From: Martin Mares <mj@ucw.cz>
Date: Thu, 18 Oct 2007 11:06:31 +0000 (+0200)
Subject: Prvni verze druhe prednasky.
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=81383c3b1ab213e35aaaf31e18368dde88b75656;p=ads2.git

Prvni verze druhe prednasky.
---

81383c3b1ab213e35aaaf31e18368dde88b75656
diff --git a/0-demo/0-demo.tex b/0-demo/0-demo.tex
new file mode 100644
index 0000000..bc5d7b7
--- /dev/null
+++ b/0-demo/0-demo.tex
@@ -0,0 +1,37 @@
+\input ../lecnotes.tex
+
+\prednaska{0}{Ukázka pou¾ití maker}{(zapsal Martin Mare¹)}
+
+% Takhle vypadá nadpis
+\h{Pøedposlední kapitola}
+
+% \> zaøídí, aby se odstavec neodsadil. Pomocí \I se sází kurzíva, \foot vyrobí poznámku pod èarou.
+\>Je svaèveèer. {\I Lysperní jezeleni} se vírnì vrtáèejí v~mokøavì.\foot{Viz Lewis Caroll: Jabberwocky.}
+
+\itemize\ibull
+\:Takhle.
+\:Vypadají.
+\:Odrá¾ky.
+\endlist
+
+\h{Druhá kapitola}
+
+\s{Vìta:} Paøez není strom.
+
+\proof
+Strom je speciálním pøípadem lesa. Les je (podle definice) graf bez kru¾nic.
+Paøez obsahuje alespoò jednu kru¾nici. Proto paøez nemù¾e být les, a~tedy ani
+strom.
+\qed
+
+\s{Algoritmus:} (tøídìní posloupnosti $a_1,\ldots,a_n$ pomocí {\sc Stupidsort}u)
+
+\algo
+\:$\pi \leftarrow \hbox{identická permutace na~mno¾inì $\{1,\ldots,n\}$}$.
+\:Opakuj:
+\::Ovìø, zda je posloupnost $a_{\pi(1)},a_{\pi(2)},\ldots,a_{\pi(n)}$ uspoøádána vzestupnì.
+   Pokud je, vra» ji jako výsledek.
+\::Nahraï $\pi$ jejím lexikografickým následníkem.
+\endalgo
+
+\bye
diff --git a/0-demo/Makefile b/0-demo/Makefile
new file mode 100644
index 0000000..98def69
--- /dev/null
+++ b/0-demo/Makefile
@@ -0,0 +1,3 @@
+P=0-demo
+
+include ../Makerules
diff --git a/2-toky/2-toky.dvi b/2-toky/2-toky.dvi
new file mode 100644
index 0000000..5896dcb
Binary files /dev/null and b/2-toky/2-toky.dvi differ
diff --git a/2-toky/2-toky.log b/2-toky/2-toky.log
new file mode 100644
index 0000000..80898a5
--- /dev/null
+++ b/2-toky/2-toky.log
@@ -0,0 +1,32 @@
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+**2-toky.tex
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+(../mjmac.tex
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new file mode 100644
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%!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
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+%%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
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+/isFixedPitch false def
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+/XHeight 431 def
+/Ascender 694 def
+/Descender -194 def
+/CapHeight 683 def
+end readonly def
+/FontName /cssl10 def
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+dup 58 /colon put
+dup 68 /D put
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+dup 101 /e put
+dup 105 /i put
+dup 107 /k put
+dup 110 /n put
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+dup 117 /u put
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+readonly def
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+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox [-65 -250 1123 857] readonly def
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+currentdict end
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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
+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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+%%CreationDate: 1991 Aug 15 07:21:52
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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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 12 /fi put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 58 /colon put
+dup 65 /A put
+dup 68 /D put
+dup 70 /F put
+dup 72 /H put
+dup 76 /L put
+dup 80 /P put
+dup 82 /R put
+dup 86 /V put
+dup 97 /a put
+dup 99 /c put
+dup 100 /d put
+dup 101 /e put
+dup 103 /g put
+dup 104 /h put
+dup 105 /i put
+dup 107 /k put
+dup 108 /l put
+dup 109 /m put
+dup 110 /n put
+dup 111 /o put
+dup 114 /r put
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+dup 116 /t put
+dup 117 /u put
+dup 118 /v put
+dup 122 /z put
+dup 225 /aacute put
+dup 236 /ecaron put
+dup 237 /iacute put
+dup 249 /uring 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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+%%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
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+/isFixedPitch false def
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+/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 11 /ff put
+dup 12 /fi put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 43 /plus put
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+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 58 /colon put
+dup 59 /semicolon put
+dup 61 /equal put
+dup 63 /question put
+dup 65 /A put
+dup 66 /B put
+dup 68 /D put
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+dup 187 /tcaron put
+dup 190 /zcaron put
+dup 200 /Ccaron put
+dup 216 /Rcaron put
+dup 225 /aacute put
+dup 232 /ccaron put
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+dup 236 /ecaron put
+dup 237 /iacute put
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+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
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%%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
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+/XHeight 444 def
+/Ascender 694 def
+/Descender -194 def
+/CapHeight 686 def
+end readonly def
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+dup 46 /period put
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+dup 250 /uacute put
+readonly def
+/PaintType 0 def
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+/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: 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 46 /period put
+dup 67 /C put
+dup 74 /J put
+dup 75 /K put
+dup 77 /M put
+dup 83 /S put
+dup 84 /T put
+dup 86 /V put
+dup 97 /a put
+dup 99 /c put
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+dup 115 /s put
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+dup 121 /y put
+dup 122 /z put
+dup 185 /scaron put
+dup 187 /tcaron put
+dup 216 /Rcaron put
+dup 225 /aacute put
+dup 237 /iacute put
+dup 248 /rcaron 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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+ipeMakeFont
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+%%CreationDate: 1991 Aug 20 16:38:05
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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+  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
+  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef ]
+ipeMakeFont
+%%BeginResource: font QWRSTQ+CMMI12
+%!PS-AdobeFont-1.1: CMMI12 1.100
+%%CreationDate: 1996 Jul 27 08:57:55
