; TeX output 1999.02.25:1514! /XYdict where not{250 dict /XYdict exch def /xy{mark exch XYdict begin countdictstack /xylevel exch def xyopen xycolor mark xypatt xypattern stopped xyclose end cleartomark}def /xyg{gsave xy}def /xyf{currentfont exch xy grestore setfont}def /xycc{{xychgcol}xy}def /xyc{XYdict begin xycolstore end}def /xyx{/xyYpos exch def /xyXpos exch def}def /xyp{currentpoint xyx}def /xyd{setupDirection XYdirection 2 mul}def /xyct{currentpoint xyt 2 copy 6 2 roll}def /xyt{xyXpos xyYpos 2 copy translate}def /xyr{neg rotate xynt}def /xyrs{neg rotate 3 -1 roll sub neg 3 1 roll sub exch moveto xynt}def /xynt{neg exch neg exch translate}def /xys{scale xynt}def /xyss{scale 3 -1 roll sub neg 3 1 roll sub exch moveto xynt}def /xyi{0 0 transform grestore gsave itransform}def }if&! /XYdict where pop begin XYdict begin! /xyopen{currentdict /XYddict known{XYddict null eq{} {XYddict begin xyopen}ifelse}if}def /xyclose{countdictstack -1 xylevel 1 add{pop end}for}def /xychgcol{/xycolor exch def}def /xysetcol{xypush xychgcol}def  ! /xypush{16 dict /XYddict exch def XYddict begin}def /undef where {pop /xypop{countdictstack xylevel eq{}{end}ifelse currentdict /XYddict undef}def} {/xypop{countdictstack xylevel eq{}{end}ifelse /XYddict null def}def}ifelse /pu /xypush load def /pp /xypop load def! /xypspt{72 72.27 div dup scale}bind def /pscorrect{.85 mul}bind def /gstartxy{gsave xypspt xywidth xycap xyjoin xymiter newpath 0 0 moveto}def /xypath{gstartxy rmoveto counttomark 2 idiv -1 1{pop lineto}for}def /xystroke{stroke grestore}bind def /xyfill{closepath fill grestore}bind def /xystfil{closepath gsave fill grestore 0 setgray 0 setlinewidth xystroke}bind def /xyeofill{closepath eofill grestore}bind def ! /xypolyline{xypath xystroke}def /xypolyfill{xypath xyfill}def /xydotsep{/@ currentlinewidth 2 mul def}def /xypolydot{xypath xydotsep [xydt @] 0 setdash xystroke}def /xypolydash{xypath xydotsep [@ @] 0 setdash xystroke}def /xypolyeofill{xypath xyeofill}def /pe /xypolyeofill load def /pl /xypolyline load def /pf /xypolyfill load def /pt /xypolydot load def /pd /xypolydash load def ! /arc4pop{arcto 4{pop}repeat}bind def /xyoval{gstartxy oval closepath xystroke}def /xycircle{gstartxy circle xystroke}def /circle{dup 0 moveto 0 0 3 -1 roll 0 360 arc}def /oval{newpath 2 copy exch 5 index add 2 div exch 3 copy 10 3 roll moveto 1 index dup 5 1 roll 3 index 7 index arc4pop dup dup 4 1 roll 4 index exch 6 index arc4pop 1 index dup 8 1 roll 4 index 4 index arc4pop arc4pop closepath}def /xyellipse{gstartxy counttomark 1 gt{squarify pop pop 1}if circle xystroke}def /ov /xyoval load def /ox /xyellipse load def P! /dotit{dup currentlinewidth 6 mul div round div /@ exch def [xydt @] 0 setdash}def /elldash{dup 4 -1 roll 10 exch div dashit}def /ovdash{dup 10 dashit}def /dashit{div round 2 mul div /@ exch def [@ @] 0 setdash}def /dotcirc{gstartxy cirlen dotit circle xystroke}def /dashcirc{gstartxy cirlen dashit circle xystroke}def /dotoval{gstartxy 5 copy ovlen dotit oval xystroke}def /dashoval{gstartxy 5 copy ovlen ovdash oval xystroke}def /cirlen{dup 6.283185 mul}bind def /ovlen{3 -1 roll sub 3 1 roll sub add exch 1.716815 mul sub}def /dotellipse{gstartxy counttomark 1 gt{squarify pop pop 1}if cirlen dotit circle closepath xystroke}def /dashellipse{gstartxy counttomark 1 gt{squarify add 2 div 1} {1 exch 1 exch}ifelse cirlen elldash circle xystroke}def /ot /dotellipse load def /od /dashellipse load def /vt /dotoval load def /vd /dashoval load def R! /filloval{gstartxy oval xyfill}def /stfiloval{gstartxy oval xystfil}def /fillcircle{gstartxy circle xyfill}def /stfilcircle{gstartxy circle xystfil}def /fillellipse{gstartxy squarify pop pop 1 circle xyfill}def /stfilellipse{gstartxy squarify pop pop 1 circle xystfil}def /squarify{4 copy sub 2 div 3 1 roll sub 2 div translate add 2 div 3 1 roll add 2 div 2 copy scale 2 copy add 2 div currentlinewidth exch div setlinewidth newpath}def /fe /fillellipse load def /sfe /stfilellipse load def /fo /filloval load def /sfo /stfiloval load def /fc /fillcircle load def /sfc /stfilcircle load def ! /xywidth{.4 pscorrect setlinewidth}bind def /xydash{[] 0 setdash}bind def /xycap{1 setlinecap}bind def /xyjoin{1 setlinejoin}bind def /xymiter{10 setmiterlimit}bind def 5! /cc{dup exec xychgcol}def /lw{dup setlinewidth /@l exch def /xywidth{@l setlinewidth}bind def}def /lc{dup setlinecap /@c exch def /xycap{@c setlinecap}bind def}def /lj{dup setlinejoin /@j exch def /xyjoin{@j setlinejoin}bind def}def /ml{dup setmitrelimit /@m exch def /xymiter{@m setmitrelimit}bind def}def ! /setupDirection{dup -2048 lt{3072 add neg 1024 exch} {dup 0 lt{1024 add neg -1024}{dup 2048 lt{1024 sub -1024 exch} {3072 sub 1024}ifelse}ifelse}ifelse atan dup 180 gt{360 sub}if dup /XYdirection exch def rotate}def ! userdict begin /gray{setgray}bind def /gray@{setgray}bind def /rgb{setrgbcolor}bind def /rgb@{setrgbcolor}bind def /hsb{sethsbcolor}bind def /hsb@{sethsbcolor}bind def /setcmykcolor where{pop}{/setcmykcolor{dup 3 1 roll dup 5 1 roll exch sub 1 add 5 1 roll exch sub 1 add 4 1 roll exch sub 1 add 3 1 roll setrgbcolor}bind def}ifelse /cmyk{setcmykcolor}bind def /cmyk@{setcmykcolor}bind def /sethalftone where{/sethalftone load /tone exch def}if /xycolarray 3 array def /xycolstore{currentrgbcolor 2 -1 0 {exch xycolarray 3 1 roll put}for}def xycolstore /xycolor{0 1 2{xycolarray exch get}for setrgbcolor}def /xypatt{}def /xypattern{cleartomark}bind def end ! end end&! /XYdict where pop begin XYdict begin! /:patt {XYddict begin 14 dict begin /BGnd exch def /FGnd exch def /PaintData exch def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne {{begin BGnd aload pop setrgbcolor 0 0 1 1 rF FGnd aload pop setrgbcolor 24 24 true PatternMtx PaintData imagemask end}} {{begin FGnd aload pop setrgbcolor 24 24 true PatternMtx PaintData imagemask end}} ifelse def currentdict PatternMtx end gsave patangle xyland{180 add}if rotate macfreq patfreq div dup neg exch scale matrix currentmatrix grestore gsave setmatrix /DeviceRGB setcolorspace makepattern grestore end}defj! /rF{gsave newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto fill grestore}bind def ! /setpatscreen{/pattstring exch store patfreq patangle xyport not{90 add}if {1 add 4 mul cvi pattstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}setscreen}bind def /setcolpattern{setpatscreen 64 div 1 exch sub currentrgbcolor 1 1 3{pop 1 exch sub 3 index mul 1 exch sub 3 1 roll}for setrgbcolor pop}def /setgraypattern{setpatscreen 64 div setgray}def /macfreq 9.375 def /patangle 0 def /patfreq 12.5 def! /checkland{/normland where{pop normland not}{false}ifelse /xyland exch def /por where{pop por}{/isls where{pop isls not /xyland true def} {/land where{pop land not}{true} ifelse}ifelse}ifelse /xyport exch def}def *! /setpatfreq{/patfreq exch def}def /setpatangle{/patangle exch def}def /setbackcolor{/backcolor exch def}def /setforecolor{/forecolor exch def}def [1 1 1] setbackcolor xycolarray setforecolor /bg /setbackcolor load def /fg /setforecolor load def /pa /setpatangle load def /pq /setpatfreq load def ! /xypattern{checkland counttomark dup 0 eq{pop} {dup 1 eq{pop setpatscreen} {dup 2 eq{pop setcolpattern} {dup 3 eq{pop /setcolorspace where { /.setcolorspace where{pop pop pop setcolpattern} {/.buildpattern where {pop forecolor backcolor :patt setpattern }{pop pop setcolpattern}ifelse}ifelse} {pop setcolpattern}ifelse} {5 eq{/setcolorspace where{ /.setcolorspace where{pop pop pop pop pop setcolpattern} {/.buildpattern where {pop :patt setpattern }{pop pop pop pop setcolpattern}ifelse}ifelse} {pop pop pop setcolpattern}ifelse }{}ifelse}ifelse}ifelse}ifelse}ifelse cleartomark }def /xysetpattern{/xypatt exch def}def /sp /xysetpattern load def ! end end&! /XYdict where pop begin XYdict begin! /xysize 10 def /T true def /F false def /dimendiv{65536 div}bind def /xysegl 327680 dimendiv def /xyopp{1 -1 scale}bind def /xynormwidth{26213 dimendiv pscorrect}bind def /xywidth{xynormwidth setlinewidth}bind def ! /xyfont{4096 add 64 div round 64 mul 4096 sub}def /xydt 0.01 def /xysdfont{4096 add 32 div round 32 mul 4096 sub}def /xydots{xywidth 1 setlinecap [xydt 2] 0 setdash}bind def /f /xyfont load def /fs /xysdfont load def! /xyCheckDir{dup 8 div 3 mul 3 -1 roll sub neg exch div 360 mul dup dup XYdirection sub 