355)
h(spl\362)n(uj\355c\355c)n(h)g(vztah)g Fs(u)1395 5751
y Fq(n)p Fr(+2)1554 5739 y Fu(=)f Fs(u)1698 5751 y Fq(n)p
Fr(+1)1848 5739 y Fu(+)21 b Fs(u)1982 5751 y Fq(n)2059
5739 y Fu(pro)31 b(v\271ec)n(hna)-135 5839 y Fs(n)23
b Fu(=)f(0)p Fs(;)14 b Fu(1)p Fs(;)g(:)g(:)g(:)o Fu(.)26
b(Ka\276d\341)e(v)n(olba)g(prvn\355c)n(h)h(dv)n(ou)g(\350len)n(\371)h
Fs(u)1563 5851 y Fr(0)1625 5839 y Fu(a)f Fs(u)1740 5851
y Fr(1)1803 5839 y Fu(jednozna\350n\354)g(ur\350uje)-135
5938 y(p)r(osloupnost)30 b(z)g Fs(W)n Fu(,)h(a)f(proto)f(dim)q(\()p
Fs(W)12 b Fu(\))28 b(=)g(2.)i(\(P)n(o)r(drobn\354ji,)f(nap\370\355klad)
h(p)r(osloup-)-135 6038 y(nosti)d(za\350\355na)5 b(j\355c\355)27
b(\(0)p Fs(;)14 b Fu(1)p Fs(;)g Fu(1)p Fs(;)g Fu(2)p
Fs(;)g Fu(3)p Fs(;)g(:)g(:)g(:)m Fu(\))28 b(a)f(\(1)p
Fs(;)14 b Fu(0)p Fs(;)g Fu(1)p Fs(;)g Fu(1)p Fs(;)g Fu(2)g
Fs(:)g(:)g(:)m Fu(\))28 b(tv)n(o\370\355)f(b\341zi)g
Fs(W)12 b Fu(.\))p eop end
PStoPSsaved restore
%%Page: (6,7) 4
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 850.393701 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 7 6 bop -182 1858 a Fu(7)1186 b Ft(Obsah)p
-182 1891 2629 4 v -57 2074 a Fu(T)-7 b(e\357)36 b(na)5
b(jdeme)37 b(\271ik)n(o)n(vnou)d(b\341zi)j(prostoru)d
Fs(W)12 b Fu(,)37 b(jej\355\276)g(prvky)f(jsou)g(d\341n)n(y)g(jed-)-182
2174 y(no)r(duc)n(h)n(\375m)e(vzore\350)n(k)n(em.)f(\376)-7
b(Vn)n(ukn)n(ut\355\377:)34 b(hledejme)h(p)r(osloupnost)f
Fs(u)h Fo(2)g Fs(W)46 b Fu(tv)n(aru)-182 2274 y Fs(u)-134
2286 y Fq(n)-42 2274 y Fu(=)g Fs(\034)114 2243 y Fq(n)202
2274 y Fu(pro)41 b(vho)r(dn\351)h(\350\355slo)f Fs(\034)9
b Fu(.)43 b(Vyjde)f(kv)n(adratic)n(k)n(\341)d(ro)n(vnice)h
Fs(\034)2042 2243 y Fr(2)2127 2274 y Fu(=)47 b Fs(\034)37
b Fu(+)28 b(1)-182 2373 y(se)36 b(dv)n(\354ma)f(r\371zn)n(\375mi)g(k)n
(o\370en)n(y)f Fs(\034)838 2385 y Fr(1)p Fq(;)p Fr(2)965
2373 y Fu(=)i(\(1)24 b Fo(\006)1252 2305 y(p)p 1321 2305
42 4 v 68 x Fu(5\))p Fs(=)p Fu(2.)35 b(Jak)g(se)g(snadno)g(o)n(v)n
(\354\370\355,)g(p)r(o-)-182 2473 y(sloupnosti)d(\()p
Fs(\034)293 2443 y Fr(0)284 2493 y(1)332 2473 y Fs(;)14
b(\034)414 2443 y Fr(1)405 2493 y(1)451 2473 y Fs(;)g(\034)533
2443 y Fr(2)524 2493 y(1)571 2473 y Fs(;)g(:)g(:)g(:)p
Fu(\))33 b(a)f(\()p Fs(\034)921 2443 y Fr(0)912 2493
y(2)960 2473 y Fs(;)14 b(\034)1042 2443 y Fr(1)1033 2493
y(2)1079 2473 y Fs(;)g(\034)1161 2443 y Fr(2)1152 2493
y(2)1199 2473 y Fs(;)g(:)g(:)g(:)p Fu(\))33 b(jsou)g(line\341rn\354)f
(nez\341)n(visl\351)f(\(sta\350\355)-182 2572 y(se)j(p)r(o)r(d\355v)n
(at)f(na)g(prvn\355)h(dv)n(a)f(\350len)n(y\),)g(a)g(tedy)h(tv)n
(o\370\355)f(b\341zi)g Fs(W)12 b Fu(.)34 b(Fib)r(onacciho)f
(\350\355sla)-182 2672 y(vyj\341d\370\355me)27 b(v)h(t\351to)f(b\341zi)
h(\(p)r(ou\276it\355m)g(prvn\355c)n(h)f(dv)n(ou)g(\350len)n(\371\).)h
(Vyjde)387 2937 y Fs(F)440 2949 y Fq(n)509 2937 y Fu(=)641
2881 y(1)p 607 2918 111 4 v 607 2935 a Fo(p)p 676 2935
42 4 v 69 x Fu(5)741 2795 y Fp(")q( )865 2881 y Fu(1)18
b(+)1008 2813 y Fo(p)p 1077 2813 V 68 x Fu(5)p 865 2918
254 4 v 971 2994 a(2)1129 2795 y Fp(!)1195 2813 y Fq(n)1258
2937 y Fo(\000)1341 2795 y Fp( )1417 2881 y Fu(1)g Fo(\000)1560
2813 y(p)p 1629 2813 42 4 v 68 x Fu(5)p 1417 2918 254
4 v 1523 2994 a(2)1681 2795 y Fp(!)1746 2813 y Fq(n)1792
2795 y Fp(#)1854 2937 y Fs(:)-57 3195 y Fu(P)n(o)r(dobn\354)27
b(to)i(funguje)g(i)g(pro)f(jin\351)h(rekurence)f(tv)n(aru)f
Fs(y)1687 3207 y Fq(n)p Fr(+)p Fq(k)1845 3195 y Fu(=)d
Fs(a)1978 3207 y Fq(k)q Fk(\000)p Fr(1)2104 3195 y Fs(y)2145
3207 y Fq(n)p Fr(+)p Fq(k)q Fk(\000)p Fr(1)2382 3195
y Fu(+)-182 3295 y Fo(\001)14 b(\001)g(\001)d Fu(+)g
Fs(a)46 3307 y Fr(0)83 3295 y Fs(y)124 3307 y Fq(n)169
3295 y Fu(,)24 b(ale)g(mohou)f(se)h(vyskytnout)f(p)r(ot\355\276e,)h
(t\370eba)g(pro)f Fs(y)1799 3307 y Fq(n)p Fr(+2)1951
3295 y Fu(=)g(2)p Fs(y)2122 3307 y Fq(n)p Fr(+1)2261
3295 y Fo(\000)11 b Fs(y)2378 3307 y Fq(n)2423 3295 y
Fu(.)-182 3395 y(P)n(ak)26 b(se)i(m)n(us\355)f(hledat)h(jin\341)g
(b\341ze,)f(co\276)g(zde)g(nebudeme)h(d\354lat.)-182
3678 y Fw(3)119 b(Klub)m(y)41 b(m\354sta)e(Li\271\341k)m(o)m(v)m(a)-182
3863 y Fu(V)-7 b(e)27 b(m\354st\354)f(\276ije)h Fs(n)f
Fu(ob)r(\350an)n(\371,)g(kte\370\355)g(jsou)h(sdru\276eni)f(v)g
Fs(m)g Fu(klub)r(ec)n(h.)h(P)n(o)r(dle)e(vyhl\341\271ky)-182
3963 y(m\354stsk)n(\351)34 b(rady)g(m\341)h(k)n(a\276d\375)f(klub)h
Fj(lich\375)44 b Fu(p)r(o)r(\350et)36 b(\350len)n(\371,)e(zat\355mco)h
(pro)f(k)n(a\276d\351)g(dv)n(a)-182 4063 y(klub)n(y)27
b(m)n(us\355)h(b)n(\375t)g(p)r(o)r(\350et)g(sp)r(ole\350n)n(\375c)n(h)e
(\350len)n(\371)i Fj(sud\375)p Fu(.)-182 4191 y Fl(V)m(\354ta.)p
Fi(V)g(t\351to)g(situaci)f(je)h(n)n(utn\354)g Fs(m)23
b Fo(\024)g Fs(n)p Fi(,)k(tj.)i(klub)r(\371)f(nen\355)g(v\355c)f
(ne\276)h(ob)r(\350an)n(\371.)-182 4319 y Fl(D\371k)m(az.)80
b Fu(Ob)r(\350an)n(y)35 b(ozna\350me)h(1)p Fs(;)14 b
Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)36 b Fu(a)g(klub)n(y)g
Fs(K)1623 4331 y Fr(1)1660 4319 y Fs(;)14 b(K)1768 4331
y Fr(2)1805 4319 y Fs(;)g(:)g(:)g(:)f(;)h(K)2060 4331
y Fq(m)2123 4319 y Fu(.)36 b(De\014n)n(u-)-182 4418 y(jeme)e(matici)g
Fs(A)f Fu(t)n(ypu)h Fs(m)22 b Fo(\002)g Fs(n)p Fu(,)34
b(kde)f Fs(a)1068 4430 y Fq(ij)1159 4418 y Fu(=)g(1)g(p)r(okud)h
Fs(j)j Fo(2)d Fs(K)1823 4430 y Fq(i)1883 4418 y Fu(a)f
Fs(a)2002 4430 y Fq(ij)2094 4418 y Fu(=)f(0)h(jinak)-182
4518 y(\(klub)n(y)14 b(=)f(\370\341dky\).)30 b(Uv)n(a\276ujeme)h
Fs(A)g Fu(nad)f(dv)n(ouprvk)n(o)n(v\375m)e(t\354lesem)j(GF\(2\).)g(Ho)r
(d-)-182 4617 y(nost)23 b Fs(A)h Fu(je)f(nejv\375\271)g
Fs(n)h Fu(\(jasn\351\).)f(P)n(o)r(dle)g(vyhl\341\271ky)f(m\354stsk)n
(\351)g(rady)h(plat\355)g Fs(AA)2160 4587 y Fq(T)2236
4617 y Fu(=)g Fs(I)2360 4629 y Fq(m)2423 4617 y Fu(,)-182
4717 y(a)i(proto\276e)g(ho)r(dnost)g(sou\350in)n(u)g(matic)h(je)g
(nejv\375\271)f(ro)n(vna)f(minim)n(u)i(z)g(ho)r(dnost\355)f(\350ini-)
-182 4817 y(tel\371,)j(je)g(ho)r(dnost)g Fs(A)g Fu(asp)r(o\362)f
Fs(m)p Fu(.)-182 4945 y Fl(P)m(ozn\341mk)m(a.)56 b Fu(P)n(o)r(dobnou)24
b(meto)r(dou)h(b)n(yla)g(dok)n(\341z\341na)e(\370ada)h(d\371le\276it)n
(\375c)n(h)h(o)r(dhad\371)-182 5044 y(pro)e(v)n(elik)n(osti)f(r\371zn)n
(\375c)n(h)h(mno\276ino)n(v\375c)n(h)f(syst\351m)n(\371.)h
(Nap\370\355klad)f(tzv.)i(Fishero)n(v)n(a)d(ne-)-182
5144 y(ro)n(vnost)c(\(v)n(e)i(zob)r(ecn\354n\351)f(p)r(o)r(dob)r
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5343 y(v)n(elik)n(ost,)c(p)r(otom)i Fs(n)23 b Fo(\025)g
Fs(m)p Fu(.)-182 5627 y Fw(4)119 b(Dl\341\276d\354n\355)41
b(ob)s(d\351ln\355k)m(a)h(\350tv)m(erci)-182 5839 y Fl(V)m(\354ta.)24
b Fi(Ob)r(d\351ln\355k)d Fs(R)g Fi(o)f(stran\341c)n(h)e
Fu(1)i Fi(a)g Fs(x)p Fi(,)h(kde)g Fs(x)f Fi(je)h(iracion\341ln\355,)e
(nelze)h(\376vydl\341\276dit\377)-182 5938 y(k)n(one\350n\354)30
b(mnoha)g(\350tv)n(erci)f(\(tak,)i(ab)n(y)e(cel\375)h
Fs(R)i Fi(b)n(yl)e(p)r(okryt)g(a)g(\276\341dn\351)g(dv)n(a)f(\350tv)n
(erce)-182 6038 y(nem\354ly)f(sp)r(ole\350n)n(\375)f(vnit\370n\355)g(b)
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TeXDict begin 8 7 bop 1051 1858 a Ft(Obsah)1186 b Fu(8)p
-135 1891 2629 4 v -135 2074 a Fl(D\371k)m(az.)136 b
Fu(Pro)62 b(sp)r(or)g(nec)n(h)n(\273)h(existuje)g(dl\341\276d\354n\355)
f(sest\341)n(v)n(a)5 b(j\355c\355)61 b(ze)i(\350tv)n(erc\371)-135
2174 y Fs(Q)-69 2186 y Fr(1)-32 2174 y Fs(;)14 b(Q)71
2186 y Fr(2)108 2174 y Fs(;)g(:)g(:)g(:)f(;)h(Q)358 2186
y Fq(n)403 2174 y Fu(,)25 b(a)f(nec)n(h)n(\273)h Fs(s)775
2186 y Fq(i)828 2174 y Fu(je)g(d\351lk)n(a)f(stran)n(y)g(\350tv)n(erce)
g Fs(Q)1726 2186 y Fq(i)1753 2174 y Fu(.)h(Uv)n(\341\276\355me)g(v)n
(ektoro)n(v\375)-135 2274 y(p)r(o)r(dprostor)31 b Fs(V)51
b Fu(prostoru)31 b Fh(R)h Fu(nad)g Fh(Q)g Fu(genero)n(v)n(an)n(\375)e
(\350\355sly)i Fs(s)1755 2286 y Fr(1)1792 2274 y Fs(;)14
b(s)1868 2286 y Fr(2)1905 2274 y Fs(;)g(:)g(:)g(:)f(;)h(s)2128
2286 y Fq(n)2173 2274 y Fu(.)33 b(De\014n)n(u-)-135 2373
y(jeme)25 b(line\341rn\355)g(zobrazen\355)f Fs(f)9 b
Fu(:)14 b Fs(V)41 b Fo(!)23 b Fh(R)i Fu(tak,)g(ab)n(y)g
Fs(f)9 b Fu(\(1\))22 b(=)h(1)i(a)f Fs(f)9 b Fu(\()p Fs(x)p
Fu(\))24 b(=)f Fo(\000)p Fu(1)h(\(a)h(jinak)-135 2473
y(lib)r(o)n(v)n(oln\354\).)i(T)-7 b(o)27 b(lze,)h(p)r(on\354v)n(ad\276)
e(1)h(a)h Fs(x)g Fu(jsou)f(line\341rn\354)g(nez\341)n(visl\351)f(nad)i
Fh(Q)p Fu(.)-11 2572 y(Pro)19 b(ob)r(d\351ln\355k)h Fs(A)h
Fu(o)e(stran\341c)n(h)g Fs(a)h Fu(a)g Fs(b)p Fu(,)g Fs(a;)14
b(b)22 b Fo(2)i Fs(V)18 b Fu(,)j(de\014n)n(ujeme)f Fs(v)s
Fu(\()p Fs(A)p Fu(\))k(=)f Fs(f)9 b Fu(\()p Fs(a)p Fu(\))p
Fs(f)g Fu(\()p Fs(b)p Fu(\).)-135 2672 y(Tvrd\355me,)34
b(\276e)h(je-li)g Fs(R)h Fu(vydl\341\276d\354n)e(\350tv)n(erci)g
Fs(Q)1353 2684 y Fr(1)1390 2672 y Fs(;)14 b(Q)1493 2684
y Fr(2)1530 2672 y Fs(;)g(:)g(:)g(:)f(;)h(Q)1780 2684
y Fq(n)1825 2672 y Fu(,)35 b(p)r(otom)g(m)n(us\355)g(pla-)-135
2772 y(tit)f Fs(v)s Fu(\()p Fs(R)q Fu(\))e(=)286 2709
y Fp(P)374 2730 y Fq(n)374 2797 y(i)p Fr(=1)499 2772
y Fs(v)s Fu(\()p Fs(Q)640 2784 y Fq(i)668 2772 y Fu(\).)i(T)-7
b(o)32 b(v)n(ede)h(k)n(e)f(sp)r(oru,)h(proto\276e)f Fs(v)s
Fu(\()p Fs(R)q Fu(\))h(=)e Fo(\000)p Fu(1,)i(zat\355mco)-135
2871 y Fs(v)s Fu(\()p Fs(Q)6 2883 y Fq(i)34 2871 y Fu(\))23
b(=)g Fs(f)9 b Fu(\()p Fs(s)298 2883 y Fq(i)325 2871
y Fu(\))357 2841 y Fr(2)418 2871 y Fo(\025)22 b Fu(0.)-11
2971 y(Ab)n(yc)n(hom)27 b(nahl\351dli)h(uv)n(eden\351)f(tvrzen\355,)h
(prot\341hneme)f(k)n(a\276dou)f(ze)h(stran)g(k)n(a\276-)-135
3071 y(d\351ho)j(\350tv)n(erce)f Fs(Q)416 3083 y Fq(i)474
3071 y Fu(z)h(h)n(yp)r(otetic)n(k)n(\351ho)g(dl\341\276d\354n\355)g
(nap\370\355\350)g(cel\375m)g Fs(R)q Fu(,)g(jak)g(je)h(nazna-)-135
3170 y(\350eno)c(na)g(obr\341zku:)-1321 6997 y @beginspecial
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@endspecial -135 4249 a(T\355m)37 b(se)g Fs(R)h Fu(rozpadne)d(na)i
(mal\351)g(ob)r(d\351ln\355\350)n(ky)-7 b(,)37 b(a)f(je)i(snadno)e
(vid\354t,)h(\276e)g Fs(v)s Fu(\()p Fs(R)q Fu(\))h(je)-135
4349 y(ro)n(vno)26 b(sou\350tu)h Fs(v)s Fu(\()p Fs(O)r
Fu(\))i(p\370es)e(v\271ec)n(hn)n(y)f(t)n(yto)h(mal\351)g(ob)r
(d\351ln\355\350)n(ky)g Fs(O)r Fu(.)i(P)n(o)r(dobn\354)d
Fs(v)s Fu(\()p Fs(Q)2433 4361 y Fq(i)2461 4349 y Fu(\))-135
4449 y(je)38 b(ro)n(vno)f(sou\350tu)h Fs(v)s Fu(\()p
Fs(O)r Fu(\))i(p\370es)d(v\271ec)n(hn)n(y)g(mal\351)h(ob)r
(d\351ln\355\350)n(ky)g(le\276\355c\355)g(v)g Fs(Q)2200
4461 y Fq(i)2227 4449 y Fu(.)h(Proto)-135 4548 y(skute\350n\354)27
b Fs(v)s Fu(\()p Fs(R)q Fu(\))d(=)487 4486 y Fp(P)574
4506 y Fq(n)574 4573 y(i)p Fr(=1)700 4548 y Fs(v)s Fu(\()p
Fs(Q)841 4560 y Fq(i)868 4548 y Fu(\).)-135 4668 y Fl(P)m(ozn\341mk)m
(a.)66 b Fu(P)n(o)r(dobnou)28 b(meto)r(dou)i(se)g(da)5
b(j\355)30 b(dok)n(\341zat)e(v\271elijak)n(\341)h(dal\271\355)g
(tvrzen\355)-135 4768 y(o)38 b(nemo\276nosti)g(dl\341\276d\354n\355,)h
(nap\370\355klad)e(\276e)i(kryc)n(hli)e(nelze)i(roz\370ezat)e(na)h(k)n
(one\350n\354)-135 4868 y(mnoho)27 b(\350\341st\355)g(a)g(z)h(nic)n(h)g
(slo\276it)f(pra)n(videln)n(\375)f(\350t)n(y\370st\354n.)-135
5138 y Fw(5)119 b(Samo)s(opra)m(vn\351)41 b(k)m(\363)s(dy)-135
5340 y Fl(Motiv)m(ace.)60 b Fu(Chceme)27 b(p\370en\341\271et)g(\(neb)r
(o)h(zapiso)n(v)n(at)e(a)h(\350\355st\))i(n\354jak)n(\341)d(data,)i
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(dobnost)e Fs(k)k Fu(c)n(h)n(yb)d(p\370i)h(p\370enosu)-135
5639 y(dan\351ho)41 b(p)r(o)r(\350tu)h(bit\371)g(je)g(p)r(o)r
(dstatn\354)f(men\271\355)h(ne\276)f(pra)n(vd\354p)r(o)r(dobnost)f
Fs(k)31 b Fo(\000)c Fu(1)41 b(\350i)-135 5739 y(m\351n\354)f(c)n(h)n
(yb.)g(Hla)n(vn\355)g(m)n(y\271lenk)n(a)f(samo)r(opra)n(vn)n(\375c)n(h)
f(k)n(\363)r(d\371)i(je)h(m\355sto)f(\370et\354zce)g
Fs(v)s Fu(,)-135 5839 y(kter\375)e(p)r(ot\370ebujeme)h(p\370en\351st,)g
(p)r(oslat)g(p)r(on\354kud)g(del\271\355)g(\370et\354zec)f
Fs(w)r Fu(,)i(sestro)5 b(jen)n(\375)-135 5938 y(tak,)28
b(ab)n(yc)n(hom)g(mal\375)g(p)r(o)r(\350et)i(c)n(h)n(yb)e(vznikl\375c)n
(h)g(p\370i)h(p\370enosu)f Fs(w)j Fu(um\354li)f(detek)n(o)n(v)n(at)-135
6038 y(\350i)e(dok)n(once)e(opra)n(vit.)p eop end
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TeXDict begin 9 8 bop -182 1858 a Fu(9)1186 b Ft(Obsah)p
-182 1891 2629 4 v -57 2074 a Fu(Samo)r(opra)n(vn\351)19
b(k)n(\363)r(dy)i(se)g(dnes)h(p)r(ou\276\355v)n(a)5 b(j\355)20
b(v)i(nejr\371zn\354j\271\355c)n(h)f(za\370\355zen\355c)n(h)f(o)r(d)i
(CD)-182 2174 y(p\370ehr\341)n(v)n(a\350\371)34 b(p)r(o)j(k)n(osmic)n
(k)n(\351)e(sondy)h(a)g(jejic)n(h)h(k)n(onstruk)n(ce)e(je)i
(rozs\341hl\341)d(mo)r(dern\355)-182 2274 y(discipl\355na.)i(T)-7
b(ady)35 b(si)g(uv)n(edeme)h(n\354k)n(olik)e(ob)r(ecn)n(\375c)n(h)h
(de\014nic)h(a)f(jedn)n(u)h(elegan)n(tn\355)-182 2373
y(k)n(onstruk)n(ci)26 b(zalo\276enou)g(na)i(line\341rn\355)f
(algeb\370e.)-57 2482 y(Uv)n(a\276me)20 b(k)n(onkr\351tn\355)h
(situaci:)g(Chceme)g(p)r(os\355lat)g(lib)r(o)n(v)n(oln\351)f(\350t)n
(y\370bito)n(v)n(\351)g(\370et\354zce)-182 2582 y Fs(v)25
b Fu(tv)n(aru)c Fs(abcd)p Fu(,)g(kde)g Fs(a;)14 b(b;)g(c;)g(d)23
b Fo(2)g(f)p Fu(0)p Fs(;)14 b Fu(1)p Fo(g)p Fu(.)20 b(Pra)n(vd\354p)r
(o)r(dobnost)f(dv)n(ou)i(neb)r(o)h(v\355ce)f(c)n(h)n(yb)-182
2681 y(p\370i)h(p\370enosu)g(je)g(zanedbateln\341,)g(zat\355mco)g
(jedna)g(c)n(h)n(yba)f(se)h(ob)r(\350as)g(ob)5 b(jev\355,)22
b(a)f(c)n(h)n(t\354li)-182 2781 y(b)n(yc)n(hom)27 b(ji)h(um\354t)g
(opra)n(vit.)-57 2890 y(Jeden)33 b(zp)r(\371sob)h(umo\276\362)n
(uj\355c\355)h(opra)n(vit)d(1)i(c)n(h)n(ybu)f(je)i(ztro)5
b(jit)33 b(k)n(a\276d\375)g(bit)i(a)f(p)r(o-)-182 2989
y(slat)e Fs(w)h Fu(=)d Fs(aaabbbcccddd)h Fu(\(12)g(bit\371\).)i
(Nap\370\355klad)f(pro)f Fs(v)i Fu(=)e(1011)f(p)r(o\271leme)h
Fs(w)j Fu(=)-182 3089 y(111000111111.)29 b(P\370ijde-li)34
b(na)h(druh\351m)f(k)n(onci)g(t\370eba)h(110000111111,)29
b(v\355me,)34 b(\276e)-182 3189 y(do\271lo)28 b(k)g(c)n(h)n(yb)r(\354)h
(v)n(e)f(t\370et\355m)h(bitu)g(a)f(b)n(ylo)g(p)r(osl\341no)g
(111000111111)23 b(\(aneb)r(o)28 b(c)n(h)n(yb)n(y)-182
3288 y(b)n(yly)f(p\370inejmen\271\355m)h(dv)n(\354\).)-57
3397 y(T)-7 b(o)18 b(je)h(dost)g(marnotratn)n(\375)e(zp)r(\371sob)i(k)n
(\363)r(do)n(v)n(\341n\355:)d(Uvid\355me,)k(\276e)f(1)f(c)n(h)n(ybu)g
(m)n(\371\276eme)-182 3497 y(opra)n(vit)39 b(p)r(omo)r(c\355)i(k)n
(\363)r(du,)f(kter\375)g(ze)g(4-bito)n(v)n(\351ho)f(\370et\354zce)g
(d\354l\341)i(7-bito)n(v\375)-7 b(,)39 b(tak\276e)-182
3596 y(k)n(\363)r(do)n(v)n(\341n\355m)26 b(se)h(zpr\341)n(v)n(a)f
(neprot\341hne)g(t\370ikr\341t,)h(ale)g(jenom)h(o)f(75\045.)-182
3739 y Fl(P\370\355klad:)e(Hamming\371v)f(k)m(\363)s(d.)e
Fu(T)-7 b(o)21 b(je)h(patrn\354)f(prvn\355)g(zn\341m)n(\375)g
(netrivi\341ln\355)h(samo-)-182 3839 y(opra)n(vn)n(\375)d(k)n(\363)r(d)
h(a)g(b)n(yl)h(ob)5 b(jev)n(en)19 b(v)i(50.)f(letec)n(h.)h(M\355sto)f
(dan\351ho)g(\350t)n(y\370bito)n(v)n(\351ho)f(\370et\354zce)-182
3938 y Fs(v)35 b Fu(=)d Fs(abcd)g Fu(se)h(p)r(o\271le)g(sedmibito)n
(v\375)f(\370et\354zec)g Fs(w)j Fu(=)c Fs(abcdef)9 b(g)s
Fu(,)32 b(kde)h Fs(e)e Fu(=)h Fs(a)22 b Fu(+)f Fs(b)h
Fu(+)f Fs(c)-182 4038 y Fu(\(s\350\355t\341n\355)k(mo)r(dulo)g(2\),)h
Fs(f)31 b Fu(=)23 b Fs(a)14 b Fu(+)g Fs(b)g Fu(+)g Fs(d)22
b Fu(a)j Fs(g)h Fu(=)d Fs(a)14 b Fu(+)g Fs(c)g Fu(+)g
Fs(d)p Fu(.)23 b(Nap\370\355klad)h(pro)g Fs(v)i Fu(=)d(1011)-182
4137 y(m\341me)f Fs(w)k Fu(=)c(1011001.)d(T)-7 b(en)n(to)22
b(zp)r(\371sob)g(k)n(\363)r(do)n(v)n(\341n\355)d(tak)n(\351)j(do)n(v)n
(oluje)f(opra)n(vit)f(c)n(h)n(ybn)n(\375)-182 4237 y(p\370enos)25
b(jednoho)h(\(lib)r(o)n(v)n(oln\351ho\))e(bitu,)j(jak)f(brzy)f(elegan)n
(tn\354)g(o)n(v)n(\354\370\355me)f(za)h(p)r(omo)r(ci)-182
4337 y(line\341rn\355)i(algebry)-7 b(.)-57 4514 y(Ne\276)23
b(se)g(k)g(tom)n(u)g(dostaneme,)f(p\370ipra)n(v\355me)g(si)h(n\354k)n
(olik)f(ob)r(ecn)n(\375c)n(h)h(de\014nic)g(z)g(te-)-182
4613 y(orie)c(k)n(\363)r(d\371.)h(Nec)n(h)n(\273)h Fs(S)k
Fu(je)20 b(k)n(one\350n\341)f(mno\276ina,)h(tzv.)h Fj(abe)l(ce)l(da)p
Fu(,)h(nap\370\355klad)d Fs(S)28 b Fu(=)22 b Fo(f)p Fu(0)p
Fs(;)14 b Fu(1)p Fo(g)-182 4713 y Fu(neb)r(o)24 b Fs(S)k
Fu(=)22 b Fo(f)p Fu(a)o Fs(;)14 b Fu(b)p Fs(;)g Fu(c)p
Fs(;)g Fu(\350)p Fs(;)g(:)g(:)g(:)f(;)h Fu(\276)p Fo(g)p
Fu(.)23 b(Z\341pis)g Fs(S)1078 4683 y Fq(n)1146 4713
y Fu(=)g Fo(f)p Fs(w)i Fu(=)e Fs(a)1492 4725 y Fr(1)1529
4713 y Fs(a)1573 4725 y Fr(2)1624 4713 y Fs(:)14 b(:)g(:)g(a)1779
4725 y Fq(n)1847 4713 y Fu(:)23 b Fs(a)1937 4725 y Fr(1)1974
4713 y Fs(;)14 b(:)g(:)g(:)g(;)g(a)2203 4725 y Fq(n)2271
4713 y Fo(2)23 b Fs(S)5 b Fo(g)-182 4812 y Fu(ozna\350uje)28
b(mno\276in)n(u)h(v\271ec)n(h)f(mo\276n)n(\375c)n(h)g
Fl(slo)m(v)g Fu(d\351lky)h Fs(n)g Fu(\(slo)n(v)n(o)e(zde)i(tedy)g
(znamen\341)-182 4912 y(lib)r(o)n(v)n(olnou)d(k)n(one\350nou)h(p)r
(osloupnost)g(p\355smen)g(ab)r(ecedy\).)-182 5055 y Fl(De\014nice.)63
b(K\363)s(d)29 b Fi(d\351lky)h Fs(n)f Fi(nad)h(ab)r(ecedou)f
Fs(S)34 b Fi(je)c(lib)r(o)n(v)n(oln\341)e(p)r(o)r(dmno\276ina)i
Fs(C)j Fo(\022)-182 5154 y Fs(S)-126 5124 y Fq(n)-81
5154 y Fi(.)-57 5331 y Fu(Nap\370\355klad)40 b(pro)h(Hamming\371v)h(k)n
(\363)r(d)f(m\341me)g Fs(S)51 b Fu(=)c Fo(f)p Fu(0)p
Fs(;)14 b Fu(1)p Fo(g)p Fu(,)39 b Fs(n)46 b Fu(=)g(7)c(a)f
Fs(C)48 b Fu(je)-182 5431 y(mno\276ina)26 b(v\271ec)n(h)g(sedmibito)n
(v\375c)n(h)g(slo)n(v,)f(kter\341)h(mohou)g(p)r(opsanou)g(k)n(\363)r
(do)n(v)n(ac\355)e(pro-)-182 5531 y(cedurou)45 b(vzniknout)h(ze)g
(v\271ec)n(h)g(2)959 5500 y Fr(4)1049 5531 y Fu(=)54
b(16)45 b(mo\276n)n(\375c)n(h)g(slo)n(v)g(\350t)n(y\370bito)n(v\375c)n
(h,)f(tj.)-182 5630 y Fs(C)38 b Fu(=)32 b Fo(f)p Fu(0000000,)d
(0001011,)g(0010101,)h(0011110,)f(0100110,)h(0101101,)g(0110011,)-182
5730 y(0111000,)69 b(1000111,)g(1001100,)f(1010010,)h(1011001,)g
(1100001,)g(1101010,)-182 5829 y(1110100,)24 b(1111111)p
Fo(g)p Fu(.)-57 5938 y(P)n(o)r(dstatn\341)32 b(vlastnost)h(tohoto)g(k)n
(\363)r(du)g(je,)h(\276e)g(se)g(k)n(a\276d\341)e(dv)n(\354)h(z)h(jeho)g
(slo)n(v)e(li\271\355)-182 6038 y(asp)r(o\362)20 b(v)n(e)f(t\370ec)n(h)
h(bitec)n(h.)g(T)-7 b(o)20 b(se)g(d\341)g(o)n(v)n(\354\370it)f(jedno)r
(du\271e,)h(i)h(kdy\276)e(pracn\354,)h(sro)n(vn\341n\355m)p
eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 428.031496 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
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-135 1891 2629 4 v -135 2074 a(k)n(a\276d\351)21 b(dv)n(o)5
b(jice)20 b(slo)n(v.)h(Zanedlouho)g(to)g(dok)n(\341\276eme)g(jinak)g(a)
h(t\351m\354\370)f(b)r(ezpracn\354.)g(Pro)-135 2174 y(ob)r(ecn)n(\375)
27 b(k)n(\363)r(d)g(se)g(za)n(v)n(\341d\354j\355)g
(n\341sleduj\355c\355)g(p)r(o)5 b(jm)n(y:)-11 2369 y
Fo(\017)41 b Fl(Hammingo)m(v)m(a)32 b(vzd\341lenost)c