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+end readonly def
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+%%BeginResource: procset ipe 6.0 60027
+/ipe 40 dict def ipe begin
+/np { newpath } def
+/m { moveto } def
+/l { lineto } def
+/c { curveto } def
+/h { closepath } def
+/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
+      neg 0 rlineto closepath } def
+/d { setdash } def
+/w { setlinewidth } def
+/J { setlinecap } def
+/j { setlinejoin } def
+/cm { [ 7 1 roll ] concat } def
+/q { gsave } def
+/Q { grestore } def
+/g { setgray } def
+/G { setgray } def
+/rg { setrgbcolor } def
+/RG { setrgbcolor } def
+/S { stroke } def
+/f* { eofill } def
+/f { fill } def
+/ipeMakeFont {
+  exch findfont
+  dup length dict begin
+    { 1 index /FID ne { def } { pop pop } ifelse } forall
+    /Encoding exch def
+    currentdict
+  end
+  definefont pop
+} def
+/ipeFontSize 0 def
+/Tf { dup /ipeFontSize exch store selectfont } def
+/Td { translate } def
+/BT { gsave } def
+/ET { grestore } def
+/TJ { 0 0 moveto { dup type /stringtype eq
+ { show } { ipeFontSize mul -0.001 mul 0 rmoveto } ifelse
+} forall } def
+end
+%%EndResource
+%%EndProlog
+%%BeginSetup
+ipe begin
+%%BeginResource: font VIAERT+CMR12
+%!PS-AdobeFont-1.1: CMR12 1.0
+%%CreationDate: 1991 Aug 20 16:38:05
+% 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 (CMR12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /VIAERT+CMR12 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 19 /acute put
+dup 20 /caron put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 65 /A put
+dup 82 /R put
+dup 83 /S put
+dup 86 /V put
+dup 97 /a put
+dup 100 /d put
+dup 101 /e put
+dup 104 /h put
+dup 108 /l put
+dup 110 /n put
+dup 114 /r put
+dup 115 /s put
+dup 121 /y put
+dup 122 /z put
+readonly def
+/FontBBox{-34 -251 988 750}readonly def
+currentdict end
+currentfile eexec
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+%%EndResource
+/F15 /VIAERT+CMR12
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+  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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+  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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+  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
+  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef ]
+ipeMakeFont
+%%BeginResource: font JZCSOB+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 /JZCSOB+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 110 /backslash put
+readonly def
+/FontBBox{-29 -960 1116 775}readonly def
+currentdict end
+currentfile eexec
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+%%EndResource
+/F17 /JZCSOB+CMSY10
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+ @endspecial -49 3945 a(P\370\355klad)f(s\355t\354.)i(Kolik)e(krok\371)
+h(m)n(us\355)g(maxim\341ln\354)g(ud\354lat)h(F)-5 b(.F)g(.)29
+b(algoritm)n(us?)1127 4241 y(5)p eop end
+%%Trailer
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diff --git a/2-toky/2-toky.tex b/2-toky/2-toky.tex
new file mode 100644
index 0000000..0c442bd
--- /dev/null
+++ b/2-toky/2-toky.tex
@@ -0,0 +1,136 @@
+\input ../lecnotes.tex
+
+\def\og{$\buildrel \rightarrow \over G$}
+\def\ogm{\buildrel \rightarrow \over G}
+
+\prednaska{2}{Toky v sítích}{(pøedná¹el T. Valla, zapsali K. Vandas a J. Machálek)}
+
+\h{Motivaèní úlohy:}
+\itemize\ibull
+\:Mìjme orientovaný graf se speciálními vrcholy ®elivka a Kanál pøedstavující pra¾ské vodovody. V tomto grafu budou vrcholy vodovodními stanicemi a hrany trubkami mezi nimi. Kolik vody proteèe ze ®elivky do Kanálu?
+\:Mìjme orientovaný graf pøedstavující ¾eleznièní sí»; graf má význaèné vrcholy Moskva a Fronta, ka¾dá hrana grafu má kapacitu, kterou mù¾e uvézt. Kolik vojákù je schopna sí» pøevézt z Moskvy a spotøebovat na Frontì?
+\endlist
+
+\s{Definice:} {\I Sí»} je uspoøádaná ètveøice $(\ogm,z,s,c)$, kde \og{} je orientovaný graf, z~a~s~jsou jeho vrcholy (z(droj) a s(tok)) a c je kapacita sítì, kterou pøedstavuje funkce $c:E(\ogm)\to R_{0}^{+}$.
+
+\par\noindent {\sl Intuice:} Toky v sítích pøedstavují rozvr¾ení, jakým suroviny sítí poteèou...
+
+\figure{sit.eps}{Pøíklad sítì. Èísla pøedstavují kapacity jednotlivých hran.}{3in}
+
+\s{Definice:} {\I Tok} je funkce $E(\ogm)\to R$ taková, ¾e
+\numlist{\ndotted}
+\:Tok ka¾dé hrany je omezen její kapacitou: $0\le f(e)\le c(e)$
+\:\uv{Kirchhoffùv zákon} - nikde se neztrácejí suroviny: $$\sum_{(x,u)\in E}{f(x,u)}=\sum_{(u,x)\in E}{f(u,x)}\quad \forall u\in V(\ogm), u\ne z, u\ne s$$
+\endlist
+
+\s{Poznámka:} Pokud bychom se chtìli v definici toku u bodu 2 vyhnout podmínkám pro z a s, mù¾eme zdroj a stok vzájemnì propojit (pak jde o tzv. cirkulaci).
+
+\s{Poznámka:} V angliètinì se obvykle zdroj znaèí \uv{s} a stok \uv{t} (zkratky source a sink, ov¹em dvì stejná písmena by byla ponìkud nepraktická\dots)
+
+\figure{tok.eps}{Pøíklad toku. Èísla pøedstavují ohodnocení funkcí toku (v závorkách jsou kapacity hran).}{4in}
+
+\s{Definice:} {\I Velikost toku} f je: $$w(f)=\sum_{(z,x)\in E}{f(z,x)}-\sum_{(x,z)\in E}{f(x,z)}$$
+
+\s{Vìta:} Pro ka¾dou sí» existuje maximální tok (bez dùkazu).
+
+\par\noindent {\sl Idea dùkazu:} Doká¾e se pomocí metod matematické analýzy s tím, ¾e mno¾ina tokù je kompaktní a funkce tokù je spojitá\dots
+
+\>Intuice. Øez grafu je mno¾ina hran oddìlující z(droj) a s(tok).
+
+\s{Definice:} {\I Øez} R v síti $(\ogm,z,s,c)$ je $R\subseteq E(\ogm)$ taková, ¾e $\not\kern -.5ex\exists$ cesta ze z do s v grafu $(V(\ogm),E(\ogm)\setminus R)$.
+
+\s{Definice:} {\I Kapacita øezu} $c(R)=\sum_{(u,v\in R)}{c(u,v)}.$
+
+\s{Vìta (Hlavní vìta o tocích, Ford-Fulkerson):} Mìjme S sí». $$\max_{f\hbox{ tok}}{w(f)=\min_{R\hbox{ øez}}{c(R)}}$$
+
+\par\noindent {\sl Intuice:} Uvá¾íme-li mno¾inu kapacit v¹ech øezù, je zdola omezená mno¾inou hodnot tokù.
+
+\par\noindent {\sl Idea dùkazu:} Dùkaz provedeme pomocí dokázání dvou neostrých nerovností.
+
+\proof
+
+\>Pomocné znaèení: Zaveïme konvenci, ¾e existují-li orientované hrany (u,v), $u\in A$, $v\in B$, znaèíme je S(A,B) (separátor). $f(A,B)=\sum_{(u,v)\in E,u\in A,v\in B}{f(u,v)}.$
+
+{\narrower
+\s{Lemma:} $A\subseteq V(\ogm),z\in A,s\not\in A,f\hbox{ je tok}$. Potom platí, ¾e $$w(f)=f(A,V\setminus~A)-f(V\setminus~A,A)$$
+
+\proof
+Dùkaz provedeme pomocí \uv{Kirchhoffova zákonu} a definice velikosti toku:
+$$\sum_{(u,x)\in E}{f(u,x)}-\sum_{(x,u)\in E}{f(x,u)}=0\quad \forall u\in A,u\neq z,u\neq s$$
+$$\sum_{(z,x)\in E}{f(z,x)}-\sum_{(x,z)\in E}{f(x,z)=w(f)}$$
+
+\>Rovnice seèteme:
+$$\sum_{u\in A}{\left(\sum_{(u,x)\in E}{f(u,x)}-\sum_{(x,u)\in E}{f(x,u)}\right)}=w(f)$$
+
+\s{Poznámka:} Tato rovnice neznamená nic jiného, ne¾ ¾e se hrany vedoucí z A do A jednou pøiètou a jednou odeètou. Projeví se pouze hrany vedoucí dovnitø a ven z $V\setminus A$, tak¾e toky vnitøních hran A se \uv{po¾erou}.