180 div round 180 mul XYdirection add dup 3 -1 roll sub abs 10 gt not{exch}if pop}def G! /xyrulth{26213 dimendiv pscorrect setlinewidth 0 setlinecap}bind def ! /gsavexy{gsave xypspt XYdirection rotate xywidth newpath 0 0 moveto}def /gchksavexy{gsave xypspt setupDirection xywidth newpath 0 0 moveto}def m! /xyswap{XYdirection 180 add /XYdirection exch def}def /xyline{gstartxy setupDirection rlineto xystroke}def ! /dash{exch gchksavexy xysegl XYdirection dup -90 lt{pop neg}{90 gt{neg}if}ifelse exch{neg}if 0 rlineto xystroke}def /stopper{gstartxy setupDirection 0 xysegl 2 div rmoveto 0 xysegl neg rlineto xystroke }def /d /dash load def /st /stopper load def! /solid{gstartxy xydash neg exch neg exch rlineto xystroke}def /dashed{gstartxy 2 copy dup mul exch dup mul add sqrt dup xysegl add xysegl 2 mul div round 2 mul 1 sub div [ exch dup ] 0 setdash neg exch neg exch rlineto xystroke}def /l /solid load def /dd /dashed load def! /dot{gstartxy 2 setlinecap [xydt 2] 0 setdash 1 0 rlineto xystroke}def /dotted{gstartxy 2 copy dup mul exch dup mul add sqrt dup 2 div round 1 add div 2 setlinecap [xydt 3 -1 roll] 0 setdash neg exch neg exch rlineto 0 0 rlineto xystroke}def /p /dot load def /dt /dotted load def! /cubic{gstartxy docubic} def /docubic{chkvalid {chkcubedge 8 -2 roll moveto curveto xystroke pop} {cleartomark grestore}ifelse}def /chkcubedge{2 copy 1.0 eq{0.0 eq{pop pop}{cubicedge}ifelse} {pop cubicedge}ifelse}def /bz /cubic load def! /dotcubic{gstartxy 1 setlinecap [xydt 2] 0 setdash docubic}def /dashcubic{gstartxy [5 5] 0 setdash docubic}def /bt /dotcubic load def /bd /dashcubic load def! /squine{gstartxy dosquine}def /dosquine{chkvalid {chksquedge 2 copy moveto xysq2cub curveto xystroke pop} {cleartomark grestore}ifelse}def /q /squine load defD! /chkvalid{2 copy lt{dup 1 gt{false}{true}ifelse}{false}ifelse}def ! /chksquedge{2 copy 1.0 eq{0.0 eq{pop pop}{squineedge}ifelse} {pop squineedge}ifelse}def /xysq2cub{xysq2cubit 6 1 roll xysq2cubit 6 1 roll 3 index 3 index xysq2cubit 6 1 roll xysq2cubit 6 1 roll pop pop}def /xysq2cubit{2 index 2 mul add 3 div}def ! /dotsquine{gstartxy 1 setlinecap [xydt 2] 0 setdash dosquine}def /dashsquine{gstartxy [5 5] 0 setdash dosquine}def /qt /dotsquine load def /qd /dashsquine load def! /xy4mul{8 copy 5 -1 roll mul 5 1 roll 6 -1 roll mul 6 1 roll 3 -1 roll mul exch 4 -1 roll mul 3 1 roll add 3 1 roll add exch 10 2 roll 7 -1 roll mul 7 1 roll 4 -1 roll mul 5 1 roll 4 -1 roll mul 4 1 roll mul add 3 1 roll add exch 3 -1 roll }def ! /xy44mul{4 copy 16 4 roll exch 3 1 roll 4 copy 12 4 roll xy4mul 12 4 roll xy4mul 12 -4 roll 4 copy 16 4 roll 8 4 roll xy4mul 12 4 roll xy4mul}def M! /cubicedge{10 2 roll exch 8 1 roll 3 -1 roll dup dup 9 2 roll 5 -1 roll dup dup 9 1 roll 8 3 roll 4 1 roll dup