Fu(slo)n(v)e Fs(u;)14 b(v)26 b Fo(2)d Fs(S)1568 2338
y Fq(n)1641 2369 y Fu(je)593 2557 y Fs(d)p Fu(\()p Fs(u;)14
b(v)s Fu(\))23 b(=)g Fo(jf)p Fs(i)f Fu(:)h Fs(u)1149
2569 y Fq(i)1199 2557 y Fo(6)p Fu(=)g Fs(v)1327 2569
y Fq(i)1355 2557 y Fs(;)14 b(i)22 b Fu(=)h(1)p Fs(;)14
b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)p Fo(gj)p Fs(;)72 2746
y Fu(kde)36 b Fs(u)283 2758 y Fq(i)346 2746 y Fu(zna\350\355)f
Fs(i)p Fu(-t\351)g(p\355smeno)g(v)n(e)g(slo)n(v)n(\354)f
Fs(u)p Fu(.)h(T)-7 b(o)36 b(jest,)f Fs(v)k Fu(se)d(d\341)f(z)g
Fs(u)g Fu(dostat)72 2845 y(nejv\375\271)28 b Fs(d)p Fu(\()p
Fs(u;)14 b(v)s Fu(\))28 b(\376c)n(h)n(ybami\377.)-11
3023 y Fo(\017)41 b Fu(K\363)r(d)28 b Fs(C)33 b Fl(opra)m(vuje)g
Fg(t)g Fl(c)m(h)m(yb)p Fu(,)c(p)r(okud)f(pro)e(k)n(a\276d\351)h
Fs(u)22 b Fo(2)i Fs(S)1887 2993 y Fq(n)1959 3023 y Fu(existuje)k
(nejv\375\271)72 3123 y(jedno)g Fs(v)e Fo(2)e Fs(C)34
b Fu(tak)n(o)n(v)n(\351,)25 b(\276e)j Fs(d)p Fu(\()p
Fs(u;)14 b(v)s Fu(\))23 b Fo(\024)g Fs(t)p Fu(.)-11 3301
y Fo(\017)41 b Fu(Pro)33 b(k)n(\363)r(d)g Fs(C)41 b Fu(ozna\350me)32
b Fs(d)p Fu(\()p Fs(C)6 b Fu(\))35 b(=)e(min)p Fo(f)p
Fs(d)p Fu(\()p Fs(u;)14 b(v)s Fu(\))34 b(:)g Fs(u;)14
b(v)36 b Fo(2)e Fs(C)q(;)14 b(u)33 b Fo(6)p Fu(=)g Fs(v)s
Fo(g)p Fu(,)h(to)g(je)72 3401 y Fl(minim\341ln\355)c(vzd\341lenost)e
Fu(k)n(\363)r(du)f Fs(C)6 b Fu(.)-11 3595 y(Je)27 b(snadn\351)f(o)n(v)n
(\354\370it,)f(\276e)i(dv)n(a)e(p)r(osledn\354)i(uv)n(eden\351)f(p)r(o)
5 b(jm)n(y)27 b(sp)r(olu)f(souvis\355)g(n\341sle-)-135
3695 y(do)n(vn\354:)f Fj(K\363d)j Fs(C)35 b Fj(opr)l(avuje)29
b Fs(t)f Fj(chyb,)h(pr)l(\341v\354)g(kdy\276)g Fs(d)p
Fu(\()p Fs(C)6 b Fu(\))24 b Fo(\025)f Fu(2)p Fs(t)14
b Fu(+)g(1)p Fj(.)54 b Fu(Kdy\276)25 b(tedy)h(pro)-135
3794 y(Hamming\371v)33 b(k)n(\363)r(d)f(dok)n(\341\276eme)g
Fs(d)p Fu(\()p Fs(C)6 b Fu(\))33 b Fo(\025)f Fu(3,)h(bude)g(z)g(toho)f
(vid\354t,)i(\276e)f(opra)n(vuje)e(1)-135 3894 y(c)n(h)n(ybu.)-135
4080 y Fl(K\363)s(do)m(v)m(\341n\355)37 b(a)g(dek)m(\363)s(do)m(v)m
(an\355.)69 b Fu(V)n(\354t\271inou)31 b(si)h(\350lo)n(v)n(\354k)e(p)r
(o)r(d)i(k)n(\363)r(dem)g(p\370edsta)n(vuje)-135 4180
y(n\354jak)n(ou)c(pro)r(ceduru)g(pro)g(k)n(\363)r(do)n(v)n(\341n\355)f
(a)i(dek)n(\363)r(do)n(v)n(\341n\355)d(zpr\341)n(v,)i(a)h(uv)n
(eden\341)f(de\014nice)-135 4280 y(k)n(\363)r(du)22 b(m)n(\371\276e)g
(proto)g(vypadat)f(divn\354.)i(Pro)e(skute\350n\351)h(p)r(ou\276it\355)
h(je)g(opra)n(vdu)e(p)r(ot\370eba)-135 4379 y(k)n(\363)r(d)g
Fs(C)28 b Fu(jak)n(o)20 b(v)h(de\014nici)h(doplnit)g(n\354jak)n(ou)e
(bijek)n(c\355)i Fs(c)p Fu(:)14 b(\006)1589 4349 y Fq(k)1652
4379 y Fo(!)23 b Fs(C)6 b Fu(,)22 b(kde)f(\006)h(je)g(ab)r(eceda,)-135
4479 y(v)g(n\355\276)h(je)g(naps\341na)e(p)r(\371v)n(o)r(dn\355)i
(zpr\341)n(v)n(a,)d(a)i Fs(k)k Fu(je)d(d\351lk)n(a)e(p)r(\371v)n(o)r
(dn\355)i(zpr\341)n(vy)e(\(neb)r(o)i(d\351lk)n(a)-135
4578 y(blok\371,)k(na)g(n\354\276)g(se)f(p)r(\371v)n(o)r(dn\355)i
(zpr\341)n(v)n(a)d(rozk)n(ouskuje\).)g(Pro)h(danou)h(zpr\341)n(vu)e
Fs(v)i Fo(2)c Fu(\006)2452 4548 y Fq(k)-135 4678 y Fu(se)34
b(vyp)r(o)r(\350te)h(k)n(\363)r(do)n(v)n(\351)d(slo)n(v)n(o)h
Fs(w)k Fu(=)d Fs(c)p Fu(\()p Fs(v)s Fu(\))h Fo(2)g Fs(C)41
b Fu(a)34 b(to)g(se)g(p)r(o\271le.)h(Pro)e(p\370ijat\351)h(slo)n(v)n(o)
-135 4778 y Fs(w)-74 4748 y Fk(0)-20 4778 y Fo(2)d Fs(S)122
4748 y Fq(n)199 4778 y Fu(se)g(pak)h(nejprv)n(e)f(na)5
b(jde)32 b(slo)n(v)n(o)e Fs(w)1265 4748 y Fk(00)1338
4778 y Fo(2)h Fs(C)38 b Fu(minimalizuj\355c\355)33 b
Fs(d)p Fu(\()p Fs(w)2199 4748 y Fk(0)2223 4778 y Fs(;)14
b(w)2321 4748 y Fk(00)2364 4778 y Fu(\),)32 b(a)-135
4877 y(pro)26 b(n\354j)i(se)f(sp)r(o)r(\350te)g Fs(v)546
4847 y Fk(0)593 4877 y Fu(=)22 b Fs(c)716 4847 y Fk(\000)p
Fr(1)805 4877 y Fu(\()p Fs(w)898 4847 y Fk(00)942 4877
y Fu(\))h Fo(2)g Fu(\006)1135 4847 y Fq(k)1176 4877 y
Fu(.)28 b(P)n(okud)e(p\370i)g(p\370enosu)h(do\271lo)f(k)h(nejv\375\271)
g Fs(t)-135 4977 y Fu(c)n(h)n(yb\341m)h(a)g Fs(C)35 b
Fu(opra)n(vuje)27 b Fs(t)h Fu(c)n(h)n(yb,)h(pak)f Fs(w)1177
4947 y Fk(00)1244 4977 y Fu(=)d Fs(w)31 b Fu(a)d(tud\355\276)h
Fs(v)1750 4947 y Fk(0)1799 4977 y Fu(=)24 b Fs(v)s Fu(,)29
b(\350ili)f(se)h(dostane)-135 5077 y(p\370esn\354)e(p)r(\371v)n(o)r
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(teorie)g(k)m(\363)s(d\371)d Fu(je)g(na)5 b(j\355t,)27
b(pro)f(danou)g(v)n(elik)n(ost)f(ab)r(ecedy)i Fs(S)k
Fu(a)-135 5307 y(dan\341)25 b Fs(t)i Fu(a)e Fs(n)p Fu(,)h(k)n(\363)r(d)
g Fs(C)33 b Fu(s)26 b(co)f(nejv)n(\354t\271\355m)h(p)r(o)r(\350tem)h
(slo)n(v,)e(ab)n(y)h(se)g(p\370enoso)n(v\375)e(k)n(an\341l)h(co)-135
5406 y(nejl\351p)r(e)30 b(vyu\276il.)g(Proto)e(se)h(k)n(\363)r(d)g
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(v\271em)-135 5506 y(t\370eba)39 b(p)r(oro)n(vn\341)n(v)n(at)d(i)k(kv)n
(alitu)f(k)n(\363)r(d\371)g(s)g(r\371zn)n(\375mi)g Fo(j)p
Fs(S)5 b Fo(j)p Fs(;)14 b(t;)g(n)p Fu(.)39 b(O)g(tom)h(p)r(o)5
b(jedn\341)n(v)n(\341)-135 5606 y Fj(Shannonova)31 b(te)l(orie)j
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(nebudeme.)-11 5708 y(P\370i)h(k)n(onstruk)n(ci)f(k)n(\363)r(d\371)h
(se)h(b)r(erou)f(v)g(\372v)n(ah)n(u)g(i)h(dal\271\355)f(hledisk)n(a,)g
(jak)n(o)f(nap\370\355klad)-135 5808 y(ryc)n(hlost)g(k)n(\363)r(do)n(v)
n(\341n\355)g(a)h(dek)n(\363)r(do)n(v)n(\341n\355.)-135
5938 y Fl(Line\341rn\355)45 b(k)m(\363)s(dy.)39 b Fu(Sp)r
(eci\341ln\355m)h(t)n(yp)r(em)f(k)n(\363)r(d\371)g(jsou)g
(line\341rn\355)f(k)n(\363)r(dy)-7 b(,)39 b(mezi)g(n\354\276)-135
6038 y(pat\370\355)24 b(i)h(Hamming\371v)f(k)n(\363)r(d.)g(Zde)g(ab)r
(eceda)g Fs(S)29 b Fu(je)c(k)n(one\350n\351)e(t\354leso)h(\(hla)n
(vn\355)h(p\370\355klad:)p eop end
PStoPSsaved restore
%%Page: (10,11) 6
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 850.393701 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 11 10 bop -182 1858 a Fu(11)1165 b Ft(Obsah)p
-182 1891 2629 4 v -182 2074 a Fs(S)47 b Fu(=)42 b(GF\(2\)\),)e(a)e
(pak)h Fs(S)650 2044 y Fq(n)734 2074 y Fu(je)g(v)n(ektoro)n(v\375)e
(prostor)g(nad)i Fs(S)5 b Fu(.)39 b(Ka\276d\375)f(v)n(ektoro)n(v\375)
-182 2174 y(p)r(o)r(dprostor)26 b Fs(S)299 2144 y Fq(n)372
2174 y Fu(se)h(naz\375v)n(\341)f Fj(line)l(\341rn\355)31
b(k\363d)p Fu(.)-182 2297 y Fj(Pozor)l(ov\341n\355:)f
Fu(Pro)d(line\341rn\355)g(k)n(\363)r(d)g Fs(C)34 b Fu(plat\355)456
2474 y Fs(d)p Fu(\()p Fs(C)6 b Fu(\))24 b(=)f(min)p Fo(f)p
Fs(d)p Fu(\(0)p Fs(;)14 b Fl(w)q Fu(\))23 b(:)h Fl(w)g
Fo(2)f Fs(C)q(;)14 b Fl(w)25 b Fo(6)p Fu(=)e Fl(0)p Fo(g)p
Fs(:)-57 2651 y Fu(Line\341rn\355)38 b(k)n(\363)r(d)h(se)h(nem)n
(us\355)f(zad\341)n(v)n(at)f(v\375\350tem)h(v\271ec)n(h)g(slo)n(v.)f
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(algebry)-7 b(,)26 b(dv)n(\354ma)h(z\341kladn\355mi)g(zp)r(\371sob)n(y)
-7 b(.)-80 2928 y(1.)41 b(B\341z\355,)33 b(neb)r(oli)h
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b(o)34 b(je)g(matice)f(t)n(ypu)h Fs(k)s Fo(\002)o Fs(n)p
Fu(,)26 3027 y(kde)27 b Fs(k)f Fu(=)d(dim\()p Fs(C)6
b Fu(\),)29 b(jej\355\276)f(\370\341dky)e(jsou)i(v)n(ektory)e(n\354jak)
n(\351)h(b\341ze)g Fs(C)6 b Fu(.)26 3159 y(Generuj\355c\355)24
b(matice)f(je)h(u\276ite\350n\341)g(pro)f(k)n(\363)r(do)n(v)n
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3259 y Fl(v)g Fo(2)g Fs(S)235 3228 y Fq(k)275 3259 y
Fu(,)k(p)r(o\271leme)g(v)n(ektor)e Fl(w)e Fu(=)f Fl(v)1131
3228 y Fq(T)1184 3259 y Fs(G)g Fo(2)h Fs(C)6 b Fu(.)26
3390 y(Vho)r(dnou)27 b(v)n(olb)r(ou)f(b\341ze)h(p)r(o)r(dprostoru)f
Fs(C)34 b Fu(m)n(\371\276eme)27 b(v\276dy)g(dostat)f(generu-)26
3490 y(j\355c\355)i(matici)h(tv)n(aru)e Fs(G)d Fu(=)g(\()p
Fs(I)885 3502 y Fq(k)926 3490 y Fo(j)p Fs(A)p Fu(\).)29
b(P)n(otom)e(v)n(ektor)g Fl(w)j Fu(m\341)e(prvn\355c)n(h)f
Fs(k)k Fu(slo\276ek)26 3590 y(sho)r(dn)n(\375c)n(h)j(s)i
Fl(v)q Fu(,)g(tedy)g(p\370i)f(k)n(\363)r(do)n(v)n(\341n\355)e(se)i(k)h
(p)r(\371v)n(o)r(dn\355m)n(u)f(v)n(ektoru)g(p\370ip\355\271e)26
3689 y Fs(n)20 b Fo(\000)h Fs(k)34 b Fu(\376k)n(on)n(troln\355c)n(h)28
b(slo\276ek\377.)i(T)-7 b(ak)n(o)n(v\375)29 b(zp)r(\371sob)i(k)n(\363)r
(do)n(v)n(\341n\355,)e(kdy)i(zak)n(\363)r(do-)26 3789
y(v)n(an\351)h(slo)n(v)n(o)f(sest\341)n(v)n(\341)f(ze)j(slo)n(v)n(a)e
(p)r(\371v)n(o)r(dn\355ho)i(a)f(n\354jak\375c)n(h)g(znak\371)g(na)n
(v\355c,)h(se)26 3888 y(naz\375v)n(\341)26 b Fj(systematick\375)p
Fu(.)26 4020 y(Hamming\371v)h(k)n(\363)r(d)g(je)h(systematic)n(k\375)f
(line\341rn\355)g(k)n(\363)r(d)g(d\351lky)h(7)f(nad)g(GF)q(\(2\))h(a)26
4120 y(m\341)f(generuj\355c\355)g(matici)621 4441 y Fs(G)c
Fu(=)797 4225 y Fp(0)797 4371 y(B)797 4421 y(B)797 4474
y(@)911 4291 y Fu(1)83 b(0)f(0)h(0)f(1)h(1)f(1)911 4391
y(0)h(1)f(0)h(0)f(1)h(1)f(0)911 4490 y(0)h(0)f(1)h(0)f(1)h(0)f(1)911
4590 y(0)h(0)f(0)h(1)f(0)h(1)f(1)1741 4225 y Fp(1)1741
4371 y(C)1741 4421 y(C)1741 4474 y(A)1828 4441 y Fs(:)-80
4795 y Fu(2.)41 b(Line\341rn\355)21 b(k)n(\363)r(d)h
Fs(C)29 b Fu(se)22 b(d\341)g(zadat)f(tak)n(\351)h(jak)n(o)f(mno\276ina)
h(v\271ec)n(h)f(\370e\271en\355)h(sousta)n(vy)26 4895
y Fs(P)12 b Fl(w)36 b Fu(=)f Fl(0)p Fu(,)f(kde)h Fs(P)47
b Fu(je)35 b(tzv.)g Fl(matice)40 b(k)m(on)m(troly)h(parit)m(y)36
b Fu(k)n(\363)r(du)e Fs(C)6 b Fu(.)35 b(T)-7 b(o)35 b(je)26
4995 y(u\276ite\350n\351)f(pro)g(dek)n(\363)r(do)n(v)n(\341n\355,)e
(viz)i(d\341le.)g(Je-li)g Fs(G)h Fu(=)f(\()p Fs(I)1771
5007 y Fq(k)1812 4995 y Fo(j)p Fs(A)p Fu(\),)h(pak)f(m)n(\371\276eme)26
5094 y(vz\355t)27 b Fs(P)35 b Fu(=)23 b(\()p Fo(\000)p
Fs(A)524 5064 y Fq(T)576 5094 y Fo(j)p Fs(I)635 5106
y Fq(n)p Fk(\000)p Fq(k)770 5094 y Fu(\))28 b(\(o)n(v)n(\354\370te,)e
(\276e)h(to)h(funguje!\).)-182 5295 y Fl(P\370\355klad:)33
b(Zob)s(ecn\354n)m(\375)h(Hamming\371v)f(k)m(\363)s(d.)61
b Fu(Hamming\371v)29 b(k)n(\363)r(d)g(m\341)f(matici)-182
5394 y(k)n(on)n(troly)e(parit)n(y)517 5666 y Fs(P)35
b Fu(=)693 5499 y Fp(0)693 5649 y(@)807 5566 y Fu(1)83
b(1)f(1)h(0)f(1)h(0)f(0)807 5665 y(1)h(1)f(0)h(1)f(0)h(1)f(0)807
5765 y(1)h(0)f(1)h(1)f(0)h(0)f(1)1637 5499 y Fp(1)1637
5649 y(A)1724 5666 y Fs(:)-182 5938 y Fu(V\271imn\354me)44
b(si,)g(\276e)f(sloup)r(ce)g(jsou)h(pr\341)n(v)n(\354)e(v\271ec)n(hn)n
(y)g(mo\276n\351)i(nen)n(ulo)n(v)n(\351)e(v)n(ektory)-182
6038 y(z)37 b(GF\(2\))117 6008 y Fr(3)154 6038 y Fu(.)g(T)-7
b(ato)36 b(k)n(onstruk)n(ce)f(se)h(d\341)h(zob)r(ecnit:)f(Zv)n
(ol\355me)g(parametr)f Fs(`)j Fo(\025)f Fu(2,)g(a)p eop
end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 422.362205 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 12 11 bop 1031 1858 a Ft(Obsah)1165 b Fu(12)p
-135 1891 2629 4 v -135 2074 a(de\014n)n(ujeme)26 b Fj(zobe)l
(cn\354n\375)i(Hamming\371v)g(k\363d)36 b Fu(p)r(omo)r(c\355)25
b(matice)h(k)n(on)n(troly)d(parit)n(y)i Fs(P)12 b Fu(.)-135
2174 y(T)-7 b(a)35 b(m\341)g Fs(`)f Fu(\370\341dek)g(a)h
Fs(n)h Fu(=)f(2)751 2144 y Fq(`)806 2174 y Fo(\000)23
b Fu(1)35 b(sloup)r(c\371,)g(a)f(sloup)r(ce)h(jsou)g(v\271ec)n(hn)n(y)f
(nen)n(ulo)n(v)n(\351)-135 2274 y(v)n(ektory)26 b(z)h
Fs(GF)12 b Fu(\(2\))465 2243 y Fq(`)498 2274 y Fu(.)27
b(T)-7 b(edy)28 b Fs(k)e Fu(=)d(2)955 2243 y Fq(`)1004
2274 y Fo(\000)18 b Fs(`)g Fo(\000)h Fu(1)27 b(a)g Fs(n)c
Fu(=)f(2)1564 2243 y Fq(`)1614 2274 y Fo(\000)c Fu(1.)-135
2395 y Fj(Tvrzen\355:)35 b Fu(Zob)r(ecn\354n)n(\375)f(Hamming\371v)g(k)
n(\363)r(d)f Fs(C)41 b Fu(m\341)34 b Fs(d)p Fu(\()p Fs(C)6
b Fu(\))35 b(=)e(3,)h(tedy)h(opra)n(vuje)d(1)-135 2495
y(c)n(h)n(ybu.)-135 2616 y Fj(D\371kaz:)58 b Fu(Sta\350\355)27
b(o)n(v)n(\354\370it,)g(\276e)g(\276\341dn)n(\375)g Fl(w)e
Fo(2)e Fs(GF)12 b Fu(\(2\))1383 2586 y Fq(n)1457 2616
y Fu(s)27 b(jednou)h(neb)r(o)g(dv)n(\354ma)f(jedni\350-)-135
2716 y(k)n(ami)i(nespl\362)n(uje)i Fs(P)12 b Fl(w)28
b Fu(=)f Fl(0)p Fu(.)j(Pro)f Fl(w)i Fu(s)f(jednou)h(jedni\350)n(k)n(ou)
e(b)n(y)h(to)g(znamenalo,)f(\276e)-135 2815 y Fs(P)44
b Fu(m\341)31 b(n)n(ulo)n(v\375)g(sloup)r(ec,)h(a)f(pro)g
Fl(w)j Fu(se)d(dv)n(\354ma)g(jedni\350)n(k)n(ami)h(b)n(yc)n(hom)f
(dostali,)g(\276e)-135 2915 y(dv)n(a)c(sloup)r(ce)g Fs(P)40
b Fu(se)27 b(ro)n(vna)5 b(j\355.)26 b(Ani)j(jedna)e(mo\276nost)g
(tud\355\276)i(nenast\341)n(v)n(\341)c(a)j(d\371k)n(az)f(je)-135
3015 y(hoto)n(v.)-11 3158 y(P)n(oznamenejme,)d(\276e)g(\(zob)r
(ecn\354n)n(\375\))g(Hamming\371v)h(k)n(\363)r(d)e(je)i
(optim\341ln\355)g(v)f(n\341sle-)-135 3271 y(duj\355c\355m)i(sm)n
(yslu:)f(\256\341dn)n(\375)g(k)n(\363)r(d)f Fs(C)30 b
Fo(\022)22 b Fs(GF)12 b Fu(\(2\))1274 3241 y Fr(2)1307
3216 y Fm(`)1337 3241 y Fk(\000)p Fr(1)1451 3271 y Fu(s)26
b Fs(d)p Fu(\()p Fs(C)6 b Fu(\))24 b Fo(\025)e Fu(3)j(nem\341)g(v\355c)
h(slo)n(v)e(ne\276)-135 3371 y(zob)r(ecn\354n)n(\375)j(Hamming\371v)g
(k)n(\363)r(d.)g(D\371k)n(az)h(p)r(onec)n(h\341)n(v)n(\341me)d(jak)n(o)
i(\(t\354\276\271\355\))h(cvi\350en\355.)-135 3492 y
Fl(Dek)m(\363)s(do)m(v)m(\341n\355)37 b(zob)s(ecn\354n\351ho)f
(Hammingo)m(v)m(a)g(k)m(\363)s(du.)67 b Fu(N\354kdo)31
b(n\341m)h(p)r(oslal)-135 3592 y(slo)n(v)n(o)e Fl(w)j
Fu(zob)r(ecn\354n\351ho)e(Hammingo)n(v)n(a)f(k)n(\363)r(du)i(a)f
(p\370ijali)h(jsme)g Fl(w)1966 3561 y Fk(0)1989 3592
y Fu(.)g(P)n(okud)f(do\271lo)-135 3691 y(k)41 b(nejv\375\271)f
(jedn\351)h(c)n(h)n(yb)r(\354,)g(m\341me)g Fl(w)1051
3661 y Fk(0)1119 3691 y Fu(=)k Fl(w)d Fu(neb)r(o)f Fl(w)1624
3661 y Fk(0)1692 3691 y Fu(=)k Fl(w)29 b Fu(+)d Fl(e)2035
3703 y Fq(i)2104 3691 y Fu(pro)40 b(n\354jak)n(\351)-135
3791 y Fs(i)23 b Fo(2)g(f)p Fu(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)e
(;)i(n)p Fo(g)p Fu(,)27 b(kde)g Fl(e)681 3803 y Fq(i)737
3791 y Fu(m\341)g(jedni\350)n(ku)h(na)f(m\355st\354)h
Fs(i)f Fu(a)g(jinde)i(n)n(uly)-7 b(.)-11 3890 y(Zda)25
b(do\271lo)f(k)h(c)n(h)n(yb)r(\354)f(p\370i)h(p\370enosu)f(a)h(kde)g
(se)g(ok)n(am\276it\354)f(p)r(ozn\341)g(p)r(o)r(dle)i(sou\350in)n(u)
-135 3990 y Fs(P)12 b Fl(w)0 3960 y Fk(0)23 3990 y Fu(.)39
b(P)n(okud)e(toti\276)i Fl(w)630 3960 y Fk(0)694 3990
y Fu(=)i Fl(w)q Fu(,)e(pak)f Fs(P)12 b Fl(w)1237 3960
y Fk(0)1301 3990 y Fu(=)41 b Fl(0)p Fu(,)d(zat\355mco)g(pro)g
Fl(w)2065 3960 y Fk(0)2130 3990 y Fu(=)i Fl(w)27 b Fu(+)f
Fl(e)2466 4002 y Fq(i)-135 4090 y Fu(je)31 b Fs(P)12
b Fl(w)93 4060 y Fk(0)145 4090 y Fu(=)28 b Fs(P)12 b
Fl(w)21 b Fu(+)g Fs(P)12 b Fl(e)588 4102 y Fq(i)643 4090
y Fu(=)28 b Fs(P)12 b Fl(e)845 4102 y Fq(i)901 4090 y
Fu(=)28 b Fl(p)1047 4102 y Fq(i)1075 4090 y Fu(,)i(co\276)h(je)g
Fs(i)p Fu(-t)n(\375)f(sloup)r(ec)g(matice)h Fs(P)12 b
Fu(.)31 b(Proto\276e)-135 4189 y(sloup)r(ce)20 b Fs(P)33
b Fu(jsou)20 b(nen)n(ulo)n(v)n(\351)f(a)h(na)n(vz\341)5
b(jem)19 b(r\371zn\351,)h(c)n(h)n(ybn\341)g(p)r(ozice)g
Fl(w)1996 4159 y Fk(0)2040 4189 y Fu(se)h(d\341)f(snadno)-135
4289 y(iden)n(ti\014k)n(o)n(v)n(at.)-11 4389 y(M\371\276eme)27
b(dok)n(once)f(p\370ero)n(vnat)f(sloup)r(ce)i(matice)f
Fs(P)39 b Fu(tak,)27 b(ab)n(y)f Fl(p)2042 4401 y Fq(i)2097
4389 y Fu(b)n(yl)g(bin\341rn\355)-135 4488 y(z\341pis)h(\350\355sla)h
Fs(i)p Fu(,)f(a)h(pak)f(v)n(ektor)g Fs(P)12 b Fl(w)959
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(oloh)n(u)i(c)n(h)n(yb)n(y)-7 b(.)27 b(Nesm\355me)-135
4588 y(o)n(v\271em)f(zap)r(omenout)i(spr\341)n(vn\354)e(p\370ero)n
(vnat)f(i)j(sloup)r(ce)f(matice)h Fs(G)p Fu(.)-135 4860
y Fw(6)119 b(Kon)m(trola)39 b(n\341sob)s(en\355)j(matic)-135
5042 y Fu(N\341sob)r(en\355)33 b(matic)h(je)g(v)n(eled\371le\276it\341)
f(op)r(erace.)f(P\370\355mo)r(\350ar\375)g(algoritm)n(us)g(na)h
(n\341so-)-135 5141 y(b)r(en\355)g(dv)n(ou)g(matic)g(t)n(ypu)g
Fs(n)22 b Fo(\002)g Fs(n)32 b Fu(vy\276aduje)h(\370\341do)n(v)n(\354)e
Fs(n)1612 5111 y Fr(3)1682 5141 y Fu(aritmetic)n(k\375c)n(h)h(op)r
(erac\355.)-135 5241 y(P\370ekv)n(apiv)n(\354)22 b(b)n(yly)i(ale)h(ob)5
b(jev)n(en)n(y)23 b(algoritm)n(y)g(s)i(lep\271\355)f(asymptotic)n(k)n
(ou)f(slo\276itost\355)h(a)-135 5340 y(nejlep\271\355m)n(u)29
b(z)g(nic)n(h)g(sta\350\355)f(\370\341do)n(v)n(\354)f(jen)i
Fs(O)r Fu(\()p Fs(n)1268 5310 y Fr(2)p Fq(:)p Fr(376)1425
5340 y Fu(\))h(op)r(erac\355.)d(Nicm\351n\354)j(k)n(onstan)n(ta)-135
5440 y(\372m\354rnosti)38 b(je)i(zat\355m)f(tak)g(astronomic)n(k)n
(\341,)d(\276e)j(ten)n(to)g(algoritm)n(us)e(je)i(za)5
b(j\355ma)n(v\375)-135 5540 y(p)r(ouze)24 b(teoretic)n(ky)-7
b(.)24 b(Matice,)g(pro)g(n\354\276)h(b)n(y)f(se)g(jeho)h(lep\271\355)f
(asymptotic)n(k)n(\341)f(efektivita)-135 5639 y(pro)5
b(jevila,)31 b(se)g(nemohou)h(v)n(ej\355t)h(do)e(\276\341dn\351ho)h
(sou\350asn\351ho)e(a)i(asi)f(ani)h(budouc\355ho)-135
5739 y(p)r(o)r(\350\355ta\350e.)-11 5839 y(P)n(okrok)g(ale)i(nejde)h
(zasta)n(vit,)e(a)h(brzy)g(m)n(\371\276e)g(n\354jak)n(\341)g(\014rma)g
(za\350\355t)g(pro)r(d\341)n(v)n(at)-135 5938 y(program)20
b(MA)-7 b(TRIX)22 b(WIZARD,)h(o)f(n\354m\276)g(tvrd\355,)g(\276e)f
(nev\355dan)n(\375m)h(no)n(v\375m)f(algorit-)-135 6038
y(mem)29 b(n\341sob\355)f(matice)h(opra)n(vdu)e(blesk)n(o)n(v)n(\354.)g
(V)-7 b(\341m)29 b(b)n(y)g(se)g(tak)n(o)n(v\375)e(program)g(ho)r(dil,)p
eop end
PStoPSsaved restore
%%Page: (12,13) 7
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 0.000000 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 13 12 bop -182 1858 a Fu(13)1165 b Ft(Obsah)p
-182 1891 2629 4 v -182 2074 a Fu(ale)29 b(nespr\341)n(vn\354)g(sp)r(o)
r(\350ten)n(\375)g(sou\350in)h(matic)g(b)n(y)f(pro)g(v)n(\341s)g(mohl)g
(m\355t)i(nedoz\355rn\351)e(n\341-)-182 2174 y(sledky)-7
b(.)29 b(P)n(ot\370eb)r(o)n(v)n(ali)d(b)n(yste)j(n\354jak\375)g(jedno)r
(duc)n(h)n(\375)g(program,)e(kter\375)h(b)n(y)h(v\276dyc)n(ky)-182
2274 y(zk)n(on)n(trolo)n(v)n(al,)20 b(jestli)k(v\375sledn\341)e(matice)
i Fs(C)29 b Fu(je)24 b(opra)n(vdu)e(sou\350inem)h(zadan)n(\375c)n(h)f
(ma-)-182 2373 y(tic)37 b Fs(A)g Fu(a)e Fs(B)t Fu(.)i(Nem\341)f
(samoz\370ejm\354)g(sm)n(ysl)f(matice)h Fs(A)h Fu(a)f
Fs(B)41 b Fu(vyn\341sobit)35 b(a)h(p)r(oro)n(v-)-182
2473 y(nat)28 b(v\375sledek)f(s)g Fs(C)6 b Fu(,)28 b(proto\276e)f
(neum\355te)h(n\341sobit)f(matice)h(ani)f(zdalek)n(a)g(tak)g(ryc)n(hle)
-182 2572 y(jak)n(o)f(MA)-7 b(TRIX)28 b(WIZARD.)f(Kdy\276)g(se)f(ale)h
(p\370ipust\355)f(mali\350)n(k)n(\341)g(pra)n(vd\354p)r(o)r(dobnost)
-182 2672 y(c)n(h)n(yb)n(y)-7 b(,)33 b(spr\341)n(vnost)g(matico)n(v)n
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n(v)n(at)c(v)n(elmi)-182 2772 y(efektivn\354.)g(Pro)e(jedno)r(duc)n
(host)i(p\370edp)r(okl\341dejme,)f(\276e)h(prvky)f(matic)g(jsou)h
(racio-)-182 2871 y(n\341ln\355)d(\350\355sla,)e(i)i(kdy\276)f
(n\341sleduj\355c\355)h(meto)r(da)f(funguje)h(pro)f(matice)g(nad)h
(jak\375mk)n(oliv)-182 2971 y(t\354lesem.)-57 3074 y(Kon)n(troln\355)i
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b Fu(t)n(ypu)30 b Fs(n)21 b Fo(\002)e Fs(n)31 b Fu(jak)n(o)e(vstup.)