+
+\>Z toho plyne:
+$$f(A,V\setminus A)-f(V\setminus A,A)=\sum_{u\in A,v\not\in A}{f(u,v)}-\sum_{u\not\in A,v\in A}{f(u,v)}=w(f)$$
+
+\qed
+
+\s{Dùsledek:} Pokud f je tok, R je øez, pak platí:  $w(f)\le c(R)$.
+
+\proof
+$w(f)=f(A,V\setminus A)-f(V\setminus A,A)\le f(A,V\setminus A)\le c(A,V\setminus A)\le c(R)$
+
+\qed
+}
+
+\s{Redefinice:} {\I Cesta} je odteï posloupnost navazujících hran, u kterých ignorujeme orientaci. Tyto cesty se obvykle nazývají \uv{zs-cesty}.
+
+
+\figure{cesta.eps}{Pøíklad zs-cesty.}{3in}
+
+\s{Definice:} {\I Cesta} P ze z do s je {\I nasycená}, pokud
+$$\exists\ e \in P\left\{{f(e)=c(e)\dots \hbox{orientovaná po smìru}}\atop{f(e)=0\dots \hbox{orientovaná proti smìru}}\right.$$
+\>Jinak je cesta nenasycená.
+
+\s{Definice:} {\I Tok} je {\I nasycený}, pokud $\forall$ cesta P je nasycená.
+
+\s{Vìta:} Tok f je nasycený $\Leftrightarrow$ f je maximální. Navíc pro $\forall$ maximální tok f $\exists$ øez R, ¾e $w(f)=c(R).$
+
+\proof
+
+\>\uv{$\Leftarrow$} sporem: Mìjme tok f maximální a nenasycený $\Rightarrow \exists$ P nenasycená. Tuto cestu P budeme \uv{vylep¹ovat}.
+\>Zvolíme:
+$$\varepsilon_1=\min_{e\in P,\hbox{ po smìru}}{\{c(e)-f(e)\}}$$
+$$\varepsilon_2=\min_{e\in P,\hbox{ proti smìru}}{\{f(e)\}}$$
+$$\varepsilon=\min{\{\varepsilon_1,\varepsilon_2\}}>0$$
+\>Poslední ostrá nerovnost vyplývá z definice nenasycené cesty. Nyní vylep¹íme tok f o $\varepsilon$: $f\to f^{'}$:
+$$f^{'}(e)=\left\{{\displaystyle f(e)+\varepsilon \dots e\in P\hbox{ po smìru}\hfill}\atop{{\displaystyle  f(e)-\varepsilon \dots e\in P\hbox{ proti smìru}\hfill}\atop{\displaystyle f(e) \dots e\not\in P\hfill}}\right.$$
+\>Nyní je potøeba ovìøit, ¾e $f^{'}$ je skuteènì tok:
+$$0\le f^{'}(e)\le c(e)\dots\hbox{platí stále díky volbì }\varepsilon $$
+
+\>Platnost \uv{Kirchhoffova zákonu} ovìøíme rozborem pøípadù:
+\figure{kirch.eps}{Rozbor pøípadù.}{4in}
+
+\>$f^{'}$ je tedy tok, ov¹em potom platí:
+$$w(f^{'})=w(f)+\varepsilon\Rightarrow w(f^{'})>w(f)\Rightarrow\hbox{SPOR}$$
+
+\>\uv{$\Rightarrow$}: Uvá¾íme $A\subseteq V(\ogm)$, ¾e $\forall\ v\in{} A\ \exists$ nenasycená cesta ze z do v. $z \in A$, $s \not\in A$. $S(A,V\setminus A)$ je hledaný øez R. Podle lemmatu:
+$$w(f)=f(A,V\setminus A)-f(V\setminus A,A)=c(A,V\setminus A)=c(R)$$
+Víme, ¾e $w(f)\le c(R)$. Staèilo uvá¾it nasycený tok f. Pak jsme sestrojili øez R a~výraz pøe¹el v rovnost $c(R)=w(f)$ (a tedy je tok f maximální).
+
+\qed
+
+\figure{nenasyc.eps}{Rozdìlení V(\og) na mno¾inu A a V$\setminus$A v dùkazu hlavní vìty o tocích.}{2.5in}
+
+\s{Algoritmus:} (Ford-Fulkerson algoritmus hledání maximálního toku)
+
+\algo
+\:$f(e) := 0\ \forall e \in E$
+\:while $\exists$ zlep¹ující cesta P, vylep¹i P jako v dùkazu hlavní vìty
+\:f je maximální
+\endalgo
+
+\h{Cvièení:}
+\itemize\ibull
+\:Je pro pøirozené kapacity F.F. algoritmus koneèný? Ano - v ka¾dém zlep¹ujícím kroku algoritmu se celkový tok zvìt¹í aspoò o 1. Proto¾e máme horní odhad na maximální tok (napø. souèet kapacit v¹ech hran), máme i~horní odhad na dobu bìhu algoritmu.
+\:Je F.F. algoritmus koneèný pro racionální kapacity hran? Ano - v¹echny kapacity vynásobíme spoleèným jmenovatelem a pøevedeme na pøedchozí pøípad (pro obecné kapacity ov¹em takto definovaný F.F. algoritmus nemusí být koneèný).