dup 5 3 roll dup dup 5 1 roll 3 -1 roll 18 -2 roll 2 copy 1 sub neg 4 1 roll 1 sub neg exch 4 1 roll xy444mul pop pop pop 13 1 roll pop pop pop 9 1 roll 10 1 roll pop 8 1 roll 7 1 roll 8 1 roll pop 5 1 roll 3 1 roll}def ! /xy444mul{4 copy 24 4 roll 12 -4 roll 16 4 roll 4 copy 16 4 roll xy44mul 20 8 roll xy44mul 12 -4 roll 4 -1 roll 7 1 roll exch 4 1 roll exch 6 -1 roll exch 4 2 roll 16 8 roll 8 4 roll 4 -1 roll 7 1 roll exch 4 1 roll exch 6 -1 roll exch 4 2 roll 8 4 roll 16 4 roll 8 4 roll 20 -4 roll exch 3 1 roll 4 copy 20 4 roll 4 copy 16 4 roll 4 copy 12 4 roll xy4mul 28 4 roll xy4mul 20 4 roll xy4mul 12 4 roll xy4mul}def ! /squineedge{8 2 roll exch 5 1 roll 3 -1 roll dup 6 2 roll 1 index exch 10 -2 roll 2 copy 1 sub neg 4 1 roll 1 sub neg exch 4 1 roll xy44mul 4 1 roll pop 5 1 roll 6 1 roll 3 -1 roll pop}def c! /xyshort{2 copy abs exch abs add xysegl .5 mul lt {pop pop grestore}{rlineto xystroke}ifelse}def s! /tipwidth{xywidth xynormwidth dup currentlinewidth exch div sqrt dup dup scale mul setlinewidth 1 setlinecap}def ! /halftip{tipwidth xysize 10 div 0 0 moveto -.25 0 3 -1 roll -2.5 mul 0 xysize 2 div neg dup .62 mul 2 div neg curveto}bind def ! /atip{gchksavexy halftip xystroke}def /btip{gchksavexy xyopp halftip xystroke}def /tip{gchksavexy gsave halftip stroke grestore xyopp halftip xystroke}def /t /tip load def /a /atip load def /b /btip load def@! /cmatip{gchksavexy halfcmtip xystroke}def /cmbtip{gchksavexy xyopp halfcmtip xystroke}def /cmtip{gchksavexy gsave halfcmtip stroke grestore xyopp halfcmtip xystroke}def /halfcmtip{tipwidth 0 0 moveto -.1333 0 .25 neg dup .125 3 -1 roll .25 curveto}bind def /ct /cmtip load def /ca /cmatip load def /cb /cmbtip load def2! /xyfscale{/xyfsize exch def}def /xyfsize{10}def /eu{-0.0551 0.0643 -0.0976 0.1386 -0.125 0.2188}def /cm{-0.105 0.0437 -0.1804 0.1380 -0.2 0.25}def /XY{-0.1753 0.0181 -0.3452 0.0708 -0.5 0.155}def /tipstart{3 -1 roll gchksavexy exch xyfscale tipwidth dup XYdict exch known{dup /xy eq{pop /XY}if}{pop /XY}ifelse XYdict exch get}def /tipend{halfxytip xystroke}def /halfxytip{1 1 6{pop xyfsize mul 6 1 roll}for 0 0 moveto curveto}def /A{tipstart D}def /B{tipstart C}def /C{xyopp D}def /D{exec tipend}def /AB{tipstart dup gsave exec halfxytip stroke grestore C}def ;! /Tip{exch gchksavexy /xyfsize{10}def tipwidth gsave dup XYdict exch known{dup /xy eq{pop /XT}if}{pop /XT}ifelse XYdict exch get dup halfTip stroke grestore xyopp halfTip xystroke}def /XT{360 32 div neg}def /Xt{-1 .31 mul 1 atan}def /ET{360 64 div 5 mul neg}def /Et{-1 .31 mul 1 atan}def /halfTip{exec rotate XY halfxytip}def /halfTtip{halfTip}def /Ttip{exch gchksavexy /xyfsize{10}def tipwidth gsave dup XYdict exch known{dup /xy eq{pop /Xt}if}{pop /Xt}ifelse XYdict exch get dup halfTtip stroke