-182 3173 y(Zv)n(ol\355)34 b(si)g(p)r(omo)r(c\355)h(gener\341toru)d
(n\341ho)r(dn)n(\375c)n(h)i(\350\355sel)g(n\341ho)r(dn)n(\375)g
Fs(n)p Fu(-slo\276k)n(o)n(v\375)e(v)n(ektor)-182 3273
y Fl(x)g Fu(z)f(n)n(ul)h(a)f(jedni\350ek.)h(P\370esn\354ji,)e(k)n
(a\276d\375)h(v)n(ektor)f(z)h Fo(f)p Fu(0)p Fs(;)14 b
Fu(1)p Fo(g)1655 3243 y Fq(n)1730 3273 y Fu(se)31 b(ob)5
b(jev\355)31 b(se)g(stejnou)-182 3373 y(pra)n(vd\354p)r(o)r
(dobnost\355,)17 b(ro)n(vnou)g(2)816 3342 y Fk(\000)p
Fq(n)912 3373 y Fu(.)i(Algoritm)n(us)e(sp)r(o)r(\350\355t\341)i
(sou\350in)f Fs(C)6 b Fl(x)19 b Fu(\(p)r(omo)r(c\355)f(\370\341-)-182
3472 y(do)n(v)n(\354)23 b Fs(n)56 3442 y Fr(2)117 3472
y Fu(op)r(erac\355\))g(a)h(sou\350in)f Fs(AB)t Fl(x)i
Fu(\(zase)e(p)r(omo)r(c\355)h(\370\341do)n(v)n(\354)e
Fs(n)1757 3442 y Fr(2)1818 3472 y Fu(op)r(erac\355)h({)h(spr\341)n
(vn\351)-182 3572 y(uz\341)n(v)n(ork)n(o)n(v)n(\341n\355)g(je)29
b(samoz\370ejm\354)e Fs(A)p Fu(\()p Fs(B)t Fl(x)p Fu(\)\).)j(P)n(okud)d
(se)h(v\375sledky)f(sho)r(duj\355,)i(o)r(dp)r(o)n(v\355)-182
3671 y(algoritm)n(us)d(ANO)i(\()p Fs(C)34 b Fu(je)28
b(sou\350inem)f Fs(A)h Fu(a)f Fs(B)t Fu(\),)h(a)g(jinak)f(NE.)-57
3774 y(P)n(okud)h(plat\355)h Fs(C)j Fu(=)25 b Fs(AB)t
Fu(,)k(o)r(dp)r(o)n(v\355)g(algoritm)n(us)f(v\276dy)g(ANO,)i(a)e(tedy)i
(spr\341)n(vn\354.)-182 3874 y(P)n(okud)24 b(ale)h Fs(C)k
Fo(6)p Fu(=)23 b Fs(AB)t Fu(,)i(m)n(\371\276e)g(o)r(dp)r(o)n(v)n
(\354d\354t)g(jak)n(o)f(NE,)h(tak)g(ANO.)g(Tvrd\355me)g(ale,)f(\276e)
-182 3973 y(\(nespr\341)n(vn\341\))31 b(o)r(dp)r(o)n(v)n(\354\357)h
(ANO)g(m\341)h(pra)n(vd\354p)r(o)r(dobnost)d(nejv\375\271)1907
3941 y Fr(1)p 1907 3955 34 4 v 1907 4002 a(2)1950 3973
y Fu(,)i(a)g(tedy)h(algo-)-182 4073 y(ritm)n(us)27 b(o)r(dhal\355)h(c)n
(h)n(ybn\351)f(matico)n(v)n(\351)f(n\341sob)r(en\355)h(s)h(pra)n
(vd\354p)r(o)r(dobnost\355)e(asp)r(o\362)2285 4040 y
Fr(1)p 2285 4054 V 2285 4102 a(2)2328 4073 y Fu(.)-57
4176 y(P)n(olo\276me)c Fs(D)j Fu(=)e Fs(C)18 b Fo(\000)12
b Fs(AB)t Fu(.)25 b(T)-7 b(e\357)24 b(sta\350\355)g(uk)n(\341zat,)g
(\276e)g(je-li)g Fs(D)j Fu(lib)r(o)n(v)n(oln\341)c(nen)n(ulo)n(v)n
(\341)-182 4275 y(matice)28 b(t)n(ypu)g Fs(n)19 b Fo(\002)f
Fs(n)28 b Fu(a)f Fl(x)i Fu(je)f(n\341ho)r(dn)n(\375)g(v)n(ektor)e
Fo(f)p Fu(0)p Fs(;)14 b Fu(1)p Fo(g)1549 4245 y Fq(n)1592
4275 y Fu(,)28 b(p)r(otom)g(v)n(ektor)f Fl(y)e Fu(=)f
Fs(D)r Fl(x)-182 4375 y Fu(je)31 b(nen)n(ulo)n(v\375)f(s)g(pra)n
(vd\354p)r(o)r(dobnost\355)f(asp)r(o\362)1256 4342 y
Fr(1)p 1256 4356 V 1256 4404 a(2)1299 4375 y Fu(.)i(Bu\357)f
Fs(d)1577 4387 y Fq(ij)1664 4375 y Fo(6)p Fu(=)e(0.)i(Ov)n
(\354\370\355me,)f(\276e)i(pak)-182 4475 y Fs(y)-141
4487 y Fq(i)-90 4475 y Fo(6)p Fu(=)22 b(0)27 b(s)h(pra)n(vd\354p)r(o)r
(dobnost\355)e(nejm\351n\354)1136 4442 y Fr(1)p 1136
4456 V 1136 4503 a(2)1179 4475 y Fu(.)i(Plat\355)316
4663 y Fs(y)357 4675 y Fq(i)407 4663 y Fu(=)23 b Fs(d)538
4675 y Fq(i)p Fr(1)599 4663 y Fs(x)646 4675 y Fr(1)702
4663 y Fu(+)18 b Fs(d)828 4675 y Fq(i)p Fr(2)889 4663
y Fs(x)936 4675 y Fr(2)992 4663 y Fu(+)g Fo(\001)c(\001)g(\001)k
Fu(+)g Fs(d)1316 4675 y Fq(in)1385 4663 y Fs(x)1432 4675
y Fq(n)1501 4663 y Fu(=)23 b Fs(d)1632 4675 y Fq(ij)1690
4663 y Fs(x)1737 4675 y Fq(j)1791 4663 y Fu(+)18 b Fs(S;)-182
4852 y Fu(kde)782 4961 y Fs(S)27 b Fu(=)1039 4882 y Fp(X)958
5049 y Fm(k)q Fn(=1)p Fm(;)p Fn(2)p Fm(;:::;n)1048 5097
y(k)q Ff(6)p Fn(=)p Fm(j)1264 4961 y Fs(d)1307 4973 y
Fq(ik)1371 4961 y Fs(x)1418 4973 y Fq(k)1460 4961 y Fs(:)-182
5238 y Fu(P\370edsta)n(vme)21 b(si,)h(\276e)g(v)n(ol\355me)g(slo\276ky)
f(v)n(ektoru)h Fl(x)g Fu(jedn)n(u)h(p)r(o)g(druh\351,)f(\370ekn\354me)g
(p)r(o)r(dle)-182 5337 y(v\375sledk\371)28 b Fs(n)g Fu(ho)r(d\371)g
(minc\355,)h(a)e(\276e)h Fs(x)919 5349 y Fq(j)983 5337
y Fu(se)g(v)n(ol\355)f(jak)n(o)g(p)r(osledn\355.)h(P\370ed)g(t\355m)n
(to)g(p)r(osled-)-182 5437 y(n\355m)j(ho)r(dem)g(minc\355)g(je)g(ho)r
(dnota)f Fs(S)5 b Fu(,)31 b(kter\341)f(na)g Fs(x)1403
5449 y Fq(j)1469 5437 y Fu(nez\341)n(vis\355,)g(u\276)g(za\014xo)n(v)n
(\341na.)e(P)n(o)-182 5537 y(p)r(osledn\355m)j(ho)r(du)h(bu\357)f(nec)n
(h\341me)f Fs(S)36 b Fu(b)r(eze)31 b(zm\354n)n(y)g(\(kdy\276)g(vyjde)g
Fs(x)1988 5549 y Fq(j)2052 5537 y Fu(=)d(0\),)j(neb)r(o)-182
5636 y(k)38 b(n\354m)n(u)g(p\370i\350teme)g(nen)n(ulo)n(v)n(\351)f
(\350\355slo)g Fs(d)1076 5648 y Fq(ij)1173 5636 y Fu(\(p)r(okud)h
Fs(x)1516 5648 y Fq(j)1592 5636 y Fu(=)i(1\).)e(V)h(asp)r(o\362)e
(jednom)-182 5736 y(z)25 b(t\354c)n(h)n(to)f(p\370\355pad\371)g
(dostaneme)g(nen)n(ulo)n(v\375)f(v\375sledek,)h(a)g(tud\355\276)h
Fs(D)r Fl(x)f Fo(6)p Fu(=)e Fl(0)j Fu(m\341)f(pra)n(v-)-182
5836 y(d\354p)r(o)r(dobnost)k(p\370inejmen\271\355m)832
5803 y Fr(1)p 832 5817 V 832 5864 a(2)875 5836 y Fu(,)g(jak)g(jsme)f
(tvrdili.)-57 5938 y(Dosud)38 b(p)r(opsan)n(\375)f(algoritm)n(us)f(k)n
(on)n(troly)h(matico)n(v)n(\351ho)f(n\341sob)r(en\355)i(je)g(ryc)n
(hl\375)-7 b(,)-182 6038 y(ale)43 b(zat\355m)g(vypad\341)f
(zna\350n\354)h(nesp)r(olehliv\375)-7 b(.)43 b(Uk)n(\341zali)g(jsme)g
(p)r(ouze,)g(\276e)g(o)r(dhal\355)p eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 428.031496 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 14 13 bop 1031 1858 a Ft(Obsah)1165 b Fu(14)p
-135 1891 2629 4 v -135 2074 a(c)n(h)n(ybu)21 b(asp)r(o\362)f(v)i(p)r
(olo)n(vin\354)e(p\370\355pad\371.)h(Kdy\276)g(ho)g(ale)g(zopakujeme)g
(pro)f(jeden)i(vstup)-135 2174 y Fs(A;)14 b(B)t(;)g(C)37
b Fu(t\370eba)30 b(pades\341tkr\341t,)g(unikne)h(m)n(u)g(c)n(h)n(yba)e
(s)i(pra)n(vd\354p)r(o)r(dobnost\355)e(nejv\375\271)-135
2274 y(2)-93 2243 y Fk(\000)p Fr(50)62 2274 y Fs(<)j
Fu(10)243 2243 y Fk(\000)p Fr(15)364 2274 y Fu(,)i(a)f(tato)g(pra)n
(vd\354p)r(o)r(dobnost)f(je)i(pro)f(praktic)n(k)n(\351)f(\372\350ely)h
(zanedba-)-135 2373 y(teln\341.)-135 2497 y Fl(P)m(ozn\341mk)m(a.)56
b Fu(My\271lenk)n(a)24 b Fj(pr)l(avd\354podobnostn\355)30
b(kontr)l(oly)e(v\375po\350t\371)p Fu(,)e(kterou)f(jsme)-135
2597 y(zde)h(vid\354li)g(v)f(jedno)r(duc)n(h\351)i(form\354,)e(se)h(uk)
n(\341zala)e(neob)n(y\350ejn\354)h(plo)r(dnou.)h(T)-7
b(akzv)n(an\341)-135 2696 y(PCP)32 b(v)n(\354ta)g(v)g(teorii)g(v\375p)r
(o)r(\350etn\355)h(slo\276itosti)f(uk)n(\341zala,)f(\276e)h(pro)g(k)n
(a\276dou)g(efektivn\354)-135 2796 y(\370e\271itelnou)d(v\375p)r(o)r
(\350etn\355)h(\372loh)n(u)f(se)h(\370e\271en\355)f(d\341)g(v)n(elmi)h
(ryc)n(hle)f(pra)n(vd\354p)r(o)r(dobnostn\354)-135 2895
y(zk)n(on)n(trolo)n(v)n(at.)e(P)n(opul\341rn\354)h(\370e\350eno,)i(p)r
(omal\375)g(osobn\355)f(p)r(o)r(\350\355ta\350)h(m)n(\371\276e)h(v)f
(principu)-135 2995 y(k)n(on)n(trolo)n(v)n(at)e(v\375p)r(o)r(\350t)n(y)
k(p)r(o)g(nejv\375k)n(onn\354j\271\355c)n(h)f(sup)r(erp)r(o)r
(\350\355ta\350\355c)n(h.)g(Na)n(v\355c)g(se)h(ob)5 b(je-)-135
3095 y(vily)27 b(p\370ekv)n(apiv)n(\351)f(souvislosti)g(t\354c)n(h)n
(to)h(v\375sledk\371)g(s)h(apro)n(xima\350n\355mi)e(algoritm)n(y)-7
b(.)-135 3368 y Fw(7)119 b(P)m(okr\375v)m(\341n\355)40
b(\372pln)m(\375mi)h(bipartitn\355mi)g(grafy)-135 3574
y Fl(V)m(\354ta.)i Fi(Je-li)36 b(mno\276ina)g Fs(E)5
b Fu(\()p Fs(K)831 3586 y Fq(n)876 3574 y Fu(\))p Fi(,)38
b(tj.)f(mno\276in)n(y)g(hran)f(\372pln\351ho)h(grafu)f(na)g
Fs(n)h Fi(vr-)-135 3674 y(c)n(holec)n(h,)h(vyj\341d\370ena)f(jak)n(o)h
(disjunktn\355)h(sjedno)r(cen\355)g(mno\276in)g(hran)f
Fs(m)g Fi(\372pln)n(\375c)n(h)-135 3774 y(bipartitn\355c)n(h)25
b(p)r(o)r(dgraf\371,)g(pak)g Fs(m)e Fo(\025)g Fs(n)13
b Fo(\000)h Fu(1)p Fi(.)50 b Fu(\(Vyj\341d\370en\355)26
b(s)f Fs(m)e Fu(=)f Fs(n)14 b Fo(\000)g Fu(1)25 b(je)g(snadn\351)-135
3873 y(na)5 b(j\355t.\))-135 3997 y Fl(D\371k)m(az.)41
b Fu(P\370edp)r(okl\341dejme,)17 b(\276e)i(\372pln\351)f(bipartitn\355)
h(grafy)e Fs(B)1760 4009 y Fr(1)1797 3997 y Fs(;)d(:)g(:)g(:)g(;)g(B)
2045 4009 y Fq(m)2126 3997 y Fu(disjunktn\354)-135 4096
y(p)r(okr\375v)n(a)5 b(j\355)36 b(v\271ec)n(hn)n(y)h(hran)n(y)g
Fs(K)886 4108 y Fq(n)931 4096 y Fu(,)h(a)g(nec)n(h)n(\273)g(\()p
Fs(X)1405 4108 y Fq(k)1446 4096 y Fs(;)14 b(Y)1531 4108
y Fq(k)1572 4096 y Fu(\))38 b(je)h(rozklad)d(mno\276in)n(y)i(vr-)-135
4196 y(c)n(hol\371)26 b Fs(B)146 4208 y Fq(k)214 4196
y Fu(na)h(dv)n(\354)f(\350\341sti)h(tak)n(o)n(v)n(\351,)e(\276e)i(hran)
n(y)e Fs(B)1355 4208 y Fq(k)1423 4196 y Fu(jdou)i(jen)h(mezi)f(nimi.)g
(\(Mno\276ina)-135 4296 y Fs(V)19 b Fu(\()p Fs(B)27 4308
y Fq(k)68 4296 y Fu(\))k(=)g Fs(X)280 4308 y Fq(k)339
4296 y Fo([)c Fs(Y)461 4308 y Fq(k)529 4296 y Fu(nem)n(us\355)28
b(b)n(\375t)g(cel\351)f Fs(V)19 b Fu(\()p Fs(K)1288 4308
y Fq(n)1333 4296 y Fu(\).\))-11 4395 y(Ka\276d\351m)n(u)36
b(grafu)g Fs(B)652 4407 y Fq(k)730 4395 y Fu(p\370i\370ad\355me)g
Fs(n)25 b Fo(\002)f Fs(n)37 b Fu(matici)g Fs(A)1694 4407
y Fq(k)1735 4395 y Fu(,)g(jej\355\276)h(prv)n(ek)d(v)i
Fs(i)p Fu(-t\351m)-135 4495 y(\370\341dku)27 b(a)g Fs(j)5
b Fu(-t\351m)27 b(sloup)r(ci)h(je)512 4718 y Fs(a)556
4675 y Fr(\()p Fq(k)q Fr(\))556 4742 y Fq(ij)672 4718
y Fu(=)746 4601 y Fp(\032)822 4668 y Fu(1)110 b(p)r(okud)28
b Fs(i)23 b Fo(2)g Fs(X)1427 4680 y Fq(k)1495 4668 y
Fu(a)k Fs(j)h Fo(2)c Fs(Y)1753 4680 y Fq(k)822 4767 y
Fu(0)110 b(jinak.)-135 4942 y(Ka\276d\341)21 b Fs(A)180
4954 y Fq(k)243 4942 y Fu(m\341)g(ho)r(dnost)h(1,)g(p)r(on\354v)n
(ad\276)f(v\271ec)n(hn)n(y)g(nen)n(ulo)n(v)n(\351)f(\370\341dky)h(jsou)
h(ro)n(vn)n(y)e(t\351-)-135 5042 y(m)n(u\276)i(v)n(ektoru,)f(toti\276)i
(v)n(ektoru)e(s)h(jedni\350)n(k)n(ami)g(v)g(p)r(ozic\355c)n(h,)g(jejic)
n(h\276)h(indexy)f(n\341le\276ej\355)-135 5141 y Fs(Y)-87
5153 y Fq(k)-46 5141 y Fu(,)28 b(a)f(s)g(n)n(ulami)h(v\271ude)f(jinde.)