+\:Kolik krokù bude muset algoritmus na následující síti maximálnì udìlat, aby úspì¹nì dobìhl? (2M krokù)
+\endlist
+
+\figure{2M.eps}{Pøíklad sítì. Kolik krokù musí maximálnì udìlat F.F. algoritmus?}{2in}
+
+\bye
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+q 442.751 375.763 m
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+q 442.751 375.763 m
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+h q f* Q S
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+showpage
+%%BeginIpeXml: /FlateDecode
+%GhTQma_oie&;KY&$A->B71l!CE%0cH"^2TDHKmL,g/`#5QDM`=dKP'n%V<hgPrP`mjeRV&kaS4E
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+%Tm-%2A\Hf]!qZ6l4jWQBDr+1Q%=Hpil5o\-KIi@sm2WRX/9.)k6pa05U0*mrLkrA4^cF-TJ?VJJ
+%hEQskM^WT>O(FuDB/1NOHUh&N)'0mbLtEUMLo@R*iuopbD2fGXCZXOf'-ethM4$YOP]=IYblqlW
+%gEC[gW#nQhkcr1D^IKhA[<r\Y?k*KSRG[HTY=:*FO_iNf"^-g;a"cr\6uU,g7P0DfMVaAYNEU5a
+%a+!B=J_?[B^%K'f\fWqQkie(m3VI7'<Gf^t*b@./1@:>D<gb*Oq,j%tU6">a&b2;*Gkh_f!;/\~>
+%%EndIpeXml
+%%Trailer
+end
+%%EOF
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..9d6901a
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,7 @@
+all:
+
+clean:
+	for a in *-* all ; do ( cd $$a && make clean ) ; done
+	rm -f *~
+
+.SECONDARY:
diff --git a/Makerules b/Makerules
new file mode 100644
index 0000000..01e71fa
--- /dev/null
+++ b/Makerules
@@ -0,0 +1,35 @@
+export TEXINPUTS=.:..:
+
+all: $P.ps
+
+%.dvi: %.tex ../lecnotes.tex ../mjmac.tex
+	csplain $<
+
+#%.pdf: %.tex ../lecnotes.tex ../mjmac.tex
+#	pdfcsplain $<
+
+%.ps: %.dvi
+	dvips -D600 -o $@ -O-15.4mm,-15.4mm -t a5 $<
+
+%.pdf: %.dvi
+	dvipdfm -o $@ -x 9mm -y 9mm -p a5 -r 600 -z 9 $<
+
+%-booklet.ps: %.ps
+	psbook <$< | pstops '2:0L(210mm,0)+1L(210mm,148mm)' | sed 's/^%%BoundingBox: .*/%%BoundingBox: 0 0 595 842/;s/^%%DocumentPaperSizes:.*/%%DocumentPaperSizes: a4\n%%Orientation: Landscape/' >$@
+
+%-2in1.ps: %.ps
+	pstops '2:0L(210mm,0mm)+1L(210mm,148mm)' <$< | sed 's/^%%BoundingBox: .*/%%BoundingBox: 0 0 595 842/;s/^%%DocumentPaperSizes:.*/%%DocumentPaperSizes: a4\n%%Orientation: Landscape/' >$@
+
+mostlyclean:
+	rm -f *.dvi *.log *~ core *.o *.aux *.bbl *.blg
+
+clean:: mostlyclean
+	rm -f *.ps *.pdf
+
+ifndef CUSTOM_UPLOAD
+upload::
+	make $P-booklet.ps
+	scp -C $P-booklet.ps jabberwock:www/vyuka/0607/ads1/$P-booklet.ps
+endif
+
+.SECONDARY:
diff --git a/all/ChangeLog b/all/ChangeLog
new file mode 100644
index 0000000..86684b9
--- /dev/null
+++ b/all/ChangeLog
@@ -0,0 +1,102 @@
+commit a748943564adddb47dd0f5fb8d7685d77b6f148b
+Author: Martin Mares <mj@ucw.cz>
+Date:   Wed Oct 3 18:54:11 2007 +0200
+
+    Stare GIFyzruseny.
+
+ 7-stromy/Insert1.gif    |  Bin
+ 7-stromy/ab-strom11.gif |  Bin
+ 7-stromy/b-klicu1.gif   |  Bin
+ 7-stromy/b-klicu2.gif   |  Bin
+ 7-stromy/delete21.gif   |  Bin
+ 7-stromy/delete22.gif   |  Bin
+ 7-stromy/delete31.gif   |  Bin
+ 7-stromy/delete32.gif   |  Bin
+ 8 files changed, 0 insertions(+), 0 deletions(-)
+
+commit 8d771d9e18da7c1b336923267ce53d3c2856405e
+Author: Martin Mares <mj@ucw.cz>
+Date:   Wed Oct 3 18:53:49 2007 +0200
+
+    GIFy zkonvertovany do PNG, ale jeste nejsou do textu zasazeny.
+
+ 7-stromy/abpic/Insert1.png    |  Bin
+ 7-stromy/abpic/ab-strom11.png |  Bin
+ 7-stromy/abpic/b-klicu1.png   |  Bin
+ 7-stromy/abpic/b-klicu2.png   |  Bin
+ 7-stromy/abpic/delete21.png   |  Bin
+ 7-stromy/abpic/delete22.png   |  Bin
+ 7-stromy/abpic/delete31.png   |  Bin
+ 7-stromy/abpic/delete32.png   |  Bin
+ 8 files changed, 0 insertions(+), 0 deletions(-)
+
+commit 6f4264dc0df979701be869585dbfb87f21603750
+Author: Martin Mares <mj@ucw.cz>
+Date:   Wed Oct 3 18:41:16 2007 +0200
+
+    Pribyly obrazky stromu z Programatorske kucharky KSP.
+
+ 7-stromy/7-stromy.tex     |   51 ++-
+ 7-stromy/treepic/t1.ipe   |  299 ++++++++++++++++++
+ 7-stromy/treepic/t10.ipe  |  389 +++++++++++++++++++++++
+ 7-stromy/treepic/t11.ipe  |  398 ++++++++++++++++++++++++
+ 7-stromy/treepic/t12.ipe  |  566 ++++++++++++++++++++++++++++++++++
+ 7-stromy/treepic/t12y.ipe |  565 ++++++++++++++++++++++++++++++++++
+ 7-stromy/treepic/t13.ipe  |  706 ++++++++++++++++++++++++++++++++++++++++++
+ 7-stromy/treepic/t2.ipe   |  465 ++++++++++++++++++++++++++++
+ 7-stromy/treepic/t3.ipe   |  749 +++++++++++++++++++++++++++++++++++++++++++++
+ 7-stromy/treepic/t35.ipe  |  357 +++++++++++++++++++++
+ 7-stromy/treepic/t4.ipe   |  424 +++++++++++++++++++++++++
+ 7-stromy/treepic/t5.ipe   |  540 ++++++++++++++++++++++++++++++++
+ 7-stromy/treepic/t6.ipe   |  460 ++++++++++++++++++++++++++++
+ 7-stromy/treepic/t7.ipe   |  398 ++++++++++++++++++++++++
+ 7-stromy/treepic/t8.ipe   |  579 +++++++++++++++++++++++++++++++++++
+ 7-stromy/treepic/t9.ipe   |  705 ++++++++++++++++++++++++++++++++++++++++++
+ mjipe.tex                 |   54 +++
+ 17 files changed, 7687 insertions(+), 18 deletions(-)
+
+commit 9a1e7f0e7ec9c6b095a9618363d451adead3dfae
+Author: Martin Mares <mj@ucw.cz>
+Date:   Wed Oct 3 18:24:06 2007 +0200
+
+    Stromy: Vycisteni TeXoveho zdrojaku a konverze cestiny.
+
+ 7-stromy/7-stromy.tex |  234 ++++++++++++++++++++++---------------------------
+ 1 files changed, 104 insertions(+), 130 deletions(-)
+
+commit 27980ec9b68061c681223cf6810ca9f9e856c852
+Merge: c62dbac... a561fef...
+Author: Martin Mares <mj@ucw.cz>
+Date:   Wed Oct 3 13:16:20 2007 +0200
+
+    Merge with git+ssh://git.ucw.cz/home/mj/GIT/ads.git
+
+
+commit c62dbac4555b0bd8da14c589cab3980819f4e7c2
+Author: Martin Mares <mj@ucw.cz>
+Date:   Wed Oct 3 13:16:09 2007 +0200
+
+    Prvni nastrel.
+
+ 7-stromy/7-stromy.tex   |  274 +++++++++++++++++++++++++++++++++++++++++++++++
+ 7-stromy/Insert1.gif    |  Bin
+ 7-stromy/Makefile       |    3 +
+ 7-stromy/ab-strom11.gif |  Bin
+ 7-stromy/b-klicu1.gif   |  Bin
+ 7-stromy/b-klicu2.gif   |  Bin
+ 7-stromy/delete21.gif   |  Bin
+ 7-stromy/delete22.gif   |  Bin
+ 7-stromy/delete31.gif   |  Bin
+ 7-stromy/delete32.gif   |  Bin
+ 10 files changed, 277 insertions(+), 0 deletions(-)
+
+commit a561fefca56a6c81337695440a55448e734b5e2e
+Author: Martin Mares <mj@ucw.cz>
+Date:   Mon Oct 1 00:25:57 2007 +0200
+
+    Pridana nulta verze Dijkstrova algoritmu.
+
+ 11-dijkstra/11-dijkstra.tex |  162 +++++++++++++++++++++++++++++++++++++++++++
+ 11-dijkstra/Makefile        |    3 +
+ all/Makefile                |    2 -
+ 3 files changed, 166 insertions(+), 1 deletions(-)
diff --git a/all/Makefile b/all/Makefile
new file mode 100644
index 0000000..9c4b409
--- /dev/null
+++ b/all/Makefile
@@ -0,0 +1,25 @@
+P=ads
+X:=$(shell for a in 1 2 3 4 5 6 8 9 10 11 12 13 ; do echo ../$$a-*/$$a-*.tex ; done)
+
+%universe: all ChangeLog
+
+CUSTOM_UPLOAD=1
+include ../Makerules
+
+ads.dvi: ads.tex body.tex
+
+body.tex: $(X) preprocess
+	./preprocess $(X) >$@
+
+ChangeLog:
+	git-log -C --pretty=medium --since='4 weeks ago' --stat | grep -v '^---' >ChangeLog
+
+clean::
+	rm -f body.tex ChangeLog
+
+upload::
+	make $P.ps $P-2in1.ps
+	scp -C $P.ps $P-2in1.ps jabberwock:www/vyuka/0607/ads1/
+	( cd .. && make clean )
+	( cd ../.. && tar czf - --exclude .git ads ) | ssh jabberwock 'cd www/vyuka/0607/ads1/ && cat >ads.tar.gz.new && mv ads.tar.gz.new ads.tar.gz'
+	make ChangeLog && cat ChangeLog | ssh jabberwock 'cd www/vyuka/0607/ads1 && cat >ChangeLog.new && mv ChangeLog.new ChangeLog'
diff --git a/all/ads.tex b/all/ads.tex
new file mode 100644
index 0000000..419ff8f
--- /dev/null
+++ b/all/ads.tex
@@ -0,0 +1,7 @@
+\input ../lecnotes.tex
+
+\def\chapterend{\bigbreak\bigbreak}
+
+\input body.tex
+
+\bye
diff --git a/all/preprocess b/all/preprocess
new file mode 100755
index 0000000..57223e3
--- /dev/null
+++ b/all/preprocess
@@ -0,0 +1,20 @@
+#!/usr/bin/perl
+
+use warnings;
+use strict;
+
+foreach my $f (@ARGV) {
+	my $d = $f;
+	$d =~ s@/[^/]*$@/@;
+	open X, $f or die;
+	while (<X>) {
+		/^\\input .*lecnotes\.tex/ && next;
+		/^\\references/ && next;
+		/^\\bye/ && last;
+		s@\\(figure|fig|inlinefig|epsfbox){([^}]+)}@\\$1\{$d$2}@g;
+		s@\\(twofigures){([^}]+)}({[^}]+}{[^}]+}){([^}]+)}@\\$1\{$d$2}$3\{$d$4}@g;
+		print;
+	}
+	close X;
+	print "\\chapterend\n";
+}
diff --git a/lecnotes.tex b/lecnotes.tex
new file mode 100644
index 0000000..a2fc069
--- /dev/null
+++ b/lecnotes.tex
@@ -0,0 +1,153 @@
+% Makra pro sazbu zapisku z prednasky
+
+\input mjmac.tex
+\input epsf.tex
+%%\input btxmac.tex
+
+\language=\czech
+\chyph
+\lefthyphenmin=2
+\righthyphenmin=2
+
+% A4 s 0.5in okraji
+%\hsize=184.6mm
+%\vsize=271.6mm
+%\parindent=0.25in
+
+% A5 s 1cm okraji, dolni rozsiren o 10pt, aby se tam veslo cislo stranky
+\hsize=128mm
+\vsize=190mm
+\advance\vsize by -10pt
+\parindent=0.8cm
+
+% Zacatek prednasky {cislo prednasky}{jmeno prednasky}{jmeno zapisovatele}
+\def\prednaska#1#2#3{%
+\line{{\Large\bf #1. #2} \hfil {\it #3}}
+\vskip 4pt
+\hrule
+\medskip
+}
+
+% Nadpis {text}
+\def\h#1{\medbreak\leftline{\bf #1}\nobreak\smallskip\nobreak}
+
+% Zvyrazneny zacatek odstavce coby podnadpis (napr. vety apod.)
+\def\s#1{\noindent {\bo #1}}
+
+% A kdyz stoji samostatne (aby se naodlamoval)
+\def\ss#1{\noindent {\bo #1}\par\nobreak}
+
+% Dùkaz
+\def\proof{\noindent {\sl Dùkaz:} }
+
+% Srdicko na konci dukazu
+\def\qed{{\parfillskip=0pt\allowbreak\hfill\nobreak $\heartsuit$\par}}
+
+% pokud je v seznamu:
+\def\qeditem{{\parfillskip=0pt\hfill\rlap{\hskip\rightskip\llap{$\heartsuit$}}\par}}
+
+% Poznamky pod carou
+\newcount\footcnt
+\footcnt=0
+\def\foot#1{\global\advance\footcnt by 1{\parindent=0.25in\parskip=0pt\footnote{$^{\left<\the\footcnt\right>}$}{#1}}}
+
+% \noindent se casto hodi, tak na nej mame zkratku
+\let\>=\noindent
+
+% Sazba algoritmu:
+%	\algo
+%	\algin popis vstupu
+%	\:krok
+%	\:krok
+%	\::vnoreny krok
+%	\algout pop
+%	\endalgo
+
+\def\algo{
+\interlistskip
+\begingroup
+\let\:=\algoitem
+\parskip=1pt plus 1pt minus 0.3pt
+\rightskip=2em
+\itemcount=0
+}
+\def\endalgo{\interlistskip\endgroup}
+\def\algopar{\par
+\parindent=2em
+\hangindent=4em
+\hangafter=1
+\leavevmode
+}
+\def\algoitem{\algopar\advance\itemcount by 1
+\hbox to 2em{\hss \the\itemcount. }%
+\futurelet\next\algoitemh}
+\def\algoitemh{\ifx\next:\let\next=\algohang\else\let\next=\relax\fi\next}
+\def\algohang:{\advance\hangindent by 2em \hskip 2em\futurelet\next\algoitemh}
+\def\algin{\:{\I Vstup:} }
+\def\algout{\:{\I Výstup:} }
+
+% Nekolikapismenkova promenna (mozno pouzit v textovem i math modu)
+\def\<#1>{\hbox{\it #1\/}}
+
+% Asymptoticke O-cko
+\def\O{{\cal O}}
+
+% Vlozeni obrazku {obrazek}{popisek}{sirka}
+\def\figure#1#2#3{\bigskip\vbox{\centerline{\epsfxsize=#3\epsfbox{#1}}\smallskip\centerline{#2}}\bigskip}
+
+% Varianta bez popisku
+\def\fig#1#2{\medskip\centerline{\epsfxsize=#2\epsfbox{#1}}\medskip}
+
+% Dva obrazky vedle sebe s popiskami
+\def\twofigures#1#2#3#4#5#6{\bigskip\centerline{\vbox{\halign{\hfil##\hfil\hskip 4em&\hfil##\hfil\cr
+\epsfxsize=#3\epsfbox{#1}&\epsfxsize=#6\epsfbox{#4}\cr
+\noalign{\smallskip}
+#2&#5\cr}}}\bigskip}
+
+% Obrazek vlozeny do praveho okraje odstavce {obrazek}{sirka}
+% Pouzit na zacatku odstavce a nejlepe celou konstrukci zavrit do vboxu, aby se nerozlomila
+\def\inlinefig#1#2{
+\setbox0=\hbox{\epsfxsize=#2\epsfbox{#1}}
+\hangindent=-\wd0
+\advance\hangindent by -3em
+\dimen0=\ht0
+\advance\dimen0 by 8ex
+\advance\dimen0 by \normalbaselineskip
+\count0=\dimen0
+\divide\count0 by \normalbaselineskip
+\hangafter=-\count0
+\dimen0=\normalbaselineskip