-11 5241 y(Uv)n(a\276me)22 b(matici)g Fs(A)h Fu(=)g Fs(A)783
5253 y Fr(1)827 5241 y Fu(+)7 b Fs(A)961 5253 y Fr(2)1006
5241 y Fu(+)g Fo(\001)14 b(\001)g(\001)7 b Fu(+)g Fs(A)1316
5253 y Fq(m)1379 5241 y Fu(.)22 b(Ho)r(dnost)g(sou\350tu)f(dv)n(ou)h
(matic)g(je)-135 5340 y(nejv\375\271)27 b(ro)n(vna)f(sou\350tu)h(jejic)
n(h)h(ho)r(dnost\355)f(\(pro)r(\350?\),)h(a)f(tud\355\276)h(ho)r(dnost)
g Fs(A)f Fu(je)h(nejv\375\271)-135 5440 y Fs(m)p Fu(.)g(Sta\350\355)f
(tedy)h(dok)n(\341zat,)e(\276e)h(tato)h(ho)r(dnost)f(je)h(asp)r(o\362)f
Fs(n)18 b Fo(\000)g Fu(1.)-11 5540 y(Ka\276d\341)i(hrana)g
Fo(f)p Fs(i;)14 b(j)5 b Fo(g)20 b Fu(n\341le\276\355)h(pr\341)n(v)n
(\354)f(jednom)n(u)h(z)g(graf\371)f Fs(B)1785 5552 y
Fq(k)1826 5540 y Fu(,)i(a)e(proto)h(pro)f(k)n(a\276d\351)-135
5639 y Fs(i)27 b Fo(6)p Fu(=)f Fs(j)35 b Fu(plat\355)30
b(bu\357)h Fs(a)490 5651 y Fq(ij)575 5639 y Fu(=)c(1,)i
Fs(a)805 5651 y Fq(j)s(i)891 5639 y Fu(=)d(0,)k(aneb)r(o)f
Fs(a)1365 5651 y Fq(ij)1451 5639 y Fu(=)d(0,)k Fs(a)1681
5651 y Fq(j)s(i)1766 5639 y Fu(=)d(1)i(\(p\370itom)h
Fs(a)2280 5651 y Fq(ii)2331 5639 y Fu(=0\).)-135 5739
y(Odtud)e Fs(A)19 b Fu(+)f Fs(A)354 5709 y Fq(T)429 5739
y Fu(=)23 b Fs(J)563 5751 y Fq(n)626 5739 y Fo(\000)18
b Fs(I)745 5751 y Fq(n)791 5739 y Fu(,)28 b(kde)f Fs(J)1042
5751 y Fq(n)1115 5739 y Fu(je)h Fs(n)19 b Fo(\002)f Fs(n)27
b Fu(matice)h(sam)n(\375c)n(h)e(jedni\350ek.)-11 5839
y(P\370edp)r(okl\341dejme,)k(pro)g(sp)r(or,)g(\276e)h(ho)r(dnost)f
Fs(A)h Fu(je)g(nejv\375\271)g Fs(n)20 b Fo(\000)g Fu(2.)30
b(P\370ip\355\271eme-)-135 5938 y(li)41 b(k)g(matici)g
Fs(A)g Fu(je\271t\354)h(jeden)f(\370\341dek)f(ze)h(sam)n(\375c)n(h)e
(jedni\350ek,)j(m\341)f(vznikl\341)f(\()p Fs(n)27 b Fu(+)-135
6038 y(1\))e Fo(\002)g Fs(n)38 b Fu(matice)g(p)r(o\370\341d)f(ho)r
(dnost)h(nejv\375\271)g Fs(n)25 b Fo(\000)g Fu(1,)37
b(a)h(tedy)g(existuje)g(netrivi\341ln\355)p eop end
PStoPSsaved restore
%%Page: (14,15) 8
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 850.393701 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 15 14 bop -182 1858 a Fu(15)1165 b Ft(Obsah)p
-182 1891 2629 4 v -182 2074 a Fu(line\341rn\355)21 b(k)n(om)n(binace)e
(jej\355c)n(h)j(sloup)r(c\371)f(ro)n(vn\341)e Fl(0)p
Fu(.)i(Jin)n(\375mi)g(slo)n(vy)-7 b(,)20 b(existuje)h(nen)n(ulo)n
(v\375)-182 2174 y(\(sloup)r(co)n(v\375\))27 b(v)n(ektor)f
Fl(x)e Fo(2)f Fh(R)734 2144 y Fq(n)807 2174 y Fu(tak)n(o)n(v\375)-7
b(,)26 b(\276e)h Fs(A)p Fl(x)d Fu(=)f Fl(0)k Fu(a)g(z\341ro)n(v)n
(e\362)1865 2112 y Fp(P)1952 2132 y Fq(n)1952 2199 y(i)p
Fr(=1)2078 2174 y Fs(x)2125 2186 y Fq(i)2176 2174 y Fu(=)c(0.)-57
2278 y(Z)k(p)r(osledn\354)h(uv)n(eden\351ho)e(vztah)n(u)i(plyne)f
Fs(J)1308 2290 y Fq(n)1353 2278 y Fl(x)d Fu(=)f Fl(0)p
Fu(.)k(Sp)r(o)r(\350\355t\341me)38 2470 y Fl(x)88 2435
y Fq(T)154 2402 y Fp(\000)192 2470 y Fs(A)19 b Fu(+)f
Fs(A)418 2435 y Fq(T)471 2402 y Fp(\001)522 2470 y Fl(x)84
b Fu(=)e Fl(x)853 2435 y Fq(T)906 2470 y Fu(\()p Fs(J)984
2482 y Fq(n)1048 2470 y Fo(\000)18 b Fs(I)1167 2482 y
Fq(n)1213 2470 y Fu(\))p Fl(x)24 b Fu(=)e Fl(x)1456 2435
y Fq(T)1509 2470 y Fu(\()p Fs(J)1587 2482 y Fq(n)1632
2470 y Fl(x)p Fu(\))e Fo(\000)e Fl(x)1867 2435 y Fq(T)1919
2470 y Fu(\()p Fs(I)1987 2482 y Fq(n)2033 2470 y Fl(x)p
Fu(\))24 b(=)656 2669 y(=)82 b(0)18 b Fo(\000)g Fl(x)996
2635 y Fq(T)1049 2669 y Fl(x)24 b Fu(=)e Fo(\000)1328
2565 y Fq(n)1289 2590 y Fp(X)1295 2767 y Fq(i)p Fr(=1)1422
2669 y Fs(x)1469 2635 y Fr(2)1469 2690 y Fq(i)1530 2669
y Fs(<)h Fu(0)p Fs(:)-182 2933 y Fu(Na)28 b(druh\351)f(stran\354)g(ale)
107 3125 y Fl(x)157 3091 y Fq(T)224 3058 y Fp(\000)262
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@endspecial eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 422.362205 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
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h(nena)5 b(jdeme:)-135 2219 y Fl(V)m(\354ta.)54 b Fi(Nejv)n
(\354t\271\355)26 b(p)r(o)r(\350et)f(p\370\355mek)g(v)g
Fh(R)1088 2188 y Fr(3)1125 2219 y Fi(,)h(z)f(nic)n(h\276)g(k)n
(a\276d\351)f(dv)n(\354)h(sv\355ra)5 b(j\355)24 b(stejn)n(\375)h
(\372hel,)-135 2318 y(je)j Fu(6)p Fi(,)f(a)g(ob)r(ecn\354)h(v)f
Fh(R)522 2288 y Fq(d)589 2318 y Fi(neexistuje)g(v\355c)h(ne\276)1255
2251 y Fp(\000)1294 2281 y Fq(d)p Fr(+1)1336 2347 y(2)1412
2251 y Fp(\001)1478 2318 y Fi(tak)n(o)n(v\375c)n(h)d(p\370\355mek.)-135
2463 y Fl(D\371k)m(az.)60 b Fu(M\354jme)28 b(k)n(on\014guraci)d
Fs(n)i Fu(p\370\355mek,)g(z)g(nic)n(h\276)h(k)n(a\276d\351)e(dv)n(\354)
h(sv\355ra)5 b(j\355)26 b(t)n(\375\276)h(\372hel)-135
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176 2543 41 4 v 180 2591 a Fr(2)227 2562 y Fu(\).)c(Bu\357)h
Fl(v)562 2574 y Fq(i)630 2562 y Fu(jednotk)n(o)n(v\375)e(v)n(ektor)g(v)
n(e)h(sm\354ru)g Fs(i)p Fu(-t\351)g(p\370\355mky)g(\(ze)h(dv)n(ou)-135
2662 y(mo\276nost\355)30 b(pro)g Fl(v)420 2674 y Fq(i)479
2662 y Fu(vyb)r(ereme)h(jedn)n(u)g(lib)r(o)n(v)n(oln\354\).)g(P)n(o)r
(dm\355nk)n(a)e(s)i(\372hly)g(p\370\355mek)g(je)-135
2761 y(ekviv)n(alen)n(tn\355)26 b(p)r(o)r(dm\355nce)646
2964 y Fo(jh)p Fl(v)751 2976 y Fq(i)794 2964 y Fo(j)14
b Fl(v)881 2976 y Fq(j)916 2964 y Fo(ij)23 b Fu(=)g(cos)13
b Fs(#)111 b Fu(pro)27 b Fs(i)22 b Fo(6)p Fu(=)h Fs(j:)-11
3176 y Fu(P)n(o)n(v)n(a\276ujme)32 b Fl(v)464 3188 y
Fq(i)526 3176 y Fu(za)h(sloup)r(co)n(v\375)f(v)n(ektor,)h(neb)r(oli)g
(matici)h Fs(d)p Fo(\002)p Fu(1.)f(P)n(otom)g Fl(v)2355
3146 y Fq(T)2354 3198 y(i)2408 3176 y Fl(v)2458 3188
y Fq(j)-135 3276 y Fu(je)28 b(sk)n(al\341rn\355)e(sou\350in)h
Fo(h)p Fl(v)601 3288 y Fq(i)643 3276 y Fo(j)14 b Fl(v)730
3288 y Fq(j)766 3276 y Fo(i)p Fu(,)28 b(neb)r(o)g(p\370esn\354ji)f
(\370e\350eno)g(matice)h(t)n(ypu)g(1)p Fo(\002)o Fu(1,)f(jej\355m\276)
-135 3375 y(jedin)n(\375m)h(prvk)n(em)f(je)g Fo(h)p Fl(v)650
3387 y Fq(i)693 3375 y Fo(j)14 b Fl(v)780 3387 y Fq(j)815
3375 y Fo(i)p Fu(.)28 b(Naproti)f(tom)n(u)g Fl(v)1469
3387 y Fq(i)1497 3375 y Fl(v)1548 3345 y Fq(T)1547 3397
y(j)1629 3375 y Fu(je)h(matice)g(t)n(ypu)f Fs(d)p Fo(\002)p
Fs(d)p Fu(.)-11 3496 y(Uk)n(\341\276eme,)i(\276e)g(matice)g
Fl(v)789 3508 y Fq(i)817 3496 y Fl(v)868 3466 y Fq(T)867
3518 y(i)921 3496 y Fu(,)g Fs(i)d Fu(=)f(1)p Fs(;)14
b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)p Fu(,)29 b(jsou)g(line\341rn\354)g
(nez\341)n(visl\351.)f(Je-)-135 3596 y(lik)n(o\276)39
b(jsou)h(to)h(prvky)e(v)n(ektoro)n(v)n(\351ho)e(prostoru)i(v\271ec)n(h)
h(re\341ln)n(\375c)n(h)e(symetric)n(k\375c)n(h)-135 3695
y(matic)28 b(t)n(ypu)h Fs(d)p Fo(\002)p Fs(d)p Fu(,)g(kter\375)f(m\341)
g(dimenzi)1161 3628 y Fp(\000)1199 3659 y Fq(d)p Fr(+1)1242
3724 y(2)1318 3628 y Fp(\001)1356 3695 y Fu(,)g(dostaneme)g(t\355m)h
Fs(n)c Fo(\024)2136 3628 y Fp(\000)2174 3659 y Fq(d)p
Fr(+1)2217 3724 y(2)2293 3628 y Fp(\001)2331 3695 y Fu(,)j(jak)-135
3795 y(jsme)g(c)n(h)n(t\354li.)-11 3905 y(Uv)n(a\276me)f
(line\341rn\355)g(k)n(om)n(binaci)937 4049 y Fq(n)898
4074 y Fp(X)904 4251 y Fq(i)p Fr(=1)1031 4153 y Fs(a)1075
4165 y Fq(i)1103 4153 y Fl(v)1153 4165 y Fq(i)1181 4153
y Fl(v)1232 4118 y Fq(T)1231 4173 y(i)1308 4153 y Fu(=)c(0)p
Fs(:)-135 4440 y Fu(Vyn\341sob\355me-li)e(ob)r(\354)h(stran)n(y)f
(t\351to)h(ro)n(vnosti)e(zlev)n(a)h Fl(v)1533 4410 y
Fq(T)1532 4461 y(j)1609 4440 y Fu(a)g(zpra)n(v)n(a)f
Fl(v)1982 4452 y Fq(j)2040 4440 y Fu(a)h(vyu\276ijeme-)-135
4539 y(li)28 b(aso)r(ciativit)n(y)e(matico)n(v)n(\351ho)g(n\341sob)r
(en\355,)h(dostaneme)94 4804 y(0)22 b(=)286 4700 y Fq(n)246
4725 y Fp(X)252 4902 y Fq(i)p Fr(=1)380 4804 y Fs(a)424
4816 y Fq(i)451 4804 y Fl(v)502 4770 y Fq(T)501 4824
y(j)555 4804 y Fu(\()p Fl(v)637 4816 y Fq(i)666 4804
y Fl(v)717 4770 y Fq(T)716 4824 y(i)770 4804 y Fu(\))p
Fl(v)852 4816 y Fq(j)910 4804 y Fu(=)1038 4700 y Fq(n)998
4725 y Fp(X)1004 4902 y Fq(i)p Fr(=1)1132 4804 y Fs(a)1176
4816 y Fq(i)1203 4804 y Fo(h)p Fl(v)1285 4816 y Fq(i)1328
4804 y Fo(j)14 b Fl(v)1415 4816 y Fq(j)1450 4804 y Fo(i)1482
4770 y Fr(2)1542 4804 y Fu(=)23 b Fs(a)1674 4816 y Fq(j)1727
4804 y Fu(+)1810 4725 y Fp(X)1818 4904 y Fq(i)p Fk(6)p
Fr(=)p Fq(j)1944 4804 y Fs(a)1988 4816 y Fq(i)2029 4804
y Fu(cos)2141 4770 y Fr(2)2192 4804 y Fs(#:)-135 5097
y Fu(Jin)n(\375mi)36 b(slo)n(vy)-7 b(,)36 b(o)r(dv)n(o)r(dili)g(jsme)h
Fs(M)9 b Fl(a)39 b Fu(=)f Fl(0)p Fu(,)e(kde)h Fl(a)i
Fu(=)f(\()p Fs(a)1724 5109 y Fr(1)1761 5097 y Fs(;)14
b(a)1842 5109 y Fr(2)1879 5097 y Fs(;)g(:)g(:)g(:)g(;)g(a)2108
5109 y Fq(n)2153 5097 y Fu(\))37 b(a)f Fs(M)47 b Fu(=)-135
5196 y(\(1)23 b Fo(\000)g Fu(cos)161 5166 y Fr(2)212
5196 y Fs(#)p Fu(\))p Fs(I)329 5208 y Fq(n)399 5196 y
Fu(+)g(\(cos)630 5166 y Fr(2)681 5196 y Fs(#)p Fu(\))p
Fs(J)808 5208 y Fq(n)854 5196 y Fu(.)35 b(Zde)g Fs(I)1117
5208 y Fq(n)1198 5196 y Fu(zna\350\355)f(jednotk)n(o)n(v)n(ou)g(matici)
h(a)f Fs(J)2274 5208 y Fq(n)2355 5196 y Fu(ma-)-135 5296
y(tici)e(sam)n(\375c)n(h)f(jedni\350ek.)h(Je)g(snadn\351)g(se)f
(p\370esv)n(\354d\350it,)h(\276e)g(matice)g Fs(M)40 b
Fu(je)33 b(regul\341rn\355)-135 5395 y(\(s)e(vyu\276it\355m)h(cos)13
b Fs(#)30 b Fo(6)p Fu(=)f(1\),)i(a)g(proto)g Fl(a)e Fu(=)g
Fl(0)p Fu(.)j(T)-7 b(ud\355\276)32 b(matice)f Fl(v)1866
5407 y Fq(i)1894 5395 y Fl(v)1945 5365 y Fq(T)1944 5417
y(i)2029 5395 y Fu(jsou)h(line\341rn\354)-135 5495 y(nez\341)n
(visl\351)26 b(a)h(v)n(\354ta)g(je)h(dok)n(\341z\341na.)-135
5639 y Fl(P)m(ozn\341mk)m(a.)87 b Fu(Zat\355mco)40 b(pro)f
Fs(d)44 b Fu(=)f(3)c(je)h(horn\355)g(o)r(dhad)g(z)f(t\351to)h(v)n
(\354t)n(y)g(nejlep\271\355)-135 5739 y(mo\276n)n(\375)-7
b(,)23 b(pro)f(v)n(\354t\271\355)h Fs(d)h Fu(se)f(n\354kdy)g(d\341)g
(zlep\271it)h(jin)n(\375mi)f(meto)r(dami,)h(a)f(nejlep\271\355)h
(mo\276n\341)-135 5839 y(ho)r(dnota)31 b(ob)r(ecn\354)g(nen\355)h
(zn\341ma.)f(Nejlep\271\355)h(zn\341m)n(\375)f(doln\355)h(o)r(dhad)f
(\(z)h(roku)f(2000\))-135 5938 y(je)-35 5906 y Fr(2)p
-35 5920 34 4 v -35 5967 a(9)8 5938 y Fu(\()p Fs(d)20
b Fu(+)e(1\))260 5908 y Fr(2)297 5938 y Fu(,)29 b(platn)n(\375)f(pro)f
(v\271ec)n(hna)g(\350\355sla)h Fs(d)g Fu(tv)n(aru)f(3)19
b Fo(\001)g Fu(2)1690 5908 y Fr(2)p Fq(t)p Fk(\000)p
Fr(1)1855 5938 y Fo(\000)g Fu(1,)28 b(kde)g Fs(t)g Fu(je)h(\350\355slo)
-135 6038 y(p\370irozen\351.)p eop end
PStoPSsaved restore
%%Page: (16,17) 9
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 0.000000 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
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-182 1891 2629 4 v -182 2074 a Fw(9)119 b(Lic)m(h\351)40
b(vzd\341lenosti)-182 2279 y Fl(V)m(\354ta.)77 b Fi(Nelze)35
b(na)5 b(j\355t)35 b Fu(4)g Fi(b)r(o)r(dy)h(v)f(ro)n(vin\354)f(tak,)h
(ab)n(y)g(vzd\341lenost)f(k)n(a\276d\375c)n(h)g(dv)n(ou)-182
2378 y(b)n(yla)27 b(lic)n(h\351)g(cel\351)h(\350\355slo.)-182
2501 y Fl(D\371k)m(az.)77 b Fu(\(P)n(ou\276\355v)n(\341)34
b(determinan)n(tu)h(a)g(sk)n(al\341rn\355ho)e(sou\350in)n(u.\))i(Pro)e
(sp)r(or)i(p\370ed-)-182 2600 y(p)r(okl\341dejme,)e(\276e)g(4)f(b)r(o)r
(dy)h(se)g(v\271emi)g(vzd\341lenostmi)f(lic)n(h)n(\375mi)h
(existuj\355.)g(M\371\276eme)-182 2700 y(p\370edp)r(okl\341dat,)27
b(\276e)h(jeden)h(z)f(nic)n(h)h(je)f Fl(0)p Fu(,)g(a)g(zb)n(\375v)n(a)5
b(j\355c\355)27 b(t\370i)h(ozna\350\355me)f Fl(a)p Fs(;)14
b Fl(b)p Fs(;)g Fl(c)p Fu(.)29 b(T)-7 b(edy)-182 2799
y Fo(k)p Fs(a)p Fo(k)p Fu(,)27 b Fo(k)p Fs(b)p Fo(k)p
Fu(,)f Fo(k)p Fs(c)p Fo(k)p Fu(,)h Fo(k)p Fs(a)18 b Fo(\000)g
Fs(b)p Fo(k)p Fu(,)27 b Fo(k)p Fs(b)17 b Fo(\000)h Fs(c)p
Fo(k)27 b Fu(a)h Fo(k)p Fs(c)17 b Fo(\000)h Fs(a)p Fo(k)27
b Fu(jsou)h(lic)n(h\341)f(cel\341)g(\350\355sla.)-57
2899 y(P)n(ozoro)n(v)n(\341n\355:)g(je-li)k Fs(m)g Fu(lic)n(h\351)g
(cel\351)f(\350\355slo,)h(pak)f Fs(m)1472 2869 y Fr(2)1540
2899 y Fu(d\341)n(v)n(\341)g(zb)n(ytek)g(1)h(mo)r(dulo)g(8.)-182
2999 y(Proto)22 b(druh\351)i(mo)r(cnin)n(y)f(uv)n(a\276o)n(v)n(an)n
(\375c)n(h)e(vzd\341lenost\355)h(d\341)n(v)n(a)5 b(j\355)22
b(zb)n(ytek)i(1)f(mo)r(dulo)h(8.)-182 3098 y(Z)32 b(k)n(osino)n(v)n
(\351)e(v)n(\354t)n(y)h(pak)g(dostaneme,)h(\276e)g(i)g(2)p
Fo(h)p Fl(a)14 b Fo(j)g Fl(b)p Fo(i)30 b Fu(=)g Fo(k)p
Fl(a)p Fo(k)1694 3068 y Fr(2)1753 3098 y Fu(+)20 b Fo(k)p
Fl(b)p Fo(k)1975 3068 y Fr(2)2033 3098 y Fo(\000)h(k)p
Fl(a)g Fo(\000)g Fl(b)p Fo(k)2409 3068 y Fr(2)-182 3198
y Fu(d\341)n(v)n(\341)26 b(zb)n(ytek)g(1)h(mo)r(dulo)g(8,)g(a)f(p)r(o)r
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Fo(i)27 b Fu(a)g(2)p Fo(h)p Fl(b)14 b Fo(j)g Fl(c)p Fo(i)p
Fu(.)28 b(Je-li)e Fs(B)31 b Fu(matice)593 3302 y Fp(0)593
3451 y(@)711 3368 y Fo(h)p Fl(a)14 b Fo(j)g Fl(a)p Fo(i)90
b(h)p Fl(a)14 b Fo(j)g Fl(b)p Fo(i)91 b(h)p Fl(a)14 b
Fo(j)g Fl(c)p Fo(i)707 3468 y(h)p Fl(b)g Fo(j)g Fl(a)p
Fo(i)84 b(h)p Fl(b)14 b Fo(j)g Fl(b)p Fo(i)83 b(h)p Fl(b)14
b Fo(j)g Fl(c)p Fo(i)713 3567 y(h)p Fl(c)g Fo(j)g Fl(a)p
Fo(i)94 b(h)p Fl(c)14 b Fo(j)g Fl(b)p Fo(i)95 b(h)p Fl(c)14
b Fo(j)g Fl(c)p Fo(i)1562 3302 y Fp(1)1562 3451 y(A)1648
3469 y Fs(;)-182 3734 y Fu(pak)27 b(2)p Fs(B)32 b Fu(je)c(k)n(ongruen)n
(tn\355)e(matici)786 4000 y Fs(Z)j Fu(=)959 3834 y Fp(0)959
3983 y(@)1074 3900 y Fu(2)82 b(1)h(1)1074 4000 y(1)f(2)h(1)1074
4099 y(1)f(1)h(2)1406 3834 y Fp(1)1406 3983 y(A)-182
4271 y Fu(mo)r(dulo)37 b(8,)g(a)g(proto)f(det)q(\()p
Fs(B)t Fu(\))k Fo(6)p Fu(=)e(0.)f(\(P)n(o)r(drobn\354ji:)g(Ka\276d\375)
f(\350len)h(v)h(de\014n)n(uj\355c\355m)-182 4371 y(v\375razu)g(pro)g
(determinan)n(t)h(matice)g(2)p Fs(B)k Fu(d\341)n(v)n(\341)38
b(stejn)n(\375)h(zb)n(ytek)g(mo)r(dulo)g(8)f(jak)n(o)-182
4470 y(o)r(dp)r(o)n(v\355da)5 b(j\355c\355)35 b(\350len)g(v)h
(determinan)n(tu)f(matice)g Fs(Z)6 b Fu(,)36 b(a)f(tedy)g(det)q(\(2)p
Fs(B)t Fu(\))g(je)h(k)n(ongru-)-182 4570 y(en)n(tn\355)e(det\()p
Fs(Z)6 b Fu(\))34 b(mo)r(dulo)g(8.)f(P\370itom)g(det\()p
Fs(Z)6 b Fu(\))34 b(d\341)n(v)n(\341)e(nen)n(ulo)n(v\375)g(zb)n(ytek,)i
(a)f(tud\355\276)h(i)-182 4669 y(det\(2)p Fs(B)t Fu(\))28
b Fo(6)p Fu(=)g(0.\))i(Ho)r(dnost)g(matice)g Fs(B)35
b Fu(je)c(tedy)f(3.)g(Na)h(druh\351)f(stran\354)f Fs(B)j
Fu(=)27 b Fs(A)2308 4639 y Fq(T)2361 4669 y Fs(A)p Fu(,)-182
4769 y(kde)728 4898 y Fs(A)c Fu(=)901 4781 y Fp(\022)1004
4847 y Fs(a)1048 4859 y Fr(1)1168 4847 y Fs(b)1204 4859
y Fr(1)1324 4847 y Fs(c)1360 4859 y Fr(1)1004 4947 y
Fs(a)1048 4959 y Fr(1)1168 4947 y Fs(b)1204 4959 y Fr(2)1324
4947 y Fs(c)1360 4959 y Fr(2)1438 4781 y Fp(\023)1513
4898 y Fs(:)-182 5085 y Fu(Matice)33 b Fs(A)f Fu(m\341)h(ho)r(dnost)f
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(matic)h(je)-182 5185 y(nejv\375\271)c(ro)n(vna)f(ho)r(dnosti)h(k)n
(a\276d\351ho)f(z)i(\350initel\371.)g(T)-7 b(ud\355\276)29
b Fs(B)34 b Fu(m\341)29 b(ho)r(dnost)g(nejv\375\271)h(2)-182
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(d\371)g Fl(p)693 5751 y Fr(1)730 5739 y Fs(;)14 b Fl(p)820
5751 y Fr(2)858 5739 y Fs(;)g(:)g(:)g(:)f(;)h Fl(p)1095
5751 y Fq(n)1169 5739 y Fu(v)29 b(ro)n(vin\354.)e(Nejd\370\355v)n(e)i
(p\370edp)r(okl\341dejme,)-182 5839 y(\276e)22 b(k)n(a\276d\351)f(dv)n
(a)g(z)h(nic)n(h)g(ma)5 b(j\355)21 b(tut\351\276)i(vzd\341lenost.)e(P)n
(otom)g(m)n(us\355)g(tv)n(o\370it)h(vrc)n(holy)e(ro)n(v-)-182
5938 y(nostrann\351ho)32 b(tro)5 b(j\372heln\355k)n(a,)32
b(a)g(tud\355\276)i Fs(n)e Fo(\024)g Fu(3.)g(Co)h(kdy\276)g
(p\370ipust\355me,)g(\276e)g(vzd\341-)-182 6038 y(lenosti)40
b(mezi)h(nimi)g(mohou)f(b)n(\375t)g(dv)n(\354)g(r\371zn\341)g
(\350\355sla)g(\(ale)g(ne)h(v\355c\)?)f(Snadno)h(se)p
eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 428.031496 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 18 17 bop 1031 1858 a Ft(Obsah)1165 b Fu(18)p
-135 1891 2629 4 v -135 2074 a(na)5 b(jde)31 b(\350t)n(y\370b)r(o)r(do)
n(v)n(\341)d(k)n(on\014gurace)h(jen)j(se)e(dv)n(\354ma)h
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(a)h(dal\271\355)g(zam)n(y\271len\355)f(o)r(dhal\355)h(i)h(p)r(\354tib)
r(o)r(do)n(v)n(ou)f(k)n(on\014guraci,)e(toti\276)i(vrc)n(holy)-135
2274 y(pra)n(videln\351ho)21 b(p)r(\354ti\372heln\355k)n(a.)i(Ale)g
(jak)g(uk)n(\341zat,)f(\276e)g(nem)n(\371\276eme)h(na)5
b(j\355t)23 b(k)n(on\014guraci)-135 2373 y(mnohem)28
b(v)n(\354t\271\355?)-11 2479 y(P)n(o)r(dobn\354)i(se)g(m)n
(\371\276eme)g(pt\341t)h(v)n(e)f(vy\271\271\355)g(dimenzi,)g(tj.)i(v)e
(prostoru)f Fh(R)2173 2449 y Fq(d)2211 2479 y Fu(,)i
Fs(d)d Fo(\025)f Fu(3:)-135 2579 y(Jak)n(\351)33 b(je)i
(maxim\341ln\355)g(\350\355slo)f Fs(n)h Fu(=)f Fs(n)p
Fu(\()p Fs(d)p Fu(\))h(tak)n(o)n(v)n(\351,)e(\276e)i(v)f
Fh(R)1681 2549 y Fq(d)1755 2579 y Fu(existuje)h Fs(n)p
Fu(-tice)f(b)r(o)r(d\371)-135 2678 y(jen)29 b(se)f(dv)n(\354ma)h
(vzd\341lenostmi?)f(N\341sleduj\355c\355)h(elegan)n(tn\355)f(meto)r(da)
g(d\341)n(v)n(\341)f(p)r(om\354rn\354)-135 2778 y(dobr\375)e(horn\355)h
(o)r(dhad)g(pro)f Fs(n)p Fu(\()p Fs(d)p Fu(\),)i(i)f(kdy\276)g
(v\375sledek)f(pro)h(ro)n(vin)n(u)f(nen\355)h(\372pln\354)h(ohro-)-135
2878 y(m)n(uj\355c\355)h(\(dostane)f(se)g(horn\355)g(o)r(dhad)h(9\).)