+\multiply\dimen0 by \count0
+\vbox to 0pt{}
+\nointerlineskip
+\vbox to 0pt{\vbox to \dimen0{\vss\rightline{\box0\hskip 1em}\vss}}
+\nointerlineskip
+}
+
+% Todo
+\def\todo#1{{\bf TODO: \it #1}}
+
+% Blackboard bold font
+\newfam\bbfam
+\font\bbten=bbold10
+\font\bbseven=bbold7
+\font\bbfive=bbold5
+\textfont\bbfam=\bbten
+\scriptfont\bbfam=\bbseven
+\scriptscriptfont\bbfam=\bbfive
+\def\bb{\bbten\fam\bbfam}
+
+% Reference na konci kapitoly
+%\bibliographystyle{abbrv}
+%\def\references{\h{Literatura}\dumprefs}
+%\def\dumprefs{
+%\def\bblhook{\parskip=2pt plus 1pt minus 0.5pt}
+%\bibliography{../ga}
+%}
+
+% Predefinujeme odsazovani odrazek z mjmacu
+\def\itemspacingrules{\ifitem\advance\leftskip by \parindent\parindent=0pt\itemfalse\else
+\advance\leftskip by 2.5em\fi\rightskip=\leftskip}
+
+% Matematicke symboly
+\def\symdiff{\mathop{\Delta}}
diff --git a/mjipe.tex b/mjipe.tex
new file mode 100644
index 0000000..f52611a
--- /dev/null
+++ b/mjipe.tex
@@ -0,0 +1,54 @@
+% Macros for importing of IPE pictures in plain TeX
+% (c) 2001 Martin Mares <mj@atrey.karlin.mff.cuni.cz>
+% ------------------------------------------------------------------------------
+
+% To access internal macros of plain TeX
+% --------------------------------------
+
+\def\makeatletter{\catcode`@=11 }
+\def\makeatother{\catcode`@=12 }
+\makeatletter
+
+% Importing of IPE pictures
+% -------------------------
+
+\newdimen\unitlength
+\newbox\picbox
+\newdimen\picht
+
+\def\IpeInput#1{{\def\IPEfile{#1}\latexemulation
+\input\IPEfile\relax
+}}
+
+\def\latexemulation{
+\def\newcommand##1[##2]##3{}
+\def\@ifundefined##1##2{##2}
+\def\begin##1(##2,##3)(##4,##5){\picht=##3\unitlength
+\setbox\picbox=\hbox to ##2\unitlength\bgroup
+\hskip -##4\unitlength\lower ##5\unitlength\hbox\bgroup
+\ignorespaces}
+\def\end##1{\egroup\hss\egroup\ht\picbox=\picht\dp\picbox=0pt\picout}
+}
+
+\def\picout{
+\nointerlineskip
+{
+\vskip 4pt plus 1pt minus 0.5pt
+\line{\hss\box\picbox\hss}
+\vskip 4pt plus 1pt minus 0.5pt
+}
+\nointerlineskip
+}
+\def\killglue{\unskip}
+\def\put(#1,#2)#3{\killglue\raise#2\unitlength\hbox to 0pt{\kern #1\unitlength #3\hss}\ignorespaces}
+
+\let\selectfont\relax
+\def\fontsize#1#2{}
+\def\IPEput#1#2#3#4{\put(0,0){\special{psfile=\IPEfile}}}
+\def\IPEmp#1#2{\MiniPagesAreNotSupported}
+\def\IPEtext#1{\hbox{#1\special{color pop}}}
+\def\IPEfs#1{\IPEcolfs{0 0 0}{#1}}
+\def\IPEcolfs#1#2{\dimen0=#2pt\fontsize{#2}{1.2\dimen0}\selectfont\special{color push rgb #1}}
+\def\IPEsize#1#2{\unitlength=1bp\ignorespaces}
+
+\makeatother
diff --git a/mjmac.tex b/mjmac.tex
new file mode 100644
index 0000000..18f81cc
--- /dev/null
+++ b/mjmac.tex
@@ -0,0 +1,335 @@
+% MJ's TeX Macro Collection
+% (c) 1995--2004 Martin Mares <mj@ucw.cz>
+% Freely distributable as long as the author's copyright is left intact
+
+% History:
+% 2.0 (05-11-95)  Itemization and list system completely rewritten. Hopefully
+%		  it's usable now.
+% 2.1 (11-05-96)  Added \fixfont.
+% 2.2 (15-02-97)  Modified \fixfont not to leave extra spaces.
+%		  Added \relax at the end of \tt.
+%		  Added a very limited support for picture drawing.
+% 2.3 (21-05-01)  Modified \fixfont to use \fntdesignsize,
+%		  Added \fntmath(|s|ss)size and used it in \setmath
+%		  Added \twelvepoint
+% 2.4 (10-07-03)  Added \bo
+% 2.5 (27-09-03)  Added \verblocaldefs
+% 2.6 (21-03-04)  Added \itemspacingrules
+% 2.7 (10-04-04)  There were collisions between our \[bB]ig and the same
+%		  macro used in plain to implement \bigl et al. Now we rename
+%		  the original \[bB]ig to \plain[bB]ig and re-define \[bB]ig[lrm]
+%		  to call the renamed version instead.
+
+% We'll use internal macros of plain TeX
+
+\catcode`@=11
+
+\newcount\mjtempcount
+
+% Page size definition
+% --------------------
+
+% Standard A4 dimensions are used. For different set of dimensions, redefine the
+% \setpagesize macro to set everything you want in true units. Don't forget to
+% call the macro immediately to refresh current setting. \magnification can be
+% set prior to inclusion of these macros.
+
+\def\setpagesize{\hsize=7truein\vsize=9.2truein}
+\def\m@g{\mag\count@\setpagesize\dimen\footins8truein}
+\setpagesize
+
+% Spacing
+% -------
+
+\parindent=1.4cm
+\parskip=3pt plus 1pt minus 1pt
+
+% We want to override \[bB]ig in plain, so save the original definition
+% ---------------------------------------------------------------------
+
+\let\plainbig=\big
+\let\plainBig=\Big
+\def\bigl{\mathopen\plainbig}
+\def\bigm{\mathrel\plainbig}
+\def\bigr{\mathclose\plainbig}
+\def\Bigl{\mathopen\plainBig}
+\def\Bigm{\mathrel\plainBig}
+\def\Bigr{\mathclose\plainBig}
+
+% Font selection system
+% ---------------------
+
+% The heart of the font selection system is the \setfont macro which selects
+% the current font according to the following settings:
+% \fntprefix - font name prefix (usually cm or cs)
+% \fntdesignsize - font design size in points (normally 10)
+% \fnttokprefix - prefix of control sequence the font is assigned to ('ten')
+% \fntmag - font magnification factor
+% \fnttoksuffix - control sequence suffix ('A' to 'G' according to mag)
+% \fntstyle - font name suffix determining font style ('bx', 'r' etc.)
+
+\def\fntprefix{cs}
+\def\fntdesignsize{10}
+\def\fnttokprefix{ten}
+\def\fntmag{\magstep0}
+\def\fnttoksuffix{A}
+\def\fntstyle{r}
+
+\def\setfont{%
+\toks0=\expandafter{\csname\fnttokprefix\fntstyle\fnttoksuffix\endcsname}%
+\expandafter\ifx\the\toks0\relax%
+%\immediate\write-1{aa \the\toks0=\fntprefix\fntstyle\fntdesignsize\space scaled \fntmag}%
+\global\expandafter\font\the\toks0=\fntprefix\fntstyle\fntdesignsize\space scaled \fntmag%
+\fi%
+\edef\currentfont{\the\toks0}\currentfont}
+
+\setfont  % Initialize the whole mechanism
+
+\def\mathf@nt#1#2#3#4{%
+\toks0=\expandafter{\csname#1#2\fnttoksuffix\endcsname}%
+\expandafter\ifx\the\toks0\relax%
+%\immediate\write-1{bb \the\toks0=#4#2#3\space scaled \fntmag}%
+\global\expandafter\font\the\toks0=#4#2#3\space scaled \fntmag%
+\fi%
+\edef\m@@f{\the\toks0}}
+
+\def\fntmathsize{10}
+\def\fntmathtok{ten}
+\def\fntmathssize{7}
+\def\fntmathstok{seven}
+\def\fntmathsssize{5}
+\def\fntmathsstok{five}
+
+\def\setmath{%
+\mathf@nt{\fntmathtok}{r}{\fntmathsize}{cs}\textfont0=\m@@f
+\mathf@nt{\fntmathstok}{r}{\fntmathssize}{cs}\scriptfont0=\m@@f
+\mathf@nt{\fntmathsstok}{r}{\fntmathsssize}{cs}\scriptscriptfont0=\m@@f
+\mathf@nt{\fntmathtok}{mi}{\fntmathsize}{cm}\skewchar\m@@f='177\textfont1=\m@@f
+\mathf@nt{\fntmathstok}{mi}{\fntmathssize}{cm}\skewchar\m@@f='177\scriptfont1=\m@@f
+\mathf@nt{\fntmathsstok}{mi}{\fntmathsssize}{cm}\skewchar\m@@f='177\scriptscriptfont1=\m@@f
+\mathf@nt{\fntmathtok}{sy}{\fntmathsize}{cm}\skewchar\m@@f='60\textfont2=\m@@f
+\mathf@nt{\fntmathstok}{sy}{\fntmathssize}{cm}\skewchar\m@@f='60\scriptfont2=\m@@f
+\mathf@nt{\fntmathsstok}{sy}{\fntmathsssize}{cm}\skewchar\m@@f='60\scriptscriptfont2=\m@@f
+\mathf@nt{\fntmathtok}{ex}{\fntmathsize}{cm}\textfont3=\m@@f\scriptfont3=\m@@f\scriptscriptfont3=\m@@f
+\mathf@nt{\fntmathtok}{ti}{\fntmathsize}{cs}\textfont\itfam=\m@@f
+\mathf@nt{\fntmathtok}{sl}{\fntmathsize}{cs}\textfont\slfam=\m@@f
+\mathf@nt{\fntmathtok}{bx}{\fntmathsize}{cs}\textfont\bffam=\m@@f
+\mathf@nt{\fntmathtok}{tt}{\fntmathsize}{cs}\hyphenchar\m@@f=-1\textfont\ttfam=\m@@f
+}
+
+% Call \fixfont to fix lineskip, math fonts and the strut box
+
+\def\fixfont{\setfont\setmath
+\mjtempcount=\fntdesignsize
+\multiply\mjtempcount by \fntmag
+\normalbaselineskip=0.12pt
+\multiply\normalbaselineskip by \mjtempcount
+\divide\normalbaselineskip by 100
+\normallineskip=0.01pt
+\multiply\normallineskip by \mjtempcount
+\divide\normallineskip by 100
+\normalbaselines
+\dimen0=0.085pt
+\multiply\dimen0 by \mjtempcount
+\divide\dimen0 by 100
+\dimen1=0.035pt
+\multiply\dimen1 by \mjtempcount
+\divide\dimen1 by 100
+\setbox\strutbox=\hbox{\vrule height\dimen0 depth\dimen1 width\z@}}
+
+% You can use the following macros to change the magnification:
+
+\def\normal{\def\fntmag{\magstep0}\def\fnttoksuffix{A}\setfont}       % Normal size
+\def\halflarge{\def\fntmag{\magstephalf}\def\fnttoksuffix{b}\setfont} % Magstephalf
+\def\large{\def\fntmag{\magstep1}\def\fnttoksuffix{B}\setfont}        % Magstep 1
+\def\Large{\def\fntmag{\magstep2}\def\fnttoksuffix{C}\setfont}
+\def\big{\def\fntmag{\magstep3}\def\fnttoksuffix{D}\setfont}
+\def\Big{\def\fntmag{\magstep4}\def\fnttoksuffix{E}\setfont}
+\def\huge{\def\fntmag{\magstep5}\def\fnttoksuffix{F}\setfont}
+\def\Huge{\def\fntmag{\magstep6}\def\fnttoksuffix{G}\setfont}         % Magstep 6
+\def\fm#1{\def\fntmag{\magstep#1}\edef\fnttoksuffix{\ifcase #1 A\or B\or C%
+\or D\or E\or F\or G\fi}\setfont}				      % User mag
+
+% And to change the style:
+
+\def\rm{\fam\z@\def\fntstyle{r}\setfont}	% Roman
+\def\it{\fam\itfam\def\fntstyle{ti}\setfont}	% Italic
+\def\bo{\fam\bffam\def\fntstyle{b}\setfont}	% Bold
+\def\bf{\fam\bffam\def\fntstyle{bx}\setfont}	% Bold extended
+\def\ss{\def\fntstyle{ss}\setfont}		% Sans serif
+\def\tt{\fam\ttfam\def\fntstyle{tt}\setfont%
+\hyphenchar\currentfont=-1\relax}		% Typewriter
+\def\sc{\def\fntstyle{csc}\setfont}		% Caps and small caps
+\def\ssi{\def\fntstyle{ssi}\setfont}		% Sans serif italic
+\def\sl{\fam\slfam\def\fntstyle{sl}\setfont}	% Slanted
+\def\ssbf{\def\fntstyle{ssbx}\setfont}		% Sans serif bold
+\def\ssdc{\def\fntstyle{ssdc}\setfont}		% Sans serif demi condensed
+
+% Switch to large font set
+
+\def\twelvepoint{
+\def\fntdesignsize{12}
+\def\fnttokprefix{twelve}
+\def\fntmathsize{12}\def\fntmathtok{twelve}
+\def\fntmathssize{8}\def\fntmathstok{eight}
+\def\fntmathsssize{6}\def\fntmathsstok{six}
+\fixfont
+}
+
+% Itemization
+% -----------
+
+\newif\ifitem\itemtrue
+\newbox\itembox
+\newcount\itemcount
+
+\def\interlistskip{\vskip 3pt plus 2pt minus 1pt}
+
+\def\itemspacingrules{\ifitem\advance\leftskip by \parindent\parindent=0pt\itemfalse\fi
+\advance\leftskip by 2.5em}
+
+\def\inititemize{\interlistskip\begingroup
+\parskip=1pt plus 0.3pt minus 0.1pt
+\itemspacingrules}
+
+\def\itemize#1{\inititemize\setbox\itembox\llap{#1\hskip 0.4em}%
+\let\:=\singleitem}
+
+\def\singleitem{\par\leavevmode\copy\itembox}
+
+\def\endlist{\interlistskip\endgroup}
+
+\def\ibull{\raise0.2ex\hbox{$\bullet$}} % Signs frequently used for \itemize
+\def\idot{\raise0.2ex\hbox{$\cdot$}}
+\def\istar{\raise0.2ex\hbox{$\ast$}}
+
+\def\numlist#1{\inititemize\itemcount=0\let\:=\numbereditem
+\let\itemnumbering=#1}
+
+\def\numbereditem{\par\leavevmode\advance\itemcount by 1
+\llap{\itemnumbering\hskip 0.4em}}
+
+\def\nnorm{\the\itemcount}
+\def\ndotted{\nnorm.}
+\def\nparen{\nnorm)}
+\def\nroman{\romannumeral\itemcount}
+\def\nromanp{\nroman)}
+\def\nalpha{\count@=96\advance\count@ by\itemcount\char\count@)}
+\def\nAlpha{\count@=64\advance\count@ by\itemcount\char\count@)}
+\def\ngreek{$\ifcase\itemcount\or\alpha\or\beta\or\gamma\or\delta\or\epsilon\or
+\zeta\or\eta\or\theta\or\iota\or\kappa\or\lambda\or\mu\or\nu\or\xi\or\pi\or\rho
+\or\sigma\or\tau\or\upsilon\or\phi\or\chi\or\psi\or\omega\fi$)}
+
+\def\itm{\:}
+
+% Additional math functions
+% -------------------------
+
+\def\mod{\;{\rm mod}\;}
+\def\div{\;{\rm div}\;}
+\def\xor{\;{\rm xor}\;}
+
+\def\mathbox#1{  % Typeset math formula enclosed in a box.