-135 3015 y Fl(V)m(\354ta.)60 b Fs(n)p Fu(\()p Fs(d)p
Fu(\))23 b Fo(\024)426 2982 y Fr(1)p 426 2996 34 4 v
426 3044 a(2)469 3015 y Fu(\()p Fs(d)544 2985 y Fr(2)600
3015 y Fu(+)18 b(5)p Fs(d)g Fu(+)g(4\).)-135 3152 y Fl(D\371k)m(az.)58
b Fu(Nec)n(h)n(\273)26 b Fl(p)500 3164 y Fr(1)537 3152
y Fs(;)14 b Fl(p)627 3164 y Fr(2)664 3152 y Fs(;)g(:)g(:)g(:)g(;)g
Fl(p)902 3164 y Fq(n)973 3152 y Fu(jsou)26 b(b)r(o)r(dy)g(v)g
Fh(R)1483 3122 y Fq(d)1522 3152 y Fu(.)g(Ozna\350me)f
Fs(D)r Fu(\()p Fl(p)2085 3164 y Fq(i)2113 3152 y Fs(;)14
b Fl(p)2203 3164 y Fq(j)2238 3152 y Fu(\))27 b(vzd\341-)-135
3252 y(lenost)g Fl(p)158 3264 y Fq(i)214 3252 y Fu(o)r(d)g
Fl(p)384 3264 y Fq(j)419 3252 y Fu(.)h(M\341me)141 3447
y Fs(D)r Fu(\()p Fl(p)297 3459 y Fq(i)325 3447 y Fs(;)14
b Fl(p)415 3459 y Fq(j)450 3447 y Fu(\))482 3413 y Fr(2)543
3447 y Fu(=)22 b(\()p Fs(p)704 3459 y Fq(i)p Fr(1)783
3447 y Fo(\000)c Fs(p)908 3459 y Fq(j)s Fr(1)976 3447
y Fu(\))1008 3413 y Fr(2)1064 3447 y Fu(+)g(\()p Fs(p)1221
3459 y Fq(i)p Fr(2)1301 3447 y Fo(\000)g Fs(p)1426 3459
y Fq(j)s Fr(2)1493 3447 y Fu(\))1525 3413 y Fr(2)1581
3447 y Fu(+)g Fo(\001)c(\001)g(\001)g Fu(\()p Fs(p)1849
3459 y Fq(id)1930 3447 y Fo(\000)k Fs(p)2055 3459 y Fq(j)s(d)2124
3447 y Fu(\))2156 3413 y Fr(2)2194 3447 y Fs(;)-135 3642
y Fu(kde)29 b Fs(p)63 3654 y Fq(ij)151 3642 y Fu(zna\350\355)h
Fs(j)5 b Fu(-tou)29 b(sou\370adnici)f(b)r(o)r(du)i Fl(p)1248
3654 y Fq(i)1276 3642 y Fu(.)g(P\370edp)r(okl\341dejme,)e(\276e)i
Fs(D)r Fu(\()p Fl(p)2226 3654 y Fq(i)2254 3642 y Fs(;)14
b Fl(p)2344 3654 y Fq(j)2379 3642 y Fu(\))27 b Fo(2)-135
3742 y(f)p Fs(a;)14 b(b)p Fo(g)26 b Fu(pro)h(k)n(a\276d\351)f
Fs(i)d Fo(6)p Fu(=)g Fs(j)5 b Fu(.)-11 3848 y(De\014n)n(ujeme)38
b(funk)n(ce)e Fs(f)741 3860 y Fr(1)778 3848 y Fs(;)14
b(f)856 3860 y Fr(2)893 3848 y Fs(;)g(:)g(:)g(:)f(;)h(f)1118
3860 y Fq(n)1163 3848 y Fu(:)g Fh(R)1260 3818 y Fq(d)1336
3848 y Fo(!)38 b Fh(R)e Fu(takto)g(\(to)h(je)g(z\341kladn\355)e(trik)
-135 3948 y(d\371k)n(azu\):)411 4066 y Fs(f)452 4078
y Fq(i)479 4066 y Fu(\()p Fl(x)p Fu(\))24 b(=)705 3999
y Fp(\000)743 4066 y Fs(D)r Fu(\()p Fl(x)p Fs(;)14 b
Fl(p)986 4078 y Fq(i)1014 4066 y Fu(\))1046 4032 y Fr(2)1102
4066 y Fo(\000)k Fs(a)1229 4032 y Fr(2)1267 3999 y Fp(\001)13
b(\000)1357 4066 y Fs(D)r Fu(\()p Fl(x)p Fs(;)h Fl(p)1600
4078 y Fq(i)1628 4066 y Fu(\))1660 4032 y Fr(2)1716 4066
y Fo(\000)k Fs(b)1835 4032 y Fr(2)1872 3999 y Fp(\001)1924
4066 y Fs(;)-135 4235 y Fu(kde)31 b Fl(x)e Fu(=)g(\()p
Fs(x)275 4247 y Fr(1)313 4235 y Fs(;)14 b(x)397 4247
y Fr(2)434 4235 y Fs(;)g(:)g(:)g(:)g(;)g(x)666 4247 y
Fq(d)705 4235 y Fu(\))29 b Fo(2)g Fh(R)910 4205 y Fq(d)949
4235 y Fu(.)i(Z)g(p\370edp)r(okladu)g(o)f(dv)n(ou)h(vzd\341lenostec)n
(h)f(do-)-135 4334 y(staneme)589 4482 y Fs(f)630 4494
y Fq(i)658 4482 y Fu(\()p Fl(p)743 4494 y Fq(j)778 4482
y Fu(\))23 b(=)907 4365 y Fp(\032)983 4432 y Fu(0)347
b(pro)27 b Fs(i)c Fo(6)p Fu(=)g Fs(j;)983 4531 y(a)1027
4501 y Fr(2)1064 4531 y Fs(b)1100 4501 y Fr(2)1160 4531
y Fo(6)p Fu(=)g(0)82 b(pro)27 b Fs(i)c Fu(=)g Fs(j:)2387
4482 y Fu(\(1\))-11 4715 y(Uv)n(a\276me)42 b(v)n(ektoro)n(v\375)d
(prostor)h(v\271ec)n(h)h(re\341ln)n(\375c)n(h)f(funk)n(c\355)i
Fh(R)1919 4685 y Fq(d)2005 4715 y Fo(!)47 b Fh(R)p Fu(,)42
b(a)f(jeho)-135 4815 y(p)r(o)r(dprostor)36 b Fs(V)57
b Fu(genero)n(v)n(an)n(\375)34 b(funk)n(cemi)k Fs(f)1250
4827 y Fr(1)1287 4815 y Fs(;)14 b(f)1365 4827 y Fr(2)1401
4815 y Fs(;)g(:)g(:)g(:)g(;)g(f)1627 4827 y Fq(n)1672
4815 y Fu(.)37 b(Nejd\370\355v)n(e)h(tvrd\355me,)f(\276e)-135
4914 y Fs(f)-94 4926 y Fr(1)-57 4914 y Fs(;)14 b(f)21
4926 y Fr(2)58 4914 y Fs(;)g(:)g(:)g(:)f(;)h(f)283 4926
y Fq(n)355 4914 y Fu(jsou)27 b(line\341rn\354)f(nez\341)n(visl\351.)g
(P\370edp)r(okl\341dejme,)h(\276e)g(line\341rn\355)f(k)n(om)n(bi-)-135
5014 y(nace)k Fs(f)38 b Fu(=)28 b Fs(\013)282 5026 y
Fr(1)320 5014 y Fs(f)361 5026 y Fr(1)418 5014 y Fu(+)21
b Fs(\013)557 5026 y Fr(2)594 5014 y Fs(f)635 5026 y
Fr(2)693 5014 y Fu(+)f Fo(\001)14 b(\001)g(\001)20 b
Fu(+)h Fs(\013)1034 5026 y Fq(n)1079 5014 y Fs(f)1120
5026 y Fq(n)1196 5014 y Fu(je)31 b(ro)n(vna)f(0,)g(tj.)i(je)g(to)f
(funk)n(ce)g Fh(R)2254 4984 y Fq(d)2321 5014 y Fo(!)e
Fh(R)-135 5114 y Fu(d\341)n(v)n(a)5 b(j\355c\355)37 b(ho)r(dnotu)i(0)f
(v)n(e)g(v\271ec)n(h)g(b)r(o)r(dec)n(h)h Fh(R)1311 5083
y Fq(d)1350 5114 y Fu(.)f(Sp)r(eci\341ln\354)h(d\341)n(v)n(\341)e(0)h
(i)h(v)g(k)n(a\276d\351m)-135 5213 y(z)23 b(b)r(o)r(d\371)h
Fl(p)186 5225 y Fq(i)237 5213 y Fu(a)f(z)h(toho)f(p)r(o)r(dle)h(\(1\))f
(dostaneme)g(0)g(=)f Fs(f)9 b Fu(\()p Fl(p)1593 5225
y Fq(i)1621 5213 y Fu(\))23 b(=)g Fs(\013)1817 5225 y
Fq(i)1844 5213 y Fs(a)1888 5183 y Fr(2)1926 5213 y Fs(b)1962
5183 y Fr(2)1998 5213 y Fu(,)h(tak\276e)f Fs(\013)2313
5225 y Fq(i)2364 5213 y Fu(=)f(0)-135 5313 y(pro)27 b(v\271ec)n(hna)f
Fs(i)p Fu(.)i(T)-7 b(edy)27 b(dim)14 b Fs(V)42 b Fu(=)23
b Fs(n)p Fu(.)-11 5419 y(Nyn\355)g(na)5 b(jdeme)22 b(p)r(okud)h
(mo\276no)f(mal\375)g(syst\351m)g(gener\341tor\371.)e(P\370esn\354ji)i
(\370e\350eno,)-135 5518 y(na)5 b(jdeme)30 b(mal\375)g(p)r(o)r(\350et)g
(funk)n(c\355)h Fh(R)948 5488 y Fq(d)1014 5518 y Fo(!)c
Fh(R)j Fu(tak)n(o)n(v\375c)n(h,)f(\276e)h(k)n(a\276dou)f
Fs(f)2020 5530 y Fq(i)2077 5518 y Fu(lze)h(vyj\341d\370it)-135
5618 y(jak)n(o)c(jejic)n(h)j(line\341rn\355)e(k)n(om)n(binac\355;)f
(p\370itom)h(t)n(yto)h(funk)n(ce)f(nem)n(usej\355)h(le\276et)g(v)n(e)f
Fs(V)19 b Fu(.)-11 5724 y(Ka\276d\341)i Fs(f)283 5736
y Fq(i)332 5724 y Fu(je)g(mnoho)r(\350len)h(v)f(prom\354nn)n(\375c)n(h)
f Fs(x)1401 5736 y Fr(1)1439 5724 y Fs(;)14 b(x)1523
5736 y Fr(2)1561 5724 y Fs(;)g(:)g(:)g(:)f(;)h(x)1792
5736 y Fq(d)1853 5724 y Fu(stupn\354)22 b(nejv\375\271)f(4,)g(a)-135
5824 y(proto)c(ji)i(lze)f(vyj\341d\370it)g(jak)n(o)g(line\341rn\355)g
(k)n(om)n(binaci)f(v\271ec)n(h)g(jedno)r(\350len)n(\371)i(v)f
Fs(x)2136 5836 y Fr(1)2174 5824 y Fs(;)c(x)2258 5836
y Fr(2)2295 5824 y Fs(;)g(:)g(:)g(:)g(;)g(x)2527 5836
y Fq(d)-135 5923 y Fu(stupn\354)25 b(nejv\375\271)g(4.)g(T)n(\354c)n(h)
f(je,)i(jak)e(se)h(d\341)g(sp)r(o)r(\350\355tat,)1467
5856 y Fp(\000)1505 5886 y Fq(d)p Fr(+4)1548 5952 y(4)1624
5856 y Fp(\001)1662 5923 y Fu(,)g(a)f(tak)h(m\341me)g(horn\355)f(o)r
(d-)-135 6038 y(had)g Fs(n)f Fu(=)g(dim)14 b Fs(V)42
b Fo(\024)514 5971 y Fp(\000)552 6001 y Fq(d)p Fr(+4)595
6066 y(4)670 5971 y Fp(\001)708 6038 y Fu(.)25 b(Na)5
b(jdeme)25 b(ale)f(je\271t\354)h(\372sp)r(orn\354j\271\355)f(syst\351m)
h(gener\341tor\371.)p eop end
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TeXDict begin 19 18 bop -182 1858 a Fu(19)1165 b Ft(Obsah)p
-182 1891 2629 4 v -57 2074 a Fu(Vyj\341d\370\355me)24
b Fs(D)r Fu(\()p Fl(x)p Fs(;)14 b Fl(p)591 2086 y Fq(i)619
2074 y Fu(\))651 2044 y Fr(2)712 2074 y Fu(=)800 2012
y Fp(P)887 2033 y Fq(d)887 2099 y(j)s Fr(=1)1006 2074
y Fu(\()p Fs(x)1085 2086 y Fq(j)1134 2074 y Fo(\000)f
Fs(p)1254 2086 y Fq(ij)1311 2074 y Fu(\))1343 2044 y
Fr(2)1404 2074 y Fu(=)22 b Fs(X)d Fo(\000)1657 2012 y
Fp(P)1744 2033 y Fq(d)1744 2099 y(j)s Fr(=1)1877 2074
y Fu(2)p Fs(x)1966 2086 y Fq(j)2001 2074 y Fs(p)2043
2086 y Fq(ij)2113 2074 y Fu(+)13 b Fs(P)2244 2086 y Fq(i)2272
2074 y Fu(,)24 b(kde)-182 2201 y(jsme)k(p)r(olo\276ili)f
Fs(X)j Fu(=)484 2139 y Fp(P)572 2159 y Fq(d)572 2226
y(j)s Fr(=1)705 2201 y Fs(x)752 2171 y Fr(2)752 2223
y Fq(j)817 2201 y Fu(a)d Fs(P)939 2213 y Fq(i)990 2201
y Fu(=)1078 2139 y Fp(P)1166 2159 y Fq(d)1166 2226 y(j)s
Fr(=1)1298 2201 y Fs(p)1340 2171 y Fr(2)1340 2223 y Fq(ij)1399
2201 y Fu(.)g(D\341le)h(m\341me)65 2409 y Fs(f)106 2421
y Fq(i)133 2409 y Fu(\()p Fl(x)p Fu(\))84 b(=)479 2342
y Fp(\000)517 2409 y Fs(D)r Fu(\()p Fl(x)p Fs(;)14 b
Fl(p)760 2421 y Fq(i)788 2409 y Fu(\))820 2375 y Fr(2)876
2409 y Fo(\000)k Fs(a)1003 2375 y Fr(2)1040 2342 y Fp(\001)c(\000)1130
2409 y Fs(D)r Fu(\()p Fl(x)p Fs(;)g Fl(p)1373 2421 y
Fq(i)1402 2409 y Fu(\))1434 2375 y Fr(2)1490 2409 y Fo(\000)k
Fs(b)1609 2375 y Fr(2)1645 2342 y Fp(\001)1707 2409 y
Fu(=)331 2624 y(=)479 2507 y Fp(\022)540 2624 y Fs(X)25
b Fo(\000)759 2520 y Fq(d)717 2545 y Fp(X)719 2722 y
Fq(j)s Fr(=1)851 2624 y Fu(2)p Fs(x)940 2636 y Fq(j)974
2624 y Fs(p)1016 2636 y Fq(ij)1093 2624 y Fu(+)18 b Fs(A)1238
2636 y Fq(i)1266 2507 y Fp(\023\022)1388 2624 y Fs(X)25
b Fo(\000)1608 2520 y Fq(d)1565 2545 y Fp(X)1568 2722
y Fq(j)s Fr(=1)1699 2624 y Fu(2)p Fs(x)1788 2636 y Fq(j)1823
2624 y Fs(p)1865 2636 y Fq(ij)1941 2624 y Fu(+)18 b Fs(B)2087
2636 y Fq(i)2115 2507 y Fp(\023)2176 2624 y Fs(;)-182
2910 y Fu(kde)28 b(p\355\271eme)f Fs(A)307 2922 y Fq(i)358
2910 y Fu(=)c Fs(P)499 2922 y Fq(i)545 2910 y Fo(\000)18
b Fs(a)672 2880 y Fr(2)737 2910 y Fu(a)27 b Fs(B)869
2922 y Fq(i)920 2910 y Fu(=)c Fs(P)1061 2922 y Fq(i)1107
2910 y Fo(\000)18 b Fs(b)1226 2880 y Fr(2)1263 2910 y
Fu(.)28 b(Dal\271\355)f(\372pra)n(v)n(ou)f(dost\341)n(v)n(\341me)193
3179 y Fs(f)234 3191 y Fq(i)261 3179 y Fu(\()p Fl(x)p
Fu(\))84 b(=)e Fs(X)682 3145 y Fr(2)737 3179 y Fo(\000)18
b Fu(4)p Fs(X)994 3075 y Fq(d)951 3100 y Fp(X)954 3277
y Fq(j)s Fr(=1)1085 3179 y Fs(p)1127 3191 y Fq(ij)1185
3179 y Fs(x)1232 3191 y Fq(j)1286 3179 y Fu(+)1369 3062
y Fp(\022)1473 3075 y Fq(d)1430 3100 y Fp(X)1433 3277
y Fq(j)s Fr(=1)1564 3179 y Fu(2)p Fs(p)1648 3191 y Fq(ij)1706
3179 y Fs(x)1753 3191 y Fq(j)1788 3062 y Fp(\023)1849
3079 y Fr(2)1905 3179 y Fu(+)680 3482 y(+)g(\()p Fs(A)857
3494 y Fq(i)904 3482 y Fu(+)g Fs(B)1050 3494 y Fq(i)1077
3482 y Fu(\))1109 3365 y Fp(\022)1171 3482 y Fs(X)25
b Fo(\000)1390 3378 y Fq(d)1348 3403 y Fp(X)1350 3580
y Fq(j)s Fr(=1)1481 3482 y Fu(2)p Fs(p)1565 3494 y Fq(ij)1623
3482 y Fs(x)1670 3494 y Fq(j)1706 3365 y Fp(\023)1785
3482 y Fu(+)18 b Fs(A)1930 3494 y Fq(i)1958 3482 y Fs(B)2021
3494 y Fq(i)2049 3482 y Fs(:)-182 3758 y Fu(Odtud)27
b(u\276)f(je)g(vid\354t,)g(\276e)g(k)n(a\276d\341)f Fs(f)883
3770 y Fq(i)936 3758 y Fu(je)i(line\341rn\355)e(k)n(om)n(binac\355)g
(n\341sleduj\355c\355c)n(h)h(funk)n(c\355:)717 3944 y
Fs(X)793 3914 y Fr(2)830 3944 y Fs(;)717 4044 y(x)764
4056 y Fq(j)800 4044 y Fs(X)r(;)87 b(j)28 b Fu(=)22 b(1)p
Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)f(;)h(d;)717 4143 y(x)764
4113 y Fr(2)764 4165 y Fq(j)802 4143 y Fs(;)156 b(j)28
b Fu(=)22 b(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)f(;)h(d;)717
4246 y(x)764 4258 y Fq(i)792 4246 y Fs(x)839 4258 y Fq(j)875
4246 y Fs(;)83 b Fu(1)22 b Fo(\024)h Fs(i)g(<)f(j)28
b Fo(\024)23 b Fs(d;)717 4346 y(x)764 4358 y Fq(j)800
4346 y Fs(;)158 b(j)28 b Fu(=)22 b(1)p Fs(;)14 b Fu(2)p
Fs(;)g(:)g(:)g(:)f(;)h(d)28 b Fu(a)717 4445 y(1)p Fs(:)-182
4643 y Fu(\(P)n(oznamenejme,)h(\276e)h Fs(X)36 b Fu(samo)29
b(je)h(line\341rn\355)g(k)n(om)n(binac\355)e Fs(x)1706
4613 y Fr(2)1706 4665 y Fq(j)1744 4643 y Fu(.\))i(T)-7
b(o)30 b(je)g(celk)n(em)f(1)20 b(+)-182 4762 y Fs(d)f
Fu(+)f Fs(d)g Fu(+)108 4695 y Fp(\000)146 4725 y Fq(d)146
4790 y Fr(2)180 4695 y Fp(\001)237 4762 y Fu(+)g Fs(d)g
Fu(+)g(1)23 b(=)626 4729 y Fr(1)p 626 4743 34 4 v 626
4790 a(2)670 4762 y Fu(\()p Fs(d)745 4732 y Fr(2)801
4762 y Fu(+)18 b(5)p Fs(d)g Fu(+)g(4\))27 b(funk)n(c\355.)h(T\355m)g
(je)g(v)n(\354ta)f(dok)n(\341z\341na.)-182 4910 y Fl(P)m(ozn\341mk)m
(a.)69 b Fu(P\370\355klad)30 b(k)n(on\014gurace)1078
4843 y Fp(\000)1116 4874 y Fq(d)1117 4939 y Fr(2)1151
4843 y Fp(\001)1220 4910 y Fu(b)r(o)r(d\371)i(v)f Fh(R)1571
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(\354ma)g(sou\370adnicemi)f(1)h(a)g(ostatn\355mi)g(0.)h(T)-7
b(ato)28 b(k)n(on-)-182 5110 y(\014gurace)e(le\276\355)h(v)g(nadro)n
(vin\354)727 5047 y Fp(P)815 5068 y Fq(d)815 5135 y(i)p
Fr(=1)941 5110 y Fs(x)988 5122 y Fq(i)1039 5110 y Fu(=)22
b(2,)27 b(tak\276e)g(ji)g(m)n(\371\276eme)g(um\355stit)h(i)f(v)g
Fh(R)2299 5080 y Fq(d)p Fk(\000)p Fr(1)2423 5110 y Fu(,)-182
5220 y(co\276)j(d\341)n(v)n(\341)f(doln\355)h(o)r(dhad)g
Fs(n)p Fu(\()p Fs(d)p Fu(\))e Fo(\025)904 5153 y Fp(\000)942
5183 y Fq(d)p Fr(+1)985 5249 y(2)1061 5153 y Fp(\001)1126
5220 y Fu(=)1229 5187 y Fr(1)p 1229 5201 V 1229 5249
a(2)1272 5220 y Fu(\()p Fs(d)1347 5190 y Fr(2)1405 5220
y Fu(+)19 b Fs(d)p Fu(\).)31 b(Dok)n(\341zan)n(\375)e(horn\355)g(o)r
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b(na)g(jeden)h(sym)n(b)r(ol.)e(Pro)g(dost)h(v)n(elk)n(\351)f
Fs(k)26 b Fu(m)n(\371\276e)c(agen)n(t)f(za)h Fs(k)j Fu(dn\355)e(p)r
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2274 y Fu(mo\276n)n(\375c)n(h)f(zpr\341)n(v,)g(a)g(v\355c)h(p)r(oslat)f
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2373 y(duj\355c\355:)-135 2551 y Fl(V)m(\354ta.)60 b
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c(grafu)h Fs(G)p Fu(.)g(Pro)f(dv)n(a)g(ob)r(ecn\351)h(grafy)f
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b Fs(H)326 3580 y Fk(0)349 3614 y Fu(\))83 b(=)g Fs(V)18
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b Fu(:)37 b(\()p Fs(u)23 b Fu(=)g Fs(v)30 b Fu(neb)r(o)e
Fo(f)p Fs(u;)14 b(v)s Fo(g)22 b(2)h Fs(E)5 b Fu(\()p
Fs(H)i Fu(\)\))778 3863 y(a)27 b(z\341ro)n(v)n(e\362)e(\()p
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Fu(N\341\271)27 b(\372k)n(ol)g(je)h(tedy)g(shora)e(omezit)h(v)n(elik)n
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/m3 {marker dup dup moveto dup dup neg lineto dup neg dup lineto dup
neg exch lineto closepath stroke grestore} bind def
/m4 {marker dup dup moveto dup dup neg lineto dup neg dup lineto dup
neg exch lineto closepath fill grestore} bind def
/m5 {marker dup dup moveto dup neg dup lineto dup dup neg moveto dup
neg exch lineto closepath stroke grestore} bind def
%% splines
systemdict /setpacking known {/savepacking currentpacking def false
setpacking} if
/q0 {0 0} def
/q1 {0 0} def
/q2 {0 0} def
/q3 {0 0} def
/p0 {0 0} def
/p1 {0 0} def
/p2 {0 0} def
/p3 {0 0} def
systemdict /setpacking known {savepacking setpacking} if
%% x y /qi -> defp -> [/qi [x y] def]
/defp {dup 4 1 roll load astore def} bind def
/midpoint { exch 4 3 roll add 2 div 3 1 roll add 2 div } bind def
/thirdpoint { exch 4 3 roll 2 mul add 3 div 3 1 roll exch 2 mul add 3
div } bind def
/prespl {/p3 defp /p2 defp /p1 defp /p0 defp
p1 p2 thirdpoint /q1 defp
p2 p1 thirdpoint /q2 defp
p1 p0 thirdpoint q1 midpoint /q0 defp
p2 p3 thirdpoint q2 midpoint /q3 defp } bind def
/postspl { q1 q2 q3 curveto p1 p2 p3 } bind def
/fspl { prespl q0 moveto postspl } bind def
/spl { prespl postspl } bind def
/xspl { pop pop pop pop pop pop } bind def
/qspl { /p2 defp /p1 defp /p0 defp
p1 p0 midpoint /q0 defp
p1 p2 midpoint /q3 defp
p1 q0 thirdpoint /q1 defp
p1 q3 thirdpoint /q2 defp q0 moveto q1 q2 q3 curveto } bind def
/cqspl { /p2 defp /p1 defp /p0 defp
p1 p0 midpoint /q0 defp
p1 p2 midpoint /q3 defp
p1 q0 thirdpoint /q1 defp
p1 q3 thirdpoint /q2 defp q0 moveto q1 q2 q3 curveto
p2 p1 midpoint /q0 defp
p2 p0 midpoint /q3 defp
p2 q0 thirdpoint /q1 defp
p2 q3 thirdpoint /q2 defp q1 q2 q3 curveto
p0 p2 midpoint /q0 defp
p0 p1 midpoint /q3 defp
p0 q0 thirdpoint /q1 defp
p0 q3 thirdpoint /q2 defp q1 q2 q3 curveto } bind def
%% bitmaps
/pix { /picstr exch string def } def
%% wd ht -> preimg -> ..stuff for image..
/preimg { 8 [ 3 index 0 0 5 index neg 0 7 index ]
{currentfile picstr readhexstring pop} } def
/img { preimg image } bind def
/kimg { preimg false 3 colorimage } bind def
%%
end
%% Ipe prologue end
IpeDict begin 362.357 407.273 translate
% Preamble 1
%%\documentclass[a4paper]{article}
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end %% of Ipe figure
%%EndDocument
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PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
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1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
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PStoPSxform concat
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(\350\355sel)g(matice)h(sousednosti)e(grafu.)-135 2400
y Fl(D\371k)m(az.)59 b Fu(Matice)27 b(sousednosti)f(grafu)f
Fs(G)j Fu(na)e(mno\276in\354)h(vrc)n(hol\371)e Fo(f)p
Fu(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)f(;)h(n)p Fo(g)26
b Fu(je)-135 2500 y(de\014no)n(v)n(\341na)g(jak)n(o)g(matice)i
Fs(A)g Fu(t)n(ypu)f Fs(n)p Fo(\002)p Fs(n)p Fu(,)g(kde)435
2730 y Fs(a)479 2742 y Fq(ij)560 2730 y Fu(=)634 2613
y Fp(\032)710 2679 y Fu(1)83 b(p)r(okud)27 b Fs(i)c Fo(6)p
Fu(=)g Fs(j)32 b Fu(a)c Fo(f)p Fs(i;)14 b(j)5 b Fo(g)21
b(2)i Fs(E)5 b Fu(\()p Fs(G)p Fu(\))p Fs(;)710 2779 y
Fu(0)83 b(jinak.)-135 2960 y(T)-7 b(edy)33 b(matice)g(sousednosti)f
(grafu)h Fs(K)1088 2972 y Fr(10)1191 2960 y Fu(je)h Fs(J)1333
2972 y Fr(10)1425 2960 y Fo(\000)22 b Fs(I)1548 2972
y Fr(10)1619 2960 y Fu(,)33 b(kde)g Fs(J)1881 2972 y
Fq(n)1960 2960 y Fu(je)h Fs(n)p Fo(\002)o Fs(n)f Fu(matice)-135
3059 y(sam)n(\375c)n(h)26 b(jedni\350ek)i(a)f Fs(I)586
3071 y Fq(n)660 3059 y Fu(je)h(jednotk)n(o)n(v)n(\341)d(matice.)-11
3160 y(P\370edp)r(okl\341dejme,)36 b(\276e)h(existuje)f(p)r(okryt\355)h
(hran)f Fs(K)1635 3172 y Fr(10)1741 3160 y Fu(p)r(o)r(dgrafy)g
Fs(P)12 b Fu(,)37 b Fs(Q)f Fu(a)g Fs(R)q Fu(,)-135 3260
y(z)27 b(nic)n(h\276)g(k)n(a\276d\375)e(je)j(isomorfn\355)e(P)n
(eterseno)n(vu)e(grafu.)i(Zna\350\355-li)h Fs(A)1894
3272 y Fq(P)1976 3260 y Fu(matici)g(soused-)-135 3359
y(nosti)33 b(grafu)g Fs(P)12 b Fu(,)33 b(a)h(p)r(o)r(dobn\354)f(pro)g
Fs(A)1050 3371 y Fq(Q)1140 3359 y Fu(a)h Fs(A)1278 3371
y Fq(R)1332 3359 y Fu(,)g(m)n(us\355)f(platit)h Fs(A)1885
3371 y Fq(P)1963 3359 y Fu(+)22 b Fs(A)2112 3371 y Fq(Q)2192
3359 y Fu(+)g Fs(A)2341 3371 y Fq(R)2428 3359 y Fu(=)-135
3459 y Fs(J)-89 3471 y Fr(10)0 3459 y Fo(\000)c Fs(I)119
3471 y Fr(10)190 3459 y Fu(.)-11 3560 y(Je)39 b(snadn\351)f(o)n(v)n
(\354\370it,)f(\276e)h(jsou-li)g(dv)n(a)g(grafy)f(isomorfn\355,)h(ma)5
b(j\355)38 b(jejic)n(h)h(matice)-135 3659 y(sousednosti)24
b(stejn)n(\375)h(soub)r(or)f(vlastn\355c)n(h)h(\350\355sel,)g(a)g(taky)
g(stejn\351)g(dimenze)h(vlastn\355c)n(h)-135 3759 y(p)r(o)r
(dprostor\371)g(p\370\355slu\271n)n(\375c)n(h)h(k)g(jednotliv\375m)h
(vlastn\355m)g(\350\355sl\371m.)-11 3860 y(Gausso)n(v)n(ou)19
b(eliminac\355)h(sp)r(o)r(\350\355t\341me,)g(\276e)h(pro)e(matici)i
(sousednosti)e(P)n(eterseno)n(v)n(a)-135 3959 y(grafu)30
b(m\341)g(vlastn\355)g(p)r(o)r(dprostor)f(p\370\355slu\271n)n(\375)h(k)
g(vlastn\355m)n(u)g(\350\355slu)h(1)f(dimenzi)h(5,)f(tj.)-135
4059 y(matice)18 b Fs(A)185 4071 y Fq(P)241 4059 y Fo(\000)p
Fs(I)342 4071 y Fr(10)432 4059 y Fu(m\341)g(5-dimenzion\341ln\355)g
(j\341dro.)f(Na)n(v\355c)h(m\341)h(tato)f(matice)g(v)h(k)n(a\276d\351m)
-135 4158 y(sloup)r(ci)26 b(p\370esn\354)g(t\370i)g(jedni\350)n(ky)h(a)
f(jedn)n(u)h Fo(\000)p Fu(1,)e(a)h(tedy)h(se\350teme-li)f(v\271ec)n(hn)
n(y)f(ro)n(vnice)-135 4258 y(ze)c(sousta)n(vy)f(\()p
Fs(A)388 4270 y Fq(P)450 4258 y Fo(\000)6 b Fs(I)557
4270 y Fr(10)627 4258 y Fu(\))p Fl(x)24 b Fu(=)f(0,)e(dostaneme)g(2)p
Fs(x)1401 4270 y Fr(1)1444 4258 y Fu(+)6 b(2)p Fs(x)1604
4270 y Fr(2)1647 4258 y Fu(+)g Fo(\001)14 b(\001)g(\001)6
b Fu(+)g(2)p Fs(x)1981 4270 y Fr(10)2074 4258 y Fu(=)22
b(0.)f(Jin)n(\375mi)-135 4358 y(slo)n(vy)-7 b(,)27 b(cel\351)i
(j\341dro)f Fs(A)533 4370 y Fq(P)608 4358 y Fo(\000)19
b Fs(I)728 4370 y Fr(10)827 4358 y Fu(je)29 b(obsa\276eno)e(v)i
(9-dimenzion\341ln\355m)f(ortogon\341ln\355m)-135 4457
y(dopl\362ku)22 b(v)n(ektoru)f(\(1)p Fs(;)14 b Fu(1)p
Fs(;)g(:)g(:)g(:)f(;)h Fu(1\).)22 b(T)-7 b(ot\351\276)22
b(plat\355)h(pro)f(j\341dro)f Fs(A)1759 4469 y Fq(Q)1824
4457 y Fo(\000)8 b Fs(I)1933 4469 y Fr(10)2003 4457 y
Fu(,)23 b(a)f(proto)f(ma)5 b(j\355)-135 4557 y(ob)r(\354)38
b(j\341dra)f(sp)r(ole\350n)n(\375)g(n\354jak\375)g(nen)n(ulo)n(v\375)g
(v)n(ektor)g Fl(x)p Fu(.)h(Pro)e(n\354j)j(v\355me)f Fs(J)2186
4569 y Fr(10)2256 4557 y Fl(x)j Fu(=)e(0)-135 4657 y(\(proto\276e)27
b(je)h(k)n(olm)n(\375)e(k)h(\(1)p Fs(;)14 b Fu(1)p Fs(;)g(:)g(:)g(:)f
(;)h Fu(1\)\),)28 b(a)f(sp)r(o)r(\350\355t\341me)19 4841
y Fs(A)81 4853 y Fq(R)136 4841 y Fl(x)83 b Fu(=)g(\()p
Fs(J)495 4853 y Fr(10)584 4841 y Fo(\000)18 b Fs(I)703
4853 y Fr(10)792 4841 y Fo(\000)g Fs(A)937 4853 y Fq(P)1011
4841 y Fo(\000)g Fs(A)1156 4853 y Fq(Q)1213 4841 y Fu(\))p
Fl(x)24 b Fu(=)269 4966 y(=)83 b Fs(J)463 4978 y Fr(10)533
4966 y Fl(x)19 b Fo(\000)f Fs(I)721 4978 y Fr(10)792
4966 y Fl(x)h Fo(\000)f Fu(\()p Fs(A)1038 4978 y Fq(P)1112
4966 y Fo(\000)g Fs(I)1231 4978 y Fr(10)1302 4966 y Fu(\))p
Fl(x)h Fo(\000)f Fu(\()p Fs(A)1580 4978 y Fq(Q)1655 4966
y Fo(\000)g Fs(I)1774 4978 y Fr(10)1845 4966 y Fu(\))p
Fl(x)h Fo(\000)f Fu(2)p Fs(I)2107 4978 y Fr(10)2178 4966
y Fl(x)23 b Fu(=)269 5090 y(=)83 b(0)18 b Fo(\000)g Fl(x)h
Fo(\000)f Fu(0)f Fo(\000)i Fu(0)e Fo(\000)h Fu(2)p Fl(x)23
b Fu(=)g Fo(\000)p Fu(3)p Fl(x)p Fs(:)-135 5275 y Fu(T)-7
b(o)26 b(znamen\341,)h(\276e)g Fo(\000)p Fu(3)f(m)n(us\355)g(b)n(\375t)
h(vlastn\355m)g(\350\355slem)g Fs(A)1581 5287 y Fq(R)1636
5275 y Fu(,)g(ale)f(matice)h(sousednosti)-135 5375 y(P)n(eterseno)n(v)n
(a)d(grafu)j(toto)g(vlastn\355)h(\350\355slo)f(nem\341)g({)g(sp)r(or.)
-135 5655 y Fw(14)119 b(Konec)40 b(pades\341tn\355k\371)-135
5839 y Fu(In)n(terneto)n(v)n(\351)e(zasilatelstv\355)g(dostalo)h
Fs(m)g Fu(ob)5 b(jedn\341)n(v)n(ek,)38 b(k)n(a\276d\341)g(z)i(nic)n(h)f
(p)r(o\276aduje)-135 5938 y(n\354k)n(olik)27 b(kus\371)i(zb)r
(o\276\355)f(r\371zn)n(\375c)n(h)f(druh)n(\371.)i(Vtom)f(vy\271el)g
(vl\341dn\355)g(v\375nos)g(ru\271\355c\355)g(pade-)-135
6038 y(s\341tn\355ky)23 b(a)h(na\370izuj\355c\355,)g(\276e)g(cena)f(k)n
(a\276d\351ho)g(zb)r(o\276\355)h(m)n(us\355)g(b)n(\375t)g(zaokrouhlena)
d(na)j(cel\351)p eop end
PStoPSsaved restore
%%Page: (26,27) 14
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 850.393701 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
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-182 1891 2629 4 v -182 2074 a Fu(k)n(orun)n(y)18 b(\(nahoru)h(neb)r(o)
h(dol\371,)f(a)h(p)r(okud)f(cena)g(u\276)h(b)n(yla)f(v)g(cel\375c)n(h)h
(k)n(orun\341c)n(h,)d(pak)j(se)-182 2174 y(nem\354n\355\).)28
b(M\371\276e)f(zasilatelstv\355)f(zaokrouhlit)f(v\271ec)n(hn)n(y)h(cen)
n(y)h(tak,)g(ab)n(y)f(se)h(celk)n(o)n(v)n(\341)-182 2274
y(cena)f(\276\341dn\351)g(ob)5 b(jedn\341)n(vky)25 b(mo)r(c)i
(nezm\354nila?)g(T)-7 b(en)n(to)26 b(zaokrouhlo)n(v)n(ac\355)d
(probl\351m)j(a)-182 2373 y(jem)n(u)i(p)r(o)r(dobn\351)f(se)g
(studuj\355)h(v)f(teorii)g Fj(diskr)l(epance)p Fu(.)i(T)-7
b(ady)27 b(uv)n(edeme)g(jedn)n(u)g(v)n(\354tu,)-182 2473
y(kter\341)g(se)g(dok)n(azuje)g(p)r(omo)r(c\355)g(line\341rn\355)g
(algebry)-7 b(.)-182 2610 y Fl(V)m(\354ta.)67 b Fi(Jestli\276e)30
b(o)r(d)h(\276\341dn\351ho)f(druh)n(u)h(zb)r(o\276\355)f(nen\355)h
(dohromady)f(ob)5 b(jedn\341no)29 b(v\355c)-182 2710
y(ne\276)36 b Fs(t)f Fi(kus\371,)h(a)f(jestli\276e)h(\276\341dn\341)f
(ob)5 b(jedn\341)n(vk)n(a)33 b(nep)r(o\276aduje)j(v\355ce)f(ne\276)g
(jeden)h(kus)-182 2810 y(zb)r(o\276\355)28 b(o)r(d)h(k)n(a\276d\351ho)e
(druh)n(u,)h(p)r(otom)g(lze)g(cen)n(y)g(zaokrouhlit)f(na)h(cel\351)g(k)
n(orun)n(y)e(tak,)-182 2909 y(\276e)32 b(cena)f(\276\341dn\351)g(ob)5
b(jedn\341)n(vky)30 b(se)h(nezm\354n\355)h(o)f(v\355c)h(ne\276)f
Fs(t)h Fi(k)n(orun.)f(\(P\371v)n(o)r(dn\355)g(cen)n(y)-182
3009 y(dok)n(once)22 b(mohou)g(b)n(\375t)h(zcela)g(lib)r(o)n(v)n
(oln\351)f(a)g(nem)n(us\355)h(b)n(\375t)g(v)g(cel\375c)n(h)g
(pades\341tn\355c\355c)n(h.\))-57 3241 y Fu(Je)29 b(p)r(ozoruho)r
(dn\351,)g(\276e)g(o)r(dhad)g(c)n(h)n(yb)n(y)g(zaokrouhlen\355)f(zde)h
(v\371b)r(ec)h(nez\341)n(vis\355)f(na)-182 3340 y(celk)n(o)n(v)n(\351m)
d(p)r(o)r(\350tu)i(ob)5 b(jedn\341)n(v)n(ek)26 b(ani)h(na)h(p)r(o)r
(\350tu)g(druh)n(\371)f(zb)r(o\276\355.)-182 3478 y Fl
(Matemati\350t\354j\271\355)21 b(vyj\341d\370en\355)h(probl\351m)m(u.)
38 b Fu(Ozna\350me)18 b(druh)n(y)g(zb)r(o\276\355)g(1)p
Fs(;)c Fu(2)p Fs(;)g(:)g(:)g(:)f(;)h(n)-182 3577 y Fu(a)30
b(bu\357)h Fs(c)95 3589 y Fq(j)160 3577 y Fu(cena)f(jednoho)g(kusu)g(o)
r(d)g Fs(j)5 b Fu(-t\351ho)30 b(druh)n(u.)g(M\371\276eme)g(p\370edp)r
(okl\341dat,)f(\276e)-182 3677 y(k)n(a\276d\351)21 b
Fs(c)79 3689 y Fq(j)137 3677 y Fo(2)i Fu(\(0)p Fs(;)14
b Fu(1\))22 b(\(proto\276e)f(v)h(probl\351m)n(u)f(hra)5
b(je)21 b(roli)g(jen)h(zm\354na)g(cen)n(y)f(zaokrouh-)-182
3777 y(len\355m\).)31 b(P)n(on\354v)n(ad\276)e(\276\341dn\341)g(ob)5
b(jedn\341)n(vk)n(a)28 b(nep)r(o\276aduje)j(v\355c)f(ne\276)g(jeden)h
(kus)f(zb)r(o\276\355)-182 3876 y(k)n(a\276d\351ho)37
b(druh)n(u,)g(m)n(\371\276eme)h Fs(i)p Fu(-tou)f(ob)5
b(jedn\341)n(vku)36 b(reprezen)n(to)n(v)n(at)g(jak)n(o)g(mno\276in)n(u)
-182 3976 y Fs(S)-131 3988 y Fq(i)-80 3976 y Fo(\022)22
b(f)p Fu(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)p
Fo(g)p Fu(,)23 b Fs(i)g Fu(=)g(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)e
(;)i(m)p Fu(.)23 b(V)n(\354ta)h(n)n(yn\355)f(tvrd\355,)g(\276e)h(p)r
(okud)f(\276\341dn\351)g Fs(j)29 b Fu(nen\355)-182 4075
y(v)n(e)e(v\355c)h(ne\276)f Fs(t)h Fu(mno\276in\341c)n(h,)f
(existuj\355)h(\350\355sla)f Fs(z)1212 4087 y Fr(1)1249
4075 y Fs(;)14 b(z)1325 4087 y Fr(2)1361 4075 y Fs(;)g(:)g(:)g(:)g(;)g
(z)1585 4087 y Fq(n)1653 4075 y Fo(2)23 b(f)p Fu(0)p
Fs(;)14 b Fu(1)p Fo(g)26 b Fu(tak)n(o)n(v)n(\341,)f(\276e)236
4200 y Fp(\014)236 4250 y(\014)236 4300 y(\014)236 4350
y(\014)275 4242 y(X)263 4420 y Fq(j)s Fk(2)p Fq(S)379
4428 y Fm(i)420 4321 y Fs(c)456 4333 y Fq(j)509 4321
y Fo(\000)604 4242 y Fp(X)592 4420 y Fq(j)s Fk(2)p Fq(S)708
4428 y Fm(i)749 4321 y Fs(z)788 4333 y Fq(j)822 4200
y Fp(\014)822 4250 y(\014)822 4300 y(\014)822 4350 y(\014)873
4321 y Fo(\024)e Fs(t;)97 b Fu(pro)26 b(k)n(a\276d\351)h
Fs(i)c Fu(=)f(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)f(;)h(m:)-182
4644 y Fl(D\371k)m(az.)76 b Fu(Pro)34 b(k)n(a\276d\375)g(index)g
Fs(j)40 b Fo(2)c(f)p Fu(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)p
Fo(g)34 b Fu(z\370\355d\355me)h(jedn)n(u)g(re\341lnou)e(pro-)-182
4744 y(m\354nnou)27 b Fs(x)178 4756 y Fq(j)237 4744 y
Fo(2)c Fu([0)p Fs(;)14 b Fu(1],)26 b(j\355\276)h(na)g(za\350\341tku)f
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4744 y Fu(,)g(a)f(kter\341)g(se)h(bude)-182 4843 y(v)g(pr\371b)r(\354h)
n(u)g(d\371k)n(azu)f(m\354nit.)h(Nak)n(onec)f(bude)h(m\355t)g(k)n
(a\276d\351)f Fs(x)1722 4855 y Fq(j)1784 4843 y Fu(ho)r(dnotu)h(0)g
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(jak)n(o)f Fs(z)1006 4955 y Fq(j)1040 4943 y Fu(.)-57
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y(ostatn\355)36 b(jsou)h(\376k)n(ol\355sa)n(v)n(\351\377.)c(Na)k
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y Fq(j)1786 5149 y Fu(k)n(ol\355sa)n(v)n(\341.)e(Ust\341len\341)-182
5248 y Fs(x)-135 5260 y Fq(j)-63 5248 y Fu(ma)5 b(j\355)37
b(ho)r(dnot)n(y)f(0)h(neb)r(o)f(1,)h(a)f(t)n(y)h(se)f(ji\276)h(nikdy)g
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n(h)25 b(prom\354nn)n(\375c)n(h)i(jsou)g(v)h(in)n(terv)n(alu)f(\(0)p
Fs(;)14 b Fu(1\).)27 b(V)h(k)n(a\276d\351m)f(kroku)f(se)i(asp)r(o\362)
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Fs(S)756 5566 y Fq(i)814 5554 y Fj(hr)l(ozivou)p Fu(,)g(jestli\276e)g
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Fs(j)-182 5653 y Fu(tak)n(o)n(v\375c)n(h,)21 b(\276e)h
Fs(x)330 5665 y Fq(j)388 5653 y Fu(je)h(je\271t\354)g(k)n(ol\355sa)n(v)
n(\341.)c(Ostatn\355)j(mno\276in)n(y)g(jsou)h Fj(ne\271kodn\351)p
Fu(.)g(Budeme)-182 5753 y(udr\276o)n(v)n(at)j(v)h(platnosti)h
(n\341sleduj\355c\355)g(p)r(o)r(dm\355nku:)419 5882 y
Fp(X)407 6060 y Fq(j)s Fk(2)p Fq(S)523 6068 y Fm(i)564
5961 y Fs(x)611 5973 y Fq(j)669 5961 y Fu(=)768 5882
y Fp(X)757 6060 y Fq(j)s Fk(2)p Fq(S)873 6068 y Fm(i)913
5961 y Fs(c)949 5973 y Fq(j)1012 5961 y Fu(pro)f(v\271ec)n(hn)n(y)f
(hroziv)n(\351)g Fs(S)1806 5973 y Fq(i)1834 5961 y Fu(.)483
b(\(2\))p eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 422.362205 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 28 27 bop 1031 1858 a Ft(Obsah)1165 b Fu(28)p
-135 1891 2629 4 v -135 2074 a(Ozna\350me)25 b Fs(F)38
b Fu(mno\276in)n(u)26 b(index\371)g(v\271ec)n(h)g(k)n(ol\355sa)n
(v\375c)n(h)d(prom\354nn)n(\375c)n(h,)i(a)h(uv)n(a\276me)f(\(2\))-135
2174 y(jak)n(o)d(syst\351m)i(line\341rn\355c)n(h)f(ro)n(vnic,)f
(jeho\276)h(nezn\341m\351)h(jsou)f(k)n(ol\355sa)n(v)n(\351)e
(prom\354nn\351)j(\(za-)-135 2274 y(t\355mco)41 b(ho)r(dnot)n(y)g
(ust\341len)n(\375c)n(h)f(prom\354nn)n(\375c)n(h)g(zde)h(vystupuj\355)g
(jak)n(o)f(k)n(onstan)n(t)n(y\).)-135 2373 y(T)-7 b(en)n(to)23
b(syst\351m)h(ur\350it\354)g(m\341)f(\370e\271en\355,)h(toti\276)g
(momen)n(t\341ln\355)f(ho)r(dnot)n(y)h(k)n(ol\355sa)n(v\375c)n(h)d
(pro-)-135 2473 y(m\354nn)n(\375c)n(h.)e(P)n(on\354v)n(ad\276)f
(p\370edp)r(okl\341d\341me,)g(\276e)h(k)n(a\276d\341)g(k)n(ol\355sa)n
(v)n(\341)d(prom\354nn\341)j(le\276\355)h(v)f(in-)-135
2572 y(terv)n(alu)e(\(0)p Fs(;)d Fu(1\),)k(zm\355n\354n\351)h
(\370e\271en\355)f(je)g(vnit\370n\355m)h(b)r(o)r(dem)g
Fo(j)p Fs(F)12 b Fo(j)p Fu(-dimenzion\341ln\355)18 b(kryc)n(hle)-135
2672 y([0)p Fs(;)c Fu(1])32 2642 y Fk(j)p Fq(F)9 b Fk(j)126
2672 y Fu(.)32 b(Chceme)g(uk)n(\341zat,)f(\276e)g(existuje)i(tak)n
(\351)e(\370e\271en\355)g(na)h(hranici)f(t\351to)h(kryc)n(hle,)-135
2772 y(tj.)c(tak)n(o)n(v)n(\351,)e(\276e)h(asp)r(o\362)g(jedna)h
(nezn\341m\341)f(m\341)g(ho)r(dnotu)h(0)f(neb)r(o)h(1.)-11
2874 y(Kl\355\350o)n(v)n(\351)33 b(p)r(ozoro)n(v)n(\341n\355)f(je,)j
(\276e)g(p)r(o)r(\350et)g(hroziv\375c)n(h)e(mno\276in)h(je)h(v)g(k)n
(a\276d\351m)f(ok)n(a-)-135 2974 y(m\276iku)23 b(ost\370e)f
(men\271\355)i(ne\276)f(p)r(o)r(\350et)g(k)n(ol\355sa)n(v\375c)n(h)e
(prom\354nn)n(\375c)n(h)h(\(k)n(a\276d\341)g(hroziv)n(\341)f(mno-)-135
3074 y(\276ina)31 b(p)r(ot\370ebuje)h(v\355c)g(ne\276)f
Fs(t)h Fu(k)n(ol\355sa)n(v\375c)n(h)d(prom\354nn)n(\375c)n(h,)i
(zat\355mco)g(jedna)h(k)n(ol\355sa)n(v)n(\341)-135 3173
y(prom\354nn\341)c(p\370isp)r(\354je)h(nejv\375\271)g
Fs(t)g Fu(hroziv\375m)f(mno\276in\341m\).)h(T)-7 b(ud\355\276)29
b(uv)n(a\276o)n(v)n(an\341)d(sou-)-135 3273 y(sta)n(v)n(a)36
b(line\341rn\355c)n(h)i(ro)n(vnic)f(m\341)h(m\351n\354)g(ro)n(vnic)f
(ne\276)h(nezn\341m)n(\375c)n(h,)f(a)h(proto)f(mno-)-135
3373 y(\276ina)25 b(\370e\271en\355)f(m\341)h(dimenzi)h(asp)r(o\362)e
(jedna.)i(Uv)n(a\276o)n(v)n(an)n(\375m)c(\370e\271en\355m)j(uvnit\370)g
(kryc)n(hle)-135 3472 y([0)p Fs(;)14 b Fu(1])32 3442
y Fk(j)p Fq(F)9 b Fk(j)153 3472 y Fu(tedy)28 b(pro)r(c)n(h\341z\355)f
(n\354jak)n(\341)f(p\370\355mk)n(a)h(\(jedno)r(dimenzion\341ln\355)h
(a\014nn\355)g(p)r(o)r(dpro-)-135 3572 y(stor\),)f(jej\355\276)h
(v\271ec)n(hn)n(y)f(b)r(o)r(dy)h(jsou)f(tak)n(\351)g
(\370e\271en\355mi.)h(T)-7 b(ak)n(o)n(v)n(\341)25 b(p\370\355mk)n(a)h
(prot\355n\341)h(hra-)-135 3671 y(nici)k(kryc)n(hle)e(v)h(n\354jak)n
(\351m)g(b)r(o)r(d\354)h Fl(y)q Fu(.)g(Sou\370adnice)f(b)r(o)r(du)h
Fl(y)h Fu(p)r(ou\276ijeme)f(jak)n(o)e(ho)r(d-)-135 3771
y(not)n(y)i(k)n(ol\355sa)n(v\375c)n(h)d(prom\354nn)n(\375c)n(h)i(pro)h
(dal\271\355)f(krok.)g(V\271ec)n(hn)n(y)h(k)n(ol\355sa)n(v)n(\351)e
(prom\354nn\351)-135 3871 y Fs(x)-88 3883 y Fq(j)-53
3871 y Fu(,)i(pro)f(n\354\276)g(o)r(dp)r(o)n(v\355da)5
b(j\355c\355)30 b(sou\370adnice)f(b)r(o)r(du)i Fl(y)i
Fu(je)e(0)f(neb)r(o)h(1,)f(budou)g(v\271ak)g(o)r(d)-135
3970 y(n\341sleduj\355c\355ho)d(kroku)g(p)r(o)r(\350\355na)5
b(je)27 b(ust\341len\351.)-11 4073 y(P)n(opsan)n(\375)g(krok)g
(opakujeme,)h(dokud)g(se)g(v\271ec)n(hn)n(y)g(prom\354nn\351)g
(neust\341l\355.)g(Tvr-)-135 4173 y(d\355me,)40 b(\276e)f(v)n
(ezmeme-li)f(za)h Fs(z)813 4185 y Fq(j)887 4173 y Fu(ust\341lenou)g(ho)
r(dnotu)g Fs(x)1661 4185 y Fq(j)1736 4173 y Fu(pro)f(v\271ec)n(hna)g
Fs(j)5 b Fu(,)40 b(bude)-135 4300 y(spln\354na)32 b(p)r(o)r(dm\355nk)n
(a)562 4205 y Fp(\014)562 4255 y(\014)562 4304 y(\014)590
4238 y(P)677 4325 y Fq(j)s Fk(2)p Fq(S)793 4333 y Fm(i)838
4300 y Fs(c)874 4312 y Fq(j)927 4300 y Fo(\000)1011 4238
y Fp(P)1098 4325 y Fq(j)s Fk(2)p Fq(S)1214 4333 y Fm(i)1259
4300 y Fs(z)1298 4312 y Fq(j)1332 4205 y Fp(\014)1332
4255 y(\014)1332 4304 y(\014)1391 4300 y Fo(\024)f Fs(t)h
Fu(pro)g(k)n(a\276d\351)f Fs(i)g Fu(=)g(1)p Fs(;)14 b
Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(m)p Fu(,)-135 4420 y(jak)21
b(jsme)h(c)n(h)n(t\354li.)g(Ab)n(yc)n(hom)f(to)g(nahl\351dli,)h(uv)n
(a\276me)e(n\354jak)n(ou)h(mno\276in)n(u)h Fs(S)2185
4432 y Fq(i)2212 4420 y Fu(.)g(V)g(ok)n(a-)-135 4520
y(m\276iku,)33 b(kdy)h(p\370estala)e(b)n(\375t)h(hroziv)n(\341,)f
(platilo)h(je\271t\354)1562 4457 y Fp(P)1650 4545 y Fq(j)s
Fk(2)p Fq(S)1766 4553 y Fm(i)1811 4520 y Fs(c)1847 4532
y Fq(j)1904 4520 y Fo(\000)1991 4457 y Fp(P)2078 4545
y Fq(j)s Fk(2)p Fq(S)2194 4553 y Fm(i)2239 4520 y Fs(x)2286
4532 y Fq(j)2354 4520 y Fu(=)f(0)-135 4619 y(p)r(o)r(dle)22
b(p)r(o)r(dm\355nky)h(\(2\).)f(T)-7 b(ehdy)22 b Fs(S)922
4631 y Fq(i)972 4619 y Fu(obsaho)n(v)n(ala)d(indexy)j(nejv\375\271)f
Fs(t)i Fu(k)n(ol\355sa)n(v\375c)n(h)c(pro-)-135 4719
y(m\354nn)n(\375c)n(h.)33 b(Ho)r(dnota)h(k)n(a\276d\351)f(z)g(t\354c)n
(h)n(to)h(k)n(ol\355sa)n(v\375c)n(h)d(prom\354nn)n(\375c)n(h)h(se)i(v)n
(e)f(zb)n(ytku)-135 4819 y(p)r(ostupu)26 b(nezm\354nila)f(v\355c)g
(ne\276)g(o)g(1)g(\(mohla)g(b)n(\375t)g(t\370eba)g(0)p
Fs(:)p Fu(001)e(a)i(pak)g(se)g(ust\341lit)g(na)-135 4918
y(1\).)i(T\355m)h(je)g(d\371k)n(az)f(hoto)n(v.)-135 5209
y Fw(15)119 b(V)-10 b(ektory)40 b(v)g(ohr\341dce)-135
5425 y Fl(V)m(\354ta.)81 b Fi(Bu\357)38 b Fs(M)47 b Fi(lib)r(o)n(v)n
(oln\341)36 b(mno\276ina)h Fs(n)h Fi(v)n(ektor\371)e(v)i
Fh(R)1735 5395 y Fq(d)1773 5425 y Fi(,)g(spl\362)n(uj\355c\355)g
Fo(k)p Fl(v)q Fo(k)i(\024)f Fu(1)-135 5524 y Fi(pro)28
b(k)n(a\276d\351)g Fl(v)g Fo(2)e Fs(M)9 b Fi(,)29 b(kde)g
Fo(k)p Fl(v)q Fo(k)g Fi(zna\350\355)g(norm)n(u)f Fl(v)j
Fi(neb)r(oli)e(ob)n(vyklou)f(euklido)n(vsk)n(ou)-135
5624 y(d\351lku,)i(a)f(d\341le)362 5562 y Fp(P)450 5649
y Fb(v)q Fk(2)p Fq(M)623 5624 y Fl(v)f Fu(=)e(0)p Fi(.)k(P)n(otom)e(se)
i(v\271ec)n(hn)n(y)e(v)n(ektory)g(z)i Fs(M)38 b Fi(da)5
b(j\355)30 b(sro)n(vnat)-135 5724 y(do)22 b(p)r(osloupnosti)f
Fu(\()p Fl(v)534 5736 y Fr(1)572 5724 y Fs(;)14 b Fl(v)659
5736 y Fr(2)696 5724 y Fs(;)g(:)g(:)g(:)g(;)g Fl(v)931
5736 y Fq(n)976 5724 y Fu(\))23 b Fi(tak,)e(\276e)h Fo(k)p
Fl(v)1381 5736 y Fr(1)1425 5724 y Fu(+)7 b Fl(v)1547
5736 y Fr(2)1592 5724 y Fu(+)g Fo(\001)14 b(\001)g(\001)6
b Fu(+)h Fl(v)1889 5736 y Fq(k)1930 5724 y Fo(k)23 b(\024)g
Fs(d)f Fi(pro)f(k)n(a\276d\351)-135 5823 y Fs(k)26 b
Fu(=)c(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)f(;)h(n)p
Fi(.)-11 6038 y Fu(Nap\370\355klad)20 b(pro)g(ro)n(vin)n(u)g(\()p
Fs(d)j Fu(=)g(2\))d(v)n(\354ta)h(zaru\350uje)f(tak)n(o)n(v)n(\351)e(p)r
(o\370ad\355,)i(\276e)h(vyjdeme-)p eop end
PStoPSsaved restore
%%Page: (28,29) 15
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 0.000000 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 29 28 bop -182 1858 a Fu(29)1165 b Ft(Obsah)p
-182 1891 2629 4 v -182 2074 a Fu(li)33 b(z)f(p)r(o)r(\350\341tku,)g(p)
r(op)r(o)5 b(jdeme)32 b(o)g Fl(v)869 2086 y Fr(1)907
2074 y Fu(,)g(pak)g(o)g Fl(v)1250 2086 y Fr(2)1287 2074
y Fu(,)h(pak)e(o)h Fl(v)1630 2086 y Fr(3)1668 2074 y
Fu(,.)14 b(.)g(.)g(,)32 b(a)g(nak)n(onec)f(o)h Fl(v)2378
2086 y Fq(n)2423 2074 y Fu(,)-182 2174 y(nikdy)22 b(nevyb)r(o)r
(\350\355me)g(z)f(kruho)n(v)n(\351)f(ohr\341dky)g(o)i(p)r(olom\354ru)f
(2)g(se)g(st\370edem)h(v)f(p)r(o)r(\350\341tku.)-182
3169 y @beginspecial -52 @llx -76 @lly 287 @urx 42 @ury
3153 @rwi @setspecial
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% separation convention operators
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exch
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gsave
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grestore
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exch 1 array astore composefont pop
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pdfMakeFont16
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% color operators
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% path segment operators
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/c { curveto } def
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neg 0 rlineto closepath } def
/h { closepath } def
% path painting operators
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/f* { fCol eofill } def
% clipping operators
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% text state operators
/Tc { /pdfCharSpacing exch def } def
/Tf { dup /pdfFontSize exch def
dup pdfHorizScaling mul exch matrix scale
pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put
exch findfont exch makefont setfont } def
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% text positioning operators
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% text string operators
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3 index 3 index rmoveto
4 index eq { 5 index 5 index rmoveto } if
} forall
6 {pop} repeat
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% Level 1 image operators
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{ currentfile pdfImBuf1 readhexstring pop } image
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/pdfIm1Sep {
/pdfImBuf1 4 index string def
/pdfImBuf2 4 index string def
/pdfImBuf3 4 index string def
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{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
1 index exch 2 copy get 255 exch sub put
} for }
6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImM {
fCol imagemask
{ currentfile pdfImBuf readline
not { pop exit } if
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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(\354t)m(y)-8 b(.)46 b Fu(Je)20 b(to)h(tro\271ku)f
(slo\276it\354j\271\355)g(v)n(ariace)f(meto)r(dy)i(z)g(o)r(dd\355lu)g