+$$\vbox{
+\hrule
+\hbox{\vrule height 10pt depth 5pt\hskip3mm\hbox{$#1$}\hskip3mm\vrule }
+\hrule
+}$$}
+
+% Italic typesetting	(automatic \/)
+% ------------------
+
+\def\I{\it\aftergroup\/}
+
+% New \frenchspacing, which doesn't leave unwanted spaces in text.
+
+\def\frenchsp@cing{\sfcode`\.\@m \sfcode`\?\@m \sfcode`\!\@m%
+\sfcode`\:\@m \sfcode`\;\@m \sfcode`\,\@m}
+
+% Typesetting of one verbatim word
+% --------------------------------
+
+\def\make@ther#1{\catcode`#1=12\relax}
+\def\setverb@tim{\tt\frenchsp@cing\catcode`\`=13\catcode`\'=13\n@ligs%
+\let\do=\make@ther\dospecials\obeyspaces}
+
+{\catcode`'=13
+\catcode``=13
+\gdef\n@ligs{\def`{\relax\lq}\def'{\relax\rq}}}
+
+{\obeyspaces
+\global\chardef\sp@ce=32
+\gdef\showspaces{\let =\sp@ce}
+\global\let =\ }
+
+\catcode124=\active % Make | active
+\def\ttst@rt{\begingroup\setverb@tim\let|=\endgroup}
+\let|=\ttst@rt
+
+% Typesetting of verbatim text  (enclosed in { } )
+% ----------------------------
+
+\newskip\verbglue\newskip\verblineglue
+\verbglue=3pt plus 1pt minus 0.3pt
+\verblineglue=0pt plus 1.5pt
+\def\verblocaldefs{}
+
+\newdimen\tabwidth
+\newcount\tabsize
+\tabsize=8
+\newdimen\t@b
+
+\newcount\vercnt
+\def\v@rbend{\par\endgroup\vskip\verbglue}
+\def\v@rbl{\ifnum\vercnt>0\{\fi\global\advance\vercnt by 1\relax}
+\def\v@rbr{\ifnum\vercnt>1\}\else\v@rbend\fi\global\advance\vercnt by -1\relax}
+\def\v@rbparams{\setverb@tim\parskip=\verblineglue\parindent=0pt\raggedbottom%
+\rightskip\z@ plus1fil\pretolerance=10000\tolerance=10000\vercnt=0%
+\catcode124=12\setupt@bs\vskip\verbglue\defb@x\obeylines}
+
+\def\startb@x{\setbox0=\hbox\bgroup}
+\def\defb@x{\def\par{\leavevmode\egroup\box0\endgraf}%
+\everypar{\startb@x}}
+
+{\catcode`\^^I=\active
+\gdef\setupt@bs{\catcode`\^^I=\active
+\setbox0=\hbox{\tt\ }\tabwidth=\wd0\multiply\tabwidth by \tabsize
+\def^^I{\leavevmode\egroup\t@b=\wd0\divide\t@b by \tabwidth%
+\multiply\t@b by \tabwidth%
+\advance\t@b by \tabwidth\advance\t@b by -\wd0\box0\hbox to \t@b{}\startb@x}
+}}
+
+{
+\catcode`[=1\catcode`]=2\catcode123=\active\catcode125=\active
+\gdef\verbatim[\begingroup\v@rbparams\catcode123=\active\catcode125=\active%
+\let{=\v@rbl\let}=\v@rbr\chardef\{=123\chardef\}=125\verblocaldefs
+]]
+
+% Input file verbatim
+% -------------------
+
+\def\verbinput#1{\begingroup\v@rbparams\input #1\endgroup}
+
+% Pictures
+% --------
+% Allowed direction vectors are 0<=x<=6, -6<=y<=6, GCD(x,y)=1
+
+\def\initlines{\font\lif=line10}
+\def\linechar#1#2{\ifnum #1=0 \hbox to 0pt{\hss\vrule height 10pt\hss}\else
+\ifnum #2=0 \vbox to 0pt{\vss\hrule width 10pt\vss}\else
+{\count255=#1\multiply\count255 by 8
+\ifnum #2>0 \advance\count255 by #2 \advance\count255 by -9
+\else\advance\count255 by -#2 \advance\count255 by 55\fi
+\lif\char\count255}\fi\fi}
+\def\picture#1#2#3{\initlines\medskip\centerline{\vbox to #2{\hbox to #1{#3\hss}\vss}}\medskip}
+\def\place#1#2#3{{\setbox0=\hbox to 0pt{#3 \hss}\ht0=0pt\dp0=0pt
+\hbox to 0pt{\hskip #1\lower #2\box0\hss}}}
+\def\pl@celine{\ifnum \count255>0 \place{\dimen0}{\dimen1}{\copy0}\advance\dimen0 by \wd0
+\advance\dimen1 by -\ht0 \advance\count255 by -1 \pl@celine\fi}
+\def\placeline#1#2#3#4#5{{\setbox0=\hbox{\linechar{#3}{#4}}\ifnum #4<0\setbox0=\hbox to -\wd0{\hss\box0}\fi
+\dimen0=#1\dimen1=#2\count255=#5\pl@celine}}
+\def\cplace#1#2#3{\place{#1}{#2}{\hss #3}}
+
+% Let's hide all internal macros
+
+\catcode`@=12