(14.)f(P)n(olo\276\355me)-182 4045 y Fs(M)-101 4057 y
Fq(n)-33 4045 y Fu(=)j Fs(M)9 b Fu(,)21 b(a)g(budeme)h(p)r(ostupn\354)f
(k)n(onstruo)n(v)n(at)e(mno\276in)n(y)i Fs(M)1762 4057
y Fq(n)p Fk(\000)p Fr(1)1892 4045 y Fu(,)g Fs(M)2017
4057 y Fq(n)p Fk(\000)p Fr(2)2147 4045 y Fu(,.)14 b(.)g(.)g(,)p
Fs(M)2385 4057 y Fq(d)2423 4045 y Fu(,)-182 4144 y(p\370i\350em\276)38
b Fs(M)219 4156 y Fq(k)q Fk(\000)p Fr(1)383 4144 y Fu(vznikne)g(z)g
Fs(M)854 4156 y Fq(k)933 4144 y Fu(ubr\341n\355m)g(jednoho)g(v)n
(ektoru)f(\(tak\276e)h Fo(j)p Fs(M)2277 4156 y Fq(k)2318
4144 y Fo(j)j Fu(=)-182 4244 y Fs(k)s Fu(\).)28 b(Sp)r(olu)g(s)f
(mno\276inou)g Fs(M)699 4256 y Fq(k)767 4244 y Fu(vyrob\355me)f(tak)n
(\351)h(soub)r(or)f(re\341ln)n(\375c)n(h)g(k)n(o)r(e\014cien)n(t\371)h
(pro)-182 4344 y(v)n(ektory)f(z)i Fs(M)264 4356 y Fq(k)304
4344 y Fu(,)g(tj.)g(\350\355sla)f Fs(\013)701 4356 y
Fq(k)q(;)p Fb(v)826 4344 y Fo(2)c Fh(R)p Fu(,)28 b Fl(v)d
Fo(2)e Fs(M)1249 4356 y Fq(k)1289 4344 y Fu(,)28 b(spl\362)n
(uj\355c\355)g(p)r(o)r(dm\355nky)-103 4499 y(\(i\))42
b(0)22 b Fo(\024)h Fs(\013)231 4511 y Fq(k)q(;)p Fb(v)355
4499 y Fo(\024)g Fu(1)k(pro)g(v\271ec)n(hna)f Fl(v)f
Fo(2)f Fs(M)1204 4511 y Fq(k)1244 4499 y Fu(,)-127 4660
y(\(ii\))26 4598 y Fp(P)113 4685 y Fb(v)q Fk(2)p Fq(M)262
4694 y Fm(k)316 4660 y Fs(\013)369 4672 y Fq(k)q(;)p
Fb(v)494 4660 y Fu(=)e Fs(k)g Fo(\000)c Fs(d)p Fu(,)-150
4821 y(\(iii\))26 4759 y Fp(P)113 4846 y Fb(v)q Fk(2)p
Fq(M)262 4855 y Fm(k)316 4821 y Fs(\013)369 4833 y Fq(k)q(;)p
Fb(v)471 4821 y Fl(v)25 b Fu(=)d(0)p Fs(:)-182 4992 y
Fu(Pro)27 b Fs(k)h Fu(=)c Fs(n)29 b Fu(v\355me,)g(\276e)543
4930 y Fp(P)631 5017 y Fb(v)q Fk(2)p Fq(M)804 4992 y
Fl(v)d Fu(=)f(0,)j(a)g(kdy\276)h(tedy)g(v)n(ezmeme)f
Fs(\013)1930 5004 y Fq(n;)p Fb(v)2060 4992 y Fu(=)2160
4959 y Fq(n)p Fk(\000)p Fq(d)p 2160 4973 128 4 v 2203
5021 a(n)2326 4992 y Fu(pro)-182 5092 y(v\271ec)n(hna)f
Fl(v)d Fo(2)g Fs(M)362 5104 y Fq(n)407 5092 y Fu(,)j(budou)h(v\271ec)n
(hn)n(y)e(t\370i)i(p)r(o)r(dm\355nky)g(spln\354n)n(y)-7
b(.)-57 5191 y(T)g(e\357)40 b(c)n(hceme)g(p)r(okro)r(\350it)f(o)r(d)i
Fs(k)i Fu(k)n(e)c Fs(k)30 b Fo(\000)c Fu(1.)40 b(Uv)n(\341\276\355me)g
(p)r(omo)r(cnou)g(sousta)n(vu)-182 5291 y(line\341rn\355c)n(h)27
b(nero)n(vnic)f(a)h(ro)n(vnic)g(pro)g(nezn\341m\351)g
Fs(x)1386 5303 y Fb(v)1431 5291 y Fu(,)h Fl(v)d Fo(2)e
Fs(M)1716 5303 y Fq(k)1756 5291 y Fu(:)670 5461 y Fs(x)717
5473 y Fb(v)845 5461 y Fo(\025)83 b Fu(0)110 b(pro)27
b(v\271ec)n(hna)f Fl(v)f Fo(2)e Fs(V)5 b(;)509 b Fu(\(3\))670
5585 y Fs(x)717 5597 y Fb(v)845 5585 y Fo(\024)83 b Fu(1)110
b(pro)27 b(v\271ec)n(hna)f Fl(v)f Fo(2)e Fs(V)5 b(;)509
b Fu(\(4\))503 5647 y Fp(X)471 5826 y Fb(v)q Fk(2)p Fq(M)620
5835 y Fm(k)670 5726 y Fs(x)717 5738 y Fb(v)845 5726
y Fu(=)83 b(\()p Fs(k)21 b Fo(\000)d Fu(1\))g Fo(\000)g
Fs(d;)927 b Fu(\(5\))452 5884 y Fp(X)419 6062 y Fb(v)q
Fk(2)p Fq(M)568 6071 y Fm(k)618 5963 y Fs(x)665 5975
y Fb(v)710 5963 y Fl(v)85 b Fu(=)e(0)p Fs(:)1282 b Fu(\(6\))p
eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 428.031496 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 30 29 bop 1031 1858 a Ft(Obsah)1165 b Fu(30)p
-135 1891 2629 4 v -135 2075 a(Sousta)n(v)n(a)23 b(m\341)i(asp)r(o\362)
g(jedno)g(\370e\271en\355,)f(proto\276e)g Fs(x)1400 2087
y Fb(v)1469 2075 y Fu(=)1566 2035 y Fr(\()p Fq(k)q Fk(\000)p
Fr(1\))p Fk(\000)p Fq(d)p 1566 2056 261 4 v 1635 2104
a(k)q Fk(\000)p Fq(d)1836 2075 y Fs(\013)1889 2087 y
Fq(k)q(;)p Fb(v)2016 2075 y Fu(je)h(p)r(o)r(dle)h(p)r(o)r(d-)-135
2175 y(m\355nek)31 b(\(i\){\(iii\))g(\370e\271en\355m.)f(Tvrd\355me,)h
(\276e)f(existuje)h(i)g(\370e\271en\355,)f(pro)g(n\354\276)h(je)f
(n\354kter\351)-135 2274 y Fs(x)-88 2286 y Fb(v)-20 2274
y Fu(=)23 b(0.)-11 2377 y(Nejd\370\355v)34 b(vy\370\355d\355me)f(sp)r
(eci\341ln\355)h(p\370\355pad:)f(Kdy\276)g Fs(k)j Fu(=)d
Fs(d)22 b Fu(+)g(1,)34 b(je)g(pra)n(v)n(\341)d(strana)-135
2476 y(v)c(\(5\))h(ro)n(vna)e(0,)h(a)g(proto)g(n)n(ulo)n(v\375)g(v)n
(ektor)f(je)i(\370e\271en\355m.)-11 2578 y(Nyn\355)i(dok)n(azujeme)e
(tvrzen\355)g(za)h(p\370edp)r(okladu)f Fs(k)g Fo(\025)d
Fs(d)19 b Fu(+)g(2)29 b(Nejd\370\355v)n(e)f(nahl\351d-)-135
2678 y(neme,)e(\276e)f(existuje)g(\370e\271en\355,)g(pro)g(n\354\276)g
(asp)r(o\362)g(v)g Fs(k)17 b Fo(\000)d Fs(d)g Fo(\000)g
Fu(1)25 b(z)g(nero)n(vnic)f(\(3\),)i(\(4\))g(na-)-135
2778 y(st\341)n(v)n(\341)20 b(ro)n(vnost.)g(V)i(sousta)n(v)n(\354)e
(m\341me)i Fs(d)7 b Fu(+)g(1)21 b(ro)n(vnic)f(\(neb)r(o\273)j(\(6\))f
(je)g(ro)n(vnost)e(dv)n(ou)h Fs(d)p Fu(-)-135 2877 y
(dimenzion\341ln\355c)n(h)h(v)n(ektor\371\),)g(a)h(proto)f(mno\276ina)g
(\370e\271en\355)h(m\341)g(dimenzi)g(p\370inejmen-)-135
2990 y(\271\355m)d Fs(k)7 b Fo(\000)t Fs(d)t Fo(\000)t
Fu(1)23 b Fo(\025)g Fu(1.)d(Vyraz\355me)g(z)g(na\271eho)g(p)r(o)r
(\350\341te\350n\355ho)g(\370e\271en\355)g Fs(x)1903
3002 y Fb(v)1971 2990 y Fu(=)2069 2950 y Fr(\()p Fq(k)q
Fk(\000)p Fr(1\))p Fk(\000)p Fq(d)p 2069 2971 V 2137
3019 a(k)q Fk(\000)p Fq(d)2339 2990 y Fs(\013)2392 3002
y Fq(k)q(;)p Fb(v)-135 3090 y Fu(a)33 b(jdeme)h(mno\276inou)f
(\370e\271en\355)f(p)r(o)i(n\354jak)n(\351)e(p\370\355mce,)i(dokud)f
(nenastane)f(v)h(n\354kter\351)-135 3189 y(z)k(nero)n(vnic)f(\(3\),)i
(\(4\))f(ro)n(vnost;)f(geometric)n(ky)-7 b(,)35 b(dokud)j
(nenaraz\355me)e(na)h(hranici)-135 3289 y(kryc)n(hle)29
b(0)e Fo(\024)g Fs(x)364 3301 y Fb(v)437 3289 y Fo(\024)g
Fu(1.)j(Plat\355-li)g(te\357)g(nap\370\355klad)f(ro)n(vnost)g
Fs(x)1770 3301 y Fb(u)1844 3289 y Fu(=)e(1)j(pro)f(n\354jak)n(\351)h
Fl(u)p Fu(,)-135 3389 y(prom\354nnou)j Fs(x)352 3401
y Fb(u)432 3389 y Fu(za\014xujeme)h(na)f(ho)r(dnotu)h(1.)g(T\355m)g
(ubude)g(jedna)g(nezn\341m\341,)f(a)-135 3488 y(dimenze)21
b(\370e\271en\355)g(na\271\355)g(sousta)n(vy)f Fs(d)6
b Fu(+)g(1)20 b(ro)n(vnic)g(klesne)h(o)g(1)g(na)g Fs(k)8
b Fo(\000)e Fs(d)g Fo(\000)g Fu(2.)20 b(P)n(okud)g(to-)-135
3588 y(hle)25 b(\350\355slo)f(je)h(p)r(o\370\341d)e(asp)r(o\362)h(1,)h
(m)n(\371\276eme)f(argumen)n(t)g(s)g(p\370\355mk)n(ou)g(a)g(hranic\355)
g(kryc)n(hle)-135 3687 y(zopak)n(o)n(v)n(at)19 b(a)j(do)r(c\355lit)h
(dal\271\355)f(ro)n(vnosti)e(v)j(jin\351)g(z)f(nero)n(vnic,)f(atd.)h(T)
-7 b(akto)22 b(dos\341hneme)-135 3787 y Fs(k)g Fo(\000)c
Fs(d)h Fo(\000)f Fu(1)28 b(ro)n(vnost\355.)f(Kdy\276)h(asp)r(o\362)f
(jedna)h(z)h(t\354c)n(h)n(to)e(ro)n(vnost\355)g(je)h
Fs(x)2025 3799 y Fb(v)2095 3787 y Fu(=)23 b(0,)28 b(m\341me)-135
3887 y(co)f(jsme)g(c)n(h)n(t\354li.)g(Kdyb)n(yc)n(hom)f(m\354li)i
Fs(k)20 b Fo(\000)e Fs(d)f Fo(\000)h Fu(1)27 b(ro)n(vnost\355)e
Fs(x)1770 3899 y Fb(v)1839 3887 y Fu(=)d(1,)27 b(pak)g(m)n(us\355)g(b)n
(\375t)-135 3986 y(n)n(ulo)n(v)n(\341)f(v\271ec)n(hna)g(ostatn\355)h
Fs(x)761 3998 y Fb(v)834 3986 y Fu(d\355ky)h(ro)n(vnici)e(\(5\),)i(a)f
(tvrzen\355)h(plat\355)f(tak)n(\351.)-11 4088 y(P)n(o)r(dle)33
b(tohoto)g(tvrzen\355)h(zv)n(ol\355me)f(n\354jak)n(\351)g
(\370e\271en\355)1597 4087 y(\026)1592 4088 y Fl(x)h
Fu(=)f(\()5 b(\026)-47 b Fs(x)1853 4100 y Fb(v)1932 4088
y Fu(:)33 b Fl(v)i Fo(2)f Fs(M)2243 4100 y Fq(k)2283
4088 y Fu(\))g(na\271\355)-135 4188 y(sousta)n(vy)j(s)i(asp)r(o\362)g
(jednou)g(n)n(ulo)n(v)n(ou)e(slo\276k)n(ou,)h(a)h(v)n(ektor)e
Fl(v)44 b Fo(2)f Fs(M)2086 4200 y Fq(k)2126 4188 y Fu(,)c(pro)g
(n\354j\276)-130 4288 y(\026)-47 b Fs(x)-88 4300 y Fb(v)-19
4288 y Fu(=)24 b(0,)j(p)r(o)5 b(jmen)n(ujeme)29 b Fl(v)725
4300 y Fq(k)794 4288 y Fu(\(m\341-li)1043 4287 y(\026)1039
4288 y Fl(x)g Fu(v\355ce)e(n)n(ulo)n(v\375c)n(h)g(slo\276ek,)g(vyb)r
(ereme)h(z)g(nic)n(h)-135 4387 y(lib)r(o)n(v)n(oln\354\).)22
b(T)-7 b(o)23 b(bude)g Fl(v)632 4399 y Fq(k)696 4387
y Fu(jak)n(o)f(v)n(e)g(v)n(\354t\354,)h(jak)f(za)h(c)n(h)n(v\355li)f
(nahl\351dneme.)h(De\014n)n(ujeme)-135 4487 y Fs(M)-54
4499 y Fq(k)q Fk(\000)p Fr(1)94 4487 y Fu(=)g Fs(M)263
4499 y Fq(k)315 4487 y Fo(n)11 b(f)p Fl(v)460 4499 y
Fq(k)500 4487 y Fo(g)p Fu(.)24 b(Samoz\370ejm\354)f(je)h(v\271e)g
(p\370ic)n(h)n(yst\341no)e(tak,)i(\276e)g(kdy\276)f(p)r(olo\276\355me)
-135 4587 y Fs(\013)-82 4599 y Fq(k)q Fk(\000)p Fr(1)p
Fq(;)p Fb(v)134 4587 y Fu(=)35 b(\026)-47 b Fs(x)276
4599 y Fb(v)353 4587 y Fu(pro)31 b Fl(v)h Fo(2)e Fs(M)753
4599 y Fq(k)q Fk(\000)p Fr(1)879 4587 y Fu(,)i(plat\355)g(p)r(o)r
(dm\355nky)g(\(i\){\(iii\))h(a)e(induk)n(\350n\355)h(krok)f(je)-135
4686 y(hoto)n(v.)-11 4788 y(T)-7 b(e\357)31 b(m\341me)g(de\014no)n(v)n
(\341no)e Fl(v)870 4800 y Fq(n)916 4788 y Fs(;)14 b Fl(v)1003
4800 y Fq(n)p Fk(\000)p Fr(1)1133 4788 y Fs(;)g(:)g(:)g(:)g(;)g
Fl(v)1368 4800 y Fq(d)p Fr(+1)1491 4788 y Fu(.)31 b(V)g
Fs(M)1719 4800 y Fq(d)1788 4788 y Fu(zb)n(\375v)n(\341)e
Fs(d)i Fu(neo)r(\350\355slo)n(v)n(a-)-135 4888 y(n)n(\375c)n(h)19
b(v)n(ektor\371,)f(a)h(t)n(y)g(o)r(\350\355slujeme)g
Fl(v)967 4900 y Fr(1)1005 4888 y Fs(;)14 b Fl(v)1092
4900 y Fr(2)1129 4888 y Fs(;)g(:)g(:)g(:)g(;)g Fl(v)1364
4900 y Fq(d)1422 4888 y Fu(\372pln\354)20 b(lib)r(o)n(v)n(oln\354.)e
(Nyn\355)i(m)n(\371\276eme)-135 4988 y(ps\341t)27 b(i)h
Fs(M)177 5000 y Fq(k)240 4988 y Fu(=)23 b Fo(f)p Fl(v)420
5000 y Fr(1)457 4988 y Fs(;)14 b Fl(v)544 5000 y Fr(2)582
4988 y Fs(;)g(:)g(:)g(:)f(;)h Fl(v)816 5000 y Fq(k)857
4988 y Fo(g)p Fu(.)-11 5090 y(Odhadn\354me)25 b(d\351lku)g(v)n(ektoru)f
Fl(v)1019 5102 y Fr(1)1070 5090 y Fu(+)13 b Fl(v)1198
5102 y Fr(2)1250 5090 y Fu(+)g Fo(\001)h(\001)g(\001)f
Fu(+)g Fl(v)1566 5102 y Fq(k)1607 5090 y Fu(.)26 b(Pro)d
Fs(k)j Fo(\024)d Fs(d)i Fu(jist\354)h(nen\355)f(v\355c)-135
5189 y(ne\276)32 b Fs(d)p Fu(,)h(p)r(on\354v)n(ad\276)f
(s\350\355t\341me)g Fs(k)k Fu(v)n(ektor\371)31 b(d\351lky)i
(nejv\375\271)f(1.)g(Pro)g Fs(k)i(>)d(d)i Fu(je)g(hla)n(vn\355)-135
5289 y(trik)21 b(o)r(de\350\355st)h(o)r(d)g(uv)n(a\276o)n(v)n(an\351ho)
d(sou\350tu)j(v\375raz)1363 5227 y Fp(P)1451 5247 y Fq(k)1451
5314 y(i)p Fr(=1)1576 5289 y Fs(\013)1629 5301 y Fq(k)q(;)p
Fb(v)1731 5289 y Fl(v)q Fu(,)g(ro)n(vn)n(\375)e(0)i(p)r(o)r(dle)g
(\(iii\):)-6 5477 y Fo(k)p Fl(v)86 5489 y Fr(1)142 5477
y Fu(+)c Fo(\001)c(\001)g(\001)k Fu(+)g Fl(v)473 5489
y Fq(k)514 5477 y Fo(k)83 b Fu(=)f Fo(k)p Fu(\(1)18 b
Fo(\000)g Fs(\013)1056 5489 y Fq(k)q(;)p Fb(v)1152 5497
y Fn(1)1189 5477 y Fu(\))p Fl(v)1271 5489 y Fr(1)1327
5477 y Fu(+)g Fo(\001)c(\001)g(\001)19 b Fu(+)f(\(1)g
Fo(\000)g Fs(\013)1837 5489 y Fq(k)q(;)p Fb(v)1933 5498
y Fm(k)1974 5477 y Fu(\))p Fl(v)2056 5489 y Fq(k)2097
5477 y Fo(k)23 b(\024)639 5601 y(\024)82 b Fu(\(1)19
b Fo(\000)f Fs(\013)1015 5613 y Fq(k)q(;)p Fb(v)1111
5621 y Fn(1)1148 5601 y Fu(\))p Fo(k)p Fl(v)1272 5613
y Fr(1)1309 5601 y Fo(k)g Fu(+)g Fo(\001)c(\001)g(\001)k
Fu(+)g(\(1)g Fo(\000)h Fs(\013)1879 5613 y Fq(k)q(;)p
Fb(v)1975 5622 y Fm(k)2015 5601 y Fu(\))p Fo(k)p Fl(v)2139
5613 y Fq(k)2180 5601 y Fo(k)k(\024)639 5726 y(\024)82
b Fu(\(1)19 b Fo(\000)f Fs(\013)1015 5738 y Fq(k)q(;)p
Fb(v)1111 5746 y Fn(1)1148 5726 y Fu(\))g(+)g Fo(\001)c(\001)g(\001)19
b Fu(+)f(\(1)g Fo(\000)g Fs(\013)1708 5738 y Fq(k)q(;)p
Fb(v)1804 5747 y Fm(k)1845 5726 y Fu(\))23 b(=)639 5850
y(=)82 b Fs(k)22 b Fo(\000)c Fu(\()p Fs(\013)1019 5862
y Fq(k)q(;)p Fb(v)1115 5870 y Fn(1)1170 5850 y Fu(+)g
Fo(\001)c(\001)g(\001)19 b Fu(+)f Fs(\013)1505 5862 y
Fq(k)q(;)p Fb(v)1601 5871 y Fm(k)1641 5850 y Fu(\))24
b(=)e Fs(k)g Fo(\000)c Fu(\()p Fs(k)j Fo(\000)d Fs(d)p
Fu(\))24 b(=)e Fs(d:)-135 6038 y Fu(T\355m)28 b(je)g(d\371k)n(az)f(v)n
(\354t)n(y)f(hoto)n(v.)p eop end
PStoPSsaved restore
%%Page: (30,31) 16
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 850.393701 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 31 30 bop -182 1858 a Fu(31)1165 b Ft(Obsah)p
-182 1891 2629 4 v -182 2074 a Fl(P)m(ozn\341mk)m(a.)83
b Fu(Z)37 b(uv)n(eden\351ho)g(d\371k)n(azu)g(v)n(e)g(skute\350nosti)g
(plyne)h(ob)r(ecn\354j\271\355)g(tvr-)-182 2174 y(zen\355,)25
b(pro)g(lib)r(o)n(v)n(olnou)f(k)n(on)n(v)n(exn\355)f(ohr\341dku,)i
(nejen)g(pro)g(kruho)n(v)n(ou:)e(Je-li)i Fs(B)i Fo(\032)c
Fh(R)2408 2144 y Fq(d)-182 2274 y Fu(omezen\341)h(k)n(on)n(v)n(exn\355)
f(mno\276ina)h(obsah)n(uj\355c\355)g(p)r(o)r(\350\341tek,)h(a)f(je-li)h
(mno\276ina)f Fs(n)h Fu(v)n(ektor\371)-182 2373 y(spl\362)n
(uj\355c\355)32 b Fl(v)e Fo(2)f Fs(B)35 b Fu(pro)c(v\271ec)n(hna)f
Fl(v)g Fo(2)f Fs(M)40 b Fu(a)1235 2311 y Fp(P)1322 2398
y Fb(v)q Fk(2)p Fq(M)1495 2373 y Fs(v)32 b Fu(=)d(0,)h(p)r(otom)h
(existuje)h(p)r(o-)-182 2473 y(\370ad\355)e(\()p Fl(v)74
2485 y Fr(1)112 2473 y Fs(;)14 b Fl(v)199 2485 y Fr(2)236
2473 y Fs(;)g(:)g(:)g(:)g(;)g Fl(v)471 2485 y Fq(n)516
2473 y Fu(\))31 b(v)n(ektor\371)e(z)i Fs(M)9 b Fu(,)30
b(pro)f(n\354\276)i Fl(v)1446 2485 y Fr(1)1504 2473 y
Fu(+)19 b Fl(v)1638 2485 y Fr(2)1696 2473 y Fu(+)h Fo(\001)14
b(\001)g(\001)20 b Fu(+)g Fl(v)2033 2485 y Fq(k)2102
2473 y Fo(2)28 b Fs(dB)35 b Fu(pro)-182 2572 y Fs(k)43
b Fu(=)d(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)p
Fu(,)38 b(kde)g Fs(dB)45 b Fu(=)39 b Fo(f)p Fs(d)p Fl(x)i
Fu(:)54 b Fl(x)40 b Fo(2)h Fs(B)t Fo(g)p Fu(.)d(Je)f(za)5
b(j\355ma)n(v)n(\351,)36 b(\276e)i(tady)g(u\276)g(je)-182
2672 y(k)n(onstan)n(ta)28 b(\376nafoukn)n(ut\355\377)g
Fs(d)h Fu(nejlep\271\355)h(mo\276n\341)e(\(nap\370\355klad)h(v)g(ro)n
(vin\354)f(to)h(uk)n(azuje)-182 2772 y Fs(B)j Fu(zv)n(olen\351)27
b(jak)n(o)f(ro)n(vnostrann)n(\375)f(tro)5 b(j\372heln\355k)27
b(se)g(st\370edem)h(v)f(p)r(o)r(\350\341tku\).)-182 3063
y Fw(16)119 b(P)m(erfektn\355)39 b(p\341ro)m(v)m(\341n\355)i(a)f
(determinan)m(t)m(y)-182 3250 y Fl(P)m(\341ro)m(v)m(\341n\355)d
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Fs(F)48 b Fo(\022)34 b Fs(E)5 b Fu(\()p Fs(G)p Fu(\))36
b(tak)n(o)n(v)n(\341,)d(\276e)i(\276\341dn)n(\375)-182
3350 y(vrc)n(hol)26 b Fs(G)i Fu(nen\355)g(obsa\276en)f(v)n(e)g(v\355c)g
(ne\276)h(jedn\351)g(hran\354)f Fs(F)12 b Fu(.)678 4056
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@endspecial -182 4260 a Fl(P)m(erfektn\355)42 b(p\341ro)m(v)m
(\341n\355)37 b Fu(je)f(p\341ro)n(v)n(\341n\355)e(p)r(okr\375v)n(a)5
b(j\355c\355)33 b(v\271ec)n(hn)n(y)i(vrc)n(holy)-7 b(.)34
b(Na)5 b(jd\354te)-182 4359 y(n\354jak)n(\351)27 b(v)h(grafu)e(na)i
(obr\341zku!)-57 4462 y(Vysv)n(\354tl\355me)41 b(p)r(om\354rn\354)g
(jedno)r(duc)n(h)n(\375)h(algoritm)n(us)e(pro)h(testo)n(v)n(\341n\355,)
f(zda)h(m\341)-182 4562 y(dan)n(\375)30 b(graf)f(p)r(erfektn\355)h
(p\341ro)n(v)n(\341n\355.)e(Z\341kladn\355)h(p\370\355stup)h(je)h(p)r
(o)r(dobn)n(\375)e(jak)n(o)g(u)i(testo-)-182 4661 y(v)n(\341n\355)23
b(matico)n(v)n(\351ho)e(n\341sob)r(en\355)h(v)h(o)r(dd\355lu)h(6.)f
(Prob)r(ereme)e(p)r(ouze)i(bipartitn\355)h(p\370\355pad,)-182
4761 y(kter\375)j(je)h(jedno)r(du\271\271\355.)-57 4864
y(Uv)n(a\276me)52 b(bipartitn\355)h(graf)g Fs(G)p Fu(.)g(V)-7
b(rc)n(holy)52 b(jsou)h(rozd\354len)n(y)f(do)h(dv)n(ou)f(t\370\355d)
-182 4963 y Fo(f)p Fs(u)-92 4975 y Fr(1)-56 4963 y Fs(;)14
b(u)29 4975 y Fr(2)66 4963 y Fs(;)g(:)g(:)g(:)g(;)g(u)299
4975 y Fq(n)343 4963 y Fo(g)33 b Fu(a)g Fo(f)p Fs(v)575
4975 y Fr(1)612 4963 y Fs(;)14 b(v)689 4975 y Fr(2)726
4963 y Fs(;)g(:)g(:)g(:)g(;)g(v)951 4975 y Fq(n)996 4963
y Fo(g)33 b Fu(a)f(hran)n(y)g(jdou)i(jen)f(mezi)g(t\370\355dami,)g
(nikdy)-182 5063 y(uvnit\370)26 b(jedn\351)g(t\370\355dy)-7
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(\351,)f(proto\276e)g(jinak)g(bipar-)-182 5162 y(titn\355)k(graf)d(p)r
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(hran)g Fs(G)h Fu(ozna\350me)e Fs(m)p Fu(.)-57 5265 y(Nec)n(h)n(\273)36
b Fs(S)240 5277 y Fq(n)322 5265 y Fu(ozna\350uje)g(mno\276in)n(u)g
(v\271ec)n(h)g(p)r(erm)n(utac\355)g(mno\276in)n(y)g Fo(f)p
Fu(1)p Fs(;)14 b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(n)p Fo(g)p
Fu(.)-182 5365 y(Ka\276d\351)29 b(p)r(erfektn\355)i(p\341ro)n(v)n
(\341n\355)c(v)j Fs(G)g Fu(o)r(dp)r(o)n(v\355d\341)f(jednozna\350n\354)
h(p)r(erm)n(utaci)f Fs(\031)i Fo(2)c Fs(S)2378 5377 y
Fq(n)2423 5365 y Fu(.)-182 5464 y(M\371\276eme)19 b(jej)g(toti\276)f
(zapsat)g(v)n(e)g(tv)n(aru)f Fo(ff)p Fs(u)1120 5476 y
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y Fq(n)2135 5464 y Fs(;)g(v)2212 5479 y Fq(\031)r Fr(\()p
Fq(n)p Fr(\))2350 5464 y Fo(gg)p Fu(.)-57 5567 y(Existenci)29
b(p)r(erfektn\355ho)i(p\341ro)n(v)n(\341n\355)d(vyj\341d\370\355me)h(p)
r(omo)r(c\355)h(determinan)n(tu.)h(Pro)-182 5667 y(k)n(a\276dou)j(hran)
n(u)h Fo(f)p Fs(u)443 5679 y Fq(i)470 5667 y Fs(;)14
b(v)547 5679 y Fq(j)582 5667 y Fo(g)35 b(2)i Fs(E)5 b
Fu(\()p Fs(G)p Fu(\))36 b(za)n(v)n(edeme)f(jedn)n(u)h(prom\354nnou)e
Fs(x)2084 5679 y Fq(ij)2143 5667 y Fu(,)i(celk)n(em)-182
5766 y(tedy)28 b Fs(m)g Fu(prom\354nn)n(\375c)n(h,)e(a)h(de\014n)n
(ujeme)h(matici)g Fs(A)g Fu(t)n(ypu)g Fs(n)18 b Fo(\002)g
Fs(n)27 b Fu(n\341sledo)n(vn\354:)453 6000 y Fs(a)497
6012 y Fq(ij)578 6000 y Fu(=)652 5883 y Fp(\032)728 5950
y Fs(x)775 5962 y Fq(ij)917 5950 y Fu(jestli\276e)h Fo(f)p
Fs(u)1282 5962 y Fq(i)1309 5950 y Fs(;)14 b(v)1386 5962
y Fq(j)1421 5950 y Fo(g)23 b(2)g Fs(E)5 b Fu(\()p Fs(G)p
Fu(\))728 6049 y(0)147 b(jinak.)p eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 422.362205 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
TeXDict begin 32 31 bop 1031 1858 a Ft(Obsah)1165 b Fu(32)p
-135 1891 2629 4 v -135 2074 a(Determinan)n(t)24 b(matice)g
Fs(A)g Fu(je)g(mnoho)r(\350len)g(v)n(e)g(zm\355n\354n)n(\375c)n(h)f
Fs(m)h Fu(prom\354nn)n(\375c)n(h.)f(P)n(o)r(dle)-135
2174 y(de\014nice)28 b(determinan)n(tu)f(dostaneme)61
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2345 y Fr(2)p Fq(;\031)r Fr(\(2\))1500 2330 y Fo(\001)14
b(\001)g(\001)g Fs(a)1655 2345 y Fq(n;\031)r Fr(\()p
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Fs(x)2075 2582 y Fq(n;\031)r Fr(\()p Fq(n)p Fr(\))2274
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Fs(x)678 3301 y Fr(2)p Fq(;\031)r Fr(\(2\))876 3286 y
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Fs(i)g Fu(tak)n(o)n(v)n(\351,)d(\276e)j Fs(\033)s Fu(\()p
Fs(i)p Fu(\))d Fo(6)p Fu(=)e Fs(\031)s Fu(\()p Fs(i)p
Fu(\),)30 b(tak\276e)e Fs(x)1581 3401 y Fq(i;\033)r Fr(\()p
Fq(i)p Fr(\))1770 3386 y Fu(=)c(0,)29 b(a)f(tedy)h(v\271ec)n(hn)n(y)
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Fs(A)p Fu(\))h(jsou)g(n)n(ulo)n(v)n(\351.)e(Pro)g(takto)h(zv)n
(olen\341)f Fs(x)1950 3497 y Fq(ij)2046 3485 y Fu(proto)g(m\341me)-135
3585 y(det\()p Fs(A)p Fu(\))24 b(=)f Fo(\006)p Fu(1.)g(Uk)n(\341zali)h
(jsme,)h(\276e)f(det\()p Fs(A)p Fu(\))k Fj(je)g(nenulov\375)f
(mnoho\350len,)h(pr)l(\341v\354)g(kdy\276)-135 3684 y(m\341)i
Fs(G)g Fj(perfektn\355)h(p\341r)l(ov\341n\355.)-11 3784
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(olit)g(mnoho)r(\350len)g(explicitn\354)h(sp)r(o)r(\350\355tat,)g
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Fs(G)p Fu(,)g(a)g(to)g(m)n(\371\276e)g(b)n(\375t)g(exp)r
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Fq(ij)1680 4083 y Fu(n\354jak)n(\341)f(k)n(onkr\351tn\355)g
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Fs(A)p Fu(\))h(snadno)e(vy\350\355slit,)h(proto\276e)f(pak)h(m\341me)g
(co)g(\350init)g(s)g(de-)-135 4282 y(terminan)n(tem)30
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b(si)h(tedy)f(m)n(yslet,)g(\276e)h(m\341me)f(mnoho)r(\350len)g(v)g
Fs(m)g Fu(prom\354nn)n(\375c)n(h)g(stupn\354)-135 4481
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n(\375t)h(jisti,)-135 4780 y(\276e)24 b(je)h(iden)n(tic)n(ky)g(0,)f(p)r
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(p)r(o)r(divuho)r(dnou)h(vlastnost:)f(Je)h(bu\357)-135
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Fi(Bu\357)g Fh(K)f Fi(lib)r(o)n(v)n(oln\351)g(t\354leso)g(a)g
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y(ne\350n\341)26 b(p)r(o)r(dmno\276ina.)h(P)n(otom)e(pro)h(k)n
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5497 y Fs(;)14 b(r)837 5509 y Fr(2)874 5497 y Fs(;)g(:)g(:)g(:)g(;)g(r)
1096 5509 y Fq(m)1196 5497 y Fo(2)36 b Fs(S)5 b Fi(,)36
b(pro)f(n\354\276)g Fs(p)p Fu(\()p Fs(r)1824 5509 y Fr(1)1862
5497 y Fs(;)14 b(r)1936 5509 y Fr(2)1974 5497 y Fs(;)g(:)g(:)g(:)f(;)h
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5597 y(nanejv\375\271)j Fs(d)p Fo(j)p Fs(S)5 b Fo(j)366
5567 y Fq(m)p Fk(\000)p Fr(1)515 5597 y Fi(.)40 b(Jinak)f
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y Fr(2)2000 5697 y Fs(;)g(:)g(:)g(:)g(;)g(r)2222 5709
y Fq(m)2285 5697 y Fu(\))24 b(=)e(0)p Fi(,)-135 5796
y(je)28 b(maxim\341ln\354)411 5764 y Fq(d)p 387 5778
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b(enhle)25 b(Sc)n(h)n(w)n(artz)i(je)d(opra)n(vdu)i(s)e(t,)h
(narozd\355l)g(o)r(d)g(toho)h(z)f(Cauc)n(h)n(yho-Sc)n(h)n(w)n(arzo)n
(vy)j(nero)n(v-)-135 6038 y(nosti.)p eop end
PStoPSsaved restore
%%Page: (32,33) 17
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 0.000000 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 33 32 bop -182 1858 a Fu(33)1165 b Ft(Obsah)p
-182 1891 2629 4 v -57 2074 a Fu(Ne\276)31 b(v)n(\354tu)h(dok)n
(\341\276eme,)e(vr\341t\355me)h(se)g(k)g(bipartitn\355m)n(u)h(p\341ro)n
(v)n(\341n\355.)d(P\370edp)r(okl\341-)-182 2174 y(dejme,)k(\276e)f
Fs(G)h Fu(m\341)f(p)r(erfektn\355)g(p\341ro)n(v)n(\341n\355,)e(a)i
(tud\355\276)h(det\()p Fs(A)p Fu(\))g(je)g(nen)n(ulo)n(v\375)e(mnoho-)
-182 2274 y(\350len.)37 b(Sc)n(h)n(w)n(artzo)n(v)n(a-Zipp)r(elo)n(v)n
(a)31 b(v)n(\354ta)36 b(uk)n(azuje,)g(\276e)h(vyp)r(o)r
(\350\355t\341me-li)f(det\()p Fs(A)p Fu(\))i(pro)-182
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n(visle)f(z)i(mno\276in)n(y)e Fs(S)43 b Fu(=)-182 2473
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y Fu(.)-57 2698 y(Ab)n(yc)n(hom)20 b(zjistili,)h(jestli)h(determinan)n
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g(v)n(elk\375mi)g(\350\355sly)g(jsou)-182 2996 y(\350aso)n(v)n(\354)f
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y(jsou)39 b(aritmetic)n(k)n(\351)e(op)r(erace)h(ryc)n(hl\351)f(\(je)j
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3495 y(tabulku)28 b(in)n(v)n(erzn\355c)n(h)e(prvk\371\).)-57
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3819 y(partitn\355)k(graf)g(p)r(erfektn\355)g(p\341ro)n(v)n(\341n\355,)
e(kter\375)i(b)r(\354\276\355)h(v)f(\350ase)f Fs(O)r
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(pak)g(dostaneme)g(asympto-)-182 4217 y(tic)n(ky)24 b(nejryc)n
(hlej\271\355)f(zn\341m)n(\375)g(algoritm)n(us)f(na)i(testo)n(v)n
(\341n\355)e(bipartitn\355ho)i(p)r(erfektn\355ho)-182
4317 y(p\341ro)n(v)n(\341n\355,)h(s)j(dob)r(ou)f(b)r(\354h)n(u)h
Fs(O)r Fu(\()p Fs(n)842 4287 y Fr(2)p Fq(:)p Fr(376)999
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g(je)f(zn\341m)h(deterministic)n(k\375)f(algoritm)n(us,)f(kter\375)-182
4542 y(\(v\276dy\))e(na)5 b(jde)33 b(maxim\341ln\355)f(p\341ro)n(v)n
(\341n\355)f(v)i(\350ase)f Fs(O)r Fu(\()p Fs(n)1484 4512
y Fr(2)p Fq(:)p Fr(5)1575 4542 y Fu(\),)i(a)f(ten)g(je)h(v)f(praxi)f(p)
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(algoritm)n(us,)g(o)h(n\354m\276)g(jsme)h(mluvili)g(zde,)f(sice)g
(um\355)h(p)r(o-)-182 4741 y(znat,)h(jestli)h(p)r(erfektn\355)g
(p\341ro)n(v)n(\341n\355)d(existuje,)i(ale)g(\276\341dn\351)g(nena)5
b(jde)29 b(\(existuj\355)h(slo\276i-)-182 4841 y(t\354j\271\355)c(v)n
(arian)n(t)n(y)-7 b(,)23 b(kter\351)h(je)i(i)f(na)5 b(jdou\).)25
b(Na)g(druh\351)g(stran\354)f(se)h(probran)n(\375)e(algoritm)n(us)-182
4940 y(d\341)32 b(efektivn\354)h(implemen)n(to)n(v)n(at)f(na)g
(paraleln\355m)f(p)r(o)r(\350\355ta\350i)i(tak,)f(\276e)h(s)f
(dostate\350n\354)-182 5040 y(mnoha)f(pro)r(cesory)f(b)r(\354\276\355)i
(v)n(e)f(v)n(elmi)g(kr\341tk)n(\351m)g(\350ase.)g(\256\341dn)n(\375)f
(jin)n(\375)i(p\370\355stup,)g(kter\375)-182 5140 y(b)n(y)27
b(d\341)n(v)n(al)g(sro)n(vnateln\354)e(ryc)n(hl\351)i(paraleln\355)g
(algoritm)n(y)-7 b(,)26 b(zn\341m)h(nen\355.)-182 5315
y Fl(D\371k)m(az)g(Sc)m(h)m(w)m(artzo)m(vy-Zipp)s(elo)m(vy)h(v)m(\354t)
m(y)-8 b(.)48 b Fu(P)n(ostupujeme)21 b(induk)n(c\355)h(p)r(o)r(dle)g(p)
r(o-)-182 5415 y(\350tu)32 b(prom\354nn)n(\375c)n(h)f
Fs(m)p Fu(.)h(P\370\355pad)f Fs(m)f Fu(=)f(1)j(je)g(zn\341m\341)f(v)n
(\354ta)g(z)h(algebry:)f(Mnoho)r(\350len)-182 5514 y
Fs(p)p Fu(\()p Fs(x)p Fu(\))g(stupn\354)e Fs(d)h Fu(v)g(jedn\351)g
(prom\354nn\351)f(m\341)g(nanejv\375\271)g Fs(d)h Fu(k)n(o\370en)n
(\371.)e(\(Dok)n(azuje)h(se)g(to)-182 5614 y(induk)n(c\355)24
b(p)r(o)r(dle)g Fs(d)p Fu(:)g(Je-li)f Fs(p)p Fu(\()p
Fs(\013)p Fu(\))h(=)e(0,)i(p)r(otom)f Fs(p)p Fu(\()p
Fs(x)p Fu(\))i(m)n(\371\276eme)f(vyd\354lit)f Fs(x)11
b Fo(\000)g Fs(\013)24 b Fu(a)f(sn\355\276it)-182 5714
y(stup)r(e\362.\))-57 5839 y(Bu\357)35 b Fs(m)g(>)g Fu(1)g(a)g
(p\370edp)r(okl\341dejme,)f(\276e)h(se)g(prom\354nn\341)f
Fs(x)1779 5851 y Fr(1)1852 5839 y Fu(vyskytuje)h(asp)r(o\362)-182
5938 y(v)20 b(jednom)g(\350len)n(u)f Fs(p)p Fu(\()p Fs(x)494
5950 y Fr(1)532 5938 y Fs(;)14 b(:)g(:)g(:)g(;)g(x)764
5950 y Fq(m)827 5938 y Fu(\))20 b(\(kdy\276)g(ne,)g(prom\354nn\351)f
(vho)r(dn\354)h(p\370ejmen)n(ujeme\).)-182 6038 y(Pi\271me)30
b Fs(p)p Fu(\()p Fs(x)188 6050 y Fr(1)226 6038 y Fs(;)14
b(:)g(:)g(:)f(;)h(x)457 6050 y Fq(m)521 6038 y Fu(\))31
b(jak)n(o)e(mnoho)r(\350len)h(v)h(prom\354nn\351)f Fs(x)1692
6050 y Fr(1)1729 6038 y Fu(,)h(p\370i\350em\276)f(k)n(a\276d\375)f(k)n
(o-)p eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
592.440945 428.031496 translate
90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
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-135 1891 2629 4 v -135 2074 a(e\014cien)n(t)28 b(je)f(mnoho)r(\350len)
h(v)f(prom\354nn)n(\375c)n(h)g Fs(x)1243 2086 y Fr(2)1280
2074 y Fs(;)14 b(:)g(:)g(:)g(;)g(x)1512 2086 y Fq(m)1575
2074 y Fu(:)442 2334 y Fs(p)p Fu(\()p Fs(x)563 2346 y
Fr(1)601 2334 y Fs(;)g(x)685 2346 y Fr(2)722 2334 y Fs(;)g(:)g(:)g(:)g
(;)g(x)954 2346 y Fq(m)1017 2334 y Fu(\))24 b(=)1202
2230 y Fq(k)1160 2255 y Fp(X)1167 2432 y Fq(i)p Fr(=0)1294
2334 y Fs(x)1341 2300 y Fq(i)1341 2355 y Fr(1)1379 2334
y Fs(p)1421 2346 y Fq(i)1448 2334 y Fu(\()p Fs(x)1527
2346 y Fr(2)1565 2334 y Fs(;)14 b(:)g(:)g(:)g(;)g(x)1797
2346 y Fq(m)1860 2334 y Fu(\))p Fs(;)-135 2594 y Fu(kde)27
b Fs(k)k Fu(je)d(nejvy\271\271\355)f(mo)r(cnina)g Fs(x)876
2606 y Fr(1)942 2594 y Fu(vyskytuj\355c\355)g(se)h(v)f
Fs(p)p Fu(\()p Fs(x)1654 2606 y Fr(1)1692 2594 y Fs(;)14
b(:)g(:)g(:)g(;)g(x)1924 2606 y Fq(n)1969 2594 y Fu(\).)-11
2694 y(Rozd\354l\355me)30 b Fs(m)p Fu(-tice)f(\()p Fs(r)722
2706 y Fr(1)760 2694 y Fs(;)14 b(r)834 2706 y Fr(2)871
2694 y Fs(;)g(:)g(:)g(:)g(;)g(r)1093 2706 y Fq(m)1156
2694 y Fu(\))30 b(spl\362)n(uj\355c\355)f Fs(p)p Fu(\()p
Fs(r)1658 2706 y Fr(1)1696 2694 y Fs(;)14 b(:)g(:)g(:)g(;)g(r)1918
2706 y Fq(m)1981 2694 y Fu(\))26 b(=)g(0)j(do)g(dv)n(ou)-135
2793 y(skupin.)18 b(V)h(prvn\355)f(skupin\354,)h(ji\276)g
(ozna\350\355me)f Fs(R)1270 2805 y Fr(1)1307 2793 y Fu(,)g(jsou)h(t)n
(y)-7 b(,)18 b(pro)g(n\354\276)g Fs(p)1940 2805 y Fq(k)1981
2793 y Fu(\()p Fs(r)2050 2805 y Fr(2)2088 2793 y Fs(;)c(:)g(:)g(:)g(;)g
(r)2310 2805 y Fq(m)2373 2793 y Fu(\))23 b(=)-135 2893
y(0.)35 b(P)n(on\354v)n(ad\276)e(mnoho)r(\350len)i Fs(p)812
2905 y Fq(k)852 2893 y Fu(\()p Fs(x)931 2905 y Fr(2)969
2893 y Fs(;)14 b(:)g(:)g(:)g(;)g(x)1201 2905 y Fq(m)1264
2893 y Fu(\))36 b(je)f(nen)n(ulo)n(v\375)f(a)h(m\341)g(stup)r(e\362)h
(maxi-)-135 2993 y(m\341ln\354)22 b Fs(d)8 b Fo(\000)g
Fs(k)s Fu(,)23 b(p)r(o)r(dle)g(induk)n(\350n\355ho)f(p\370edp)r(okladu)
g(m\341me)h(pro)e(\()p Fs(r)1886 3005 y Fr(2)1924 2993
y Fs(;)14 b(:)g(:)g(:)g(;)g(r)2146 3005 y Fq(m)2209 2993
y Fu(\))23 b(nejv\375\271)-135 3092 y(\()p Fs(d)c Fo(\000)f
Fs(k)s Fu(\))p Fo(j)p Fs(S)5 b Fo(j)222 3062 y Fq(m)p
Fk(\000)p Fr(2)398 3092 y Fu(mo\276nost\355,)27 b(a)g(proto)f
Fo(j)p Fs(R)1148 3104 y Fr(1)1186 3092 y Fo(j)d(\024)f
Fu(\()p Fs(d)d Fo(\000)f Fs(k)s Fu(\))p Fo(j)p Fs(S)5
b Fo(j)1676 3062 y Fq(m)p Fk(\000)p Fr(1)1824 3092 y
Fu(.)-11 3192 y(V)-7 b(e)101 b(druh\351)g(skupin\354)g
Fs(R)930 3204 y Fr(2)1068 3192 y Fu(jsou)g(zb)n(\375v)n(a)5
b(j\355c\355)99 b Fs(m)p Fu(-tice,)i(pro)f(kter\351)-135
3291 y Fs(p)p Fu(\()p Fs(r)-24 3303 y Fr(1)14 3291 y
Fs(;)14 b(r)88 3303 y Fr(2)125 3291 y Fs(;)g(:)g(:)g(:)g(;)g(r)347
3303 y Fq(m)410 3291 y Fu(\))66 b(=)e(0,)53 b(ale)f Fs(p)951
3303 y Fq(k)992 3291 y Fu(\()p Fs(r)1061 3303 y Fr(2)1099
3291 y Fs(;)14 b(:)g(:)g(:)g(;)g(r)1321 3303 y Fq(m)1384
3291 y Fu(\))65 b Fo(6)p Fu(=)g(0.)53 b(Jejic)n(h)f(p)r(o)r(\350et)i(o)
r(dhad-)-135 3391 y(neme)c(takto:)f(ho)r(dnot)n(y)h Fs(r)753
3403 y Fr(2)840 3391 y Fu(a\276)f Fs(r)1005 3403 y Fq(m)1119
3391 y Fu(lze)g(zv)n(olit)h(nejv\375\271)f Fo(j)p Fs(S)5
b Fo(j)1894 3361 y Fq(m)p Fk(\000)p Fr(1)2092 3391 y
Fu(zp)r(\371sob)n(y)-7 b(,)49 b(a)-135 3491 y(jsou-li)33
b Fs(r)155 3503 y Fr(2)193 3491 y Fs(;)14 b(:)g(:)g(:)f(;)h(r)414
3503 y Fq(m)511 3491 y Fu(ji\276)34 b(zv)n(olen)n(y)f(tak,)g(\276e)g
Fs(p)1255 3503 y Fq(k)1296 3491 y Fu(\()p Fs(r)1365 3503
y Fr(2)1403 3491 y Fs(;)14 b(:)g(:)g(:)g(;)g(r)1625 3503
y Fq(m)1688 3491 y Fu(\))33 b Fo(6)p Fu(=)g(0,)g(p)r(otom)h
Fs(r)2253 3503 y Fr(1)2324 3491 y Fu(m)n(us\355)-135
3590 y(b)n(\375t)44 b(k)n(o\370enem)g(mnoho)r(\350len)n(u)g
Fs(q)s Fu(\()p Fs(x)976 3602 y Fr(1)1014 3590 y Fu(\))52
b(=)e Fs(p)p Fu(\()p Fs(x)1334 3602 y Fr(1)1372 3590
y Fs(;)14 b(r)1446 3602 y Fr(2)1484 3590 y Fs(;)g(:)g(:)g(:)f(;)h(r)
1705 3602 y Fq(n)1751 3590 y Fu(\).)45 b(T)-7 b(en)n(to)44
b(mnoho)r(\350len)-135 3690 y(v)26 b(jedn\351)i(prom\354nn\351)e(m\341)
g(stup)r(e\362)i(p\370esn\354)e Fs(k)s Fu(,)g(tud\355\276)i(m\341)e
(nejv\375\271)h Fs(k)i Fu(k)n(o\370en)n(\371,)d(a)g(tedy)-135
3790 y Fo(j)p Fs(R)-49 3802 y Fr(2)-12 3790 y Fo(j)41
b(\024)g Fs(k)s Fo(j)p Fs(S)5 b Fo(j)306 3759 y Fq(m)p
Fk(\000)p Fr(1)454 3790 y Fu(.)38 b(V)-7 b(elik)n(ost)38
b(ob)r(ou)g(skupin)h(dohromady)e(tedy)h(nen\355)h(v)n(\354t\271\355)f
(ne\276)-135 3889 y Fs(d)p Fo(j)p Fs(S)5 b Fo(j)10 3859
y Fq(m)p Fk(\000)p Fr(1)158 3889 y Fu(,)28 b(a)f(t\355m)h(je)g(Sc)n(h)n
(w)n(artzo)n(v)n(a-Zipp)r(elo)n(v)n(a)23 b(v)n(\354ta)j(dok)n
(\341z\341na.)-135 4164 y Fw(Dal\271\355)40 b(\350ten\355)-135
4346 y Fu(Vynik)n(a)5 b(j\355c\355)34 b(u\350ebnici)g(o)g
(line\341rn\354)f(algebraic)n(k\375c)n(h)f(meto)r(d\341c)n(h)i(v)g(k)n
(om)n(binatorice)-135 4445 y(napsali)27 b(Babai)h(a)g(F)-7
b(rankl)27 b([BF92].)h(Do)r(dnes)h(o\014ci\341ln\354)e(nevy\271la)h(a)g
(je)g(\(nesnadno\))-135 4545 y(dostupn\341)e(jak)n(o)f(skripta)h(c)n
(hicagsk)n(\351)e(univ)n(ersit)n(y)-7 b(.)26 b(Je)g(v)g(n\355)h
(l\341tk)n(a)e(sek)n(c\355)h(3,)g(7)g(a)g(10)f(a)-135
4645 y(mnoho)d(dal\271\355ho)g(materi\341lu)g(v)h(p)r(o)r(dobn\351m)g
(duc)n(h)n(u,)g(jak)n(o\276)f(i)h(p)r(\354kn)n(\375)f(v\375klad)g
(n\354kte-)-135 4744 y(r\375c)n(h)j(parti\355)h(line\341rn\355)g
(algebry)-7 b(.)25 b(O)h(algebraic)n(k)n(\351)d(teorii)j(graf\371)f(p)r
(o)5 b(jedn\341)n(v)n(a)g(j\355)25 b(nap\370\355-)-135
4844 y(klad)20 b(kn\355\276ky)h(Biggs)e([Big93)o(])i(a)f(Go)r(dsil)h(a)
f(Ro)n(yle)g([GR01)o(].)h(V)g(p)r(osledn\354)g(jmeno)n(v)n(an\351)-135
4943 y(se)32 b(na)5 b(jdou)32 b(v\375sledky)f(sek)n(c\355)g(13)h(a)f
(8.)h(Pra)n(vd\354p)r(o)r(dobnostn\355)f(algoritm)n(y)f(v)i(duc)n(h)n
(u)-135 5043 y(o)r(dd\355l\371)38 b(6)g(a)g(16)f(jsou)h(p)r(\354kn\354)
h(vysv)n(\354tlen)n(y)e(v)h(knize)g(Mot)n(w)n(aniho)f(a)h(Ragha)n(v)n
(ana)-135 5143 y([MR95)o(].)33 b(V)g(\350esk)n(\351m)f(textu)h
(Matou\271ek)e(a)h(Ne\271et\370il)h([MN03)o(])g(je)g(aplik)n(ac\355m)e
(line-)-135 5242 y(\341rn\355)25 b(algebry)f(v)i(k)n(om)n(binatorice)e
(v)n(\354no)n(v)n(\341na)f(k)n(apitola)h(11,)h(a)h(dal\271\355)f(p)r
(\354kn\341)h(p)r(ou\276it\355)-135 5342 y(jsou)h(v)h(sek)n(c\355c)n(h)
e(7.5)h(a)g(8.2.)p eop end
PStoPSsaved restore
%%Page: (34,35) 18
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 850.393701 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
/showpage{}def/copypage{}def/erasepage{}def
PStoPSxform concat
TeXDict begin 35 34 bop -182 2697 a Fx(Literatura)-182
3129 y Fu([BF92])51 b(L.)29 b(Babai)f(and)h(P)n(.)f(F)-7
b(rankl.)40 b Fj(Line)l(ar)31 b(A)n(lgebr)l(a)h(Methods)g(in)f
(Combinato-)112 3228 y(rics)h(\(Pr)l(eliminary)h(version)g(2\))p
Fu(.)43 b(Departmen)n(t)29 b(of)h(Computer)f(Science,)112
3328 y(The)f(Univ)n(ersit)n(y)e(of)i(Chicago,)e(1992.)-182
3494 y([Big93])40 b(N.)k(Biggs.)84 b Fj(A)n(lgebr)l(aic)45
b(Gr)l(aph)h(The)l(ory)p Fu(.)86 b(Cam)n(bridge)43 b(Univ.)h(Press,)112
3594 y(Cam)n(bridge,)26 b(1993.)35 b(2nd)28 b(edition.)-182
3760 y([GR01])41 b(C.)27 b(Go)r(dsil)f(and)h(G.)g(Ro)n(yle.)f
Fj(A)n(lgebr)l(aic)k(Gr)l(aph)g(The)l(ory.)e Fu(Springer,)e(New)112
3859 y(Y)-7 b(ork,)27 b(NY)h(2001.)-182 4025 y([MN03])41
b(J.)29 b(Matou\271ek)g(a)g(J.)g(Ne\271et\370il.)h Fj(Kapitoly)j(z)e
(diskr)l(\351tn\355)h(matematiky)p Fu(.)f(Na-)112 4125
y(kladatelstv\355)c(Karolin)n(um,)f(Praha,)g(opra)n(v)n(en)n(\375)f
(dotisk)i(2.)h(vyd\341n\355,)f(2003.)-182 4291 y([MR95])41
b(R.)80 b(Mot)n(w)n(ani)f(and)g(P)n(.)g(Ragha)n(v)n(an.)f
Fj(R)l(andomize)l(d)g(A)n(lgorithms)p Fu(.)112 4391 y(Cam)n(bridge)26
b(Univ)n(ersit)n(y)h(Press,)f(Cam)n(bridge,)h(1995.)p
eop end
PStoPSsaved restore
userdict/PStoPSsaved save put
PStoPSmatrix setmatrix
2.834646 422.362205 translate
-90 rotate
1.000000 dup scale
userdict/PStoPSmatrix matrix currentmatrix put
userdict/PStoPSclip{0 0 moveto
595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto
closepath}put initclip
PStoPSxform concat
showpage
PStoPSsaved restore
%%Trailer
userdict /end-hook known{end-hook}if
%%EOF