grestore xyopp halfTtip xystroke}def /tt /Tip load def /tT /Ttip load def! /halfturn{xysegl 2 div dup dup neg exch rmoveto 0 exch dup exch -180 -90 arc}bind def /aturn{gchksavexy halfturn xystroke}def /bturn{gchksavexy xyopp halfturn xystroke}def /ta /aturn load def /tb /bturn load def! /xysqll 231705 dimendiv def /squigl{gchksavexy xysqll dup neg 0 rmoveto 2 div dup dup neg dup 3 -1 roll 2 sqrt mul dup 5 1 roll 135 45 arcn dup 3 -1 roll -135 -45 arc xystroke}def /g /squigl load defk! /fullhook{0 xysegl 2 div dup -90 90 arcn}bind def /halfhook{xysegl 2 div dup 0 exch 180 90 arcn}bind def ! /ahook{gchksavexy fullhook xystroke}def /bhook{gchksavexy xyopp fullhook xystroke}def /hook{gchksavexy gsave halfhook stroke grestore xyopp halfhook xystroke}def /h /hook load def /ha /ahook load def /hb /bhook load defe! /xyqcirc{dup dup neg exch translate newpath dup neg 0 exch moveto 0 0 3 -1 roll -90 0 arc}bind def x! /circ{gstartxy 3 copy pop 2 copy cos mul 3 1 roll sin mul rmoveto 0 0 5 2 roll arc xystroke}bind def /o /circ load def! /circhar{gsave dup 3 gt{7 sub neg}if dup 3 eq{pop dup 2 sqrt -2 div mul}{dup 1 eq{pop dup 2 sqrt 2 div mul} {0 eq{dup}{0}ifelse}ifelse}ifelse 0 translate 3 1 roll circ grestore}bind def /c /circhar load def ! end end*tj??]wheader=color.pro4 bDtGGcmr17X>Y-pic7tUser'sGuide!xXQ cmr12Kristo erH.Rose !", cmsy10hkrisrose@ens-lyron.fri2 K cmsy8gVVersion3.7,February16,1999(1t^"t : cmbx9Abstract X0o cmr9X9Y-picisapac9k|ragefortypAesettinggraphsanddiagrams usingKn9uth'sTuAEXtypAesettingsystem.X9Y }-picworkswithmostAfoftheman9yformatsav|railable;Wn#j cmti9e.g.,iplainTuAEX,L5Aacmr6A TuAEX,and% cmsy9AuAM]>S-TuAEX.Sev9eralstylesofinputforv|rariousdiagram8t9ypAesaresupported;Jtheyallshareamnemonicnotationbasedonthelogical/compositionofvisualcom-ponents. ( Thisnguideconcen9tratesonhowtotypAeset\matrix-lik9e"diagrams,6suchascommutativediagrams,inTthefollo9wingstyle:9ps: SDict begin xyc end$5" cmmi9UgE" {mark 50.14008 -73.29996 15.18234 -43.44832 0.0 0.0 1.0 0.0708 q}xy)r;cmmi6y2sA#" {2131 10 /xy AB}xygI" {mark 50.14008 -73.29996 15.18234 -43.44832 0.0 0.0 0.0708 0.90125 q}xygF" {mark 50.14008 -73.29996 15.18234 -43.44832 0.0 0.0 1.0 0.90125 q}xygF" {mark 100.82085 -36.64998 54.62184 -7.08963 0.0 0.0 1.0 0.06104 q}xy:真zxdI#'" {2451 10 /xy AB}xygJ" {mark 100.82085 -36.64998 54.62184 -7.08963 0.0 0.0 0.06104 0.92297 q}xygF" {mark 100.82085 -36.64998 54.62184 -7.08963 0.0 0.0 1.0 0.92297 q}xy GbǤ" {0.01512 -0.0732 dt}xye@(x;y7)m S@" {13.16548 -9.61855 dt}xy/^" {2324 10 /xy AB}xy/^" {13.18306 -9.61855 dt}xy/^" {0.0327 -0.05577 dt}xy(C%X“ZGYg8ŝ+9" {0.0 0.0 l}xy;ŝ5Sq8ŝA" {1024 10 /xy AB}xyg8ŝC9" {0.0 -24.0 l}xyg8ŝC9" {0.0 0.0 l}xyLG"" {0.0 0.0 l}xyP/U( pdG"" {3072 10 /xy AB}xydG"" {24.0 0.0 l}xydG"" {0.0 0.0 l}xygG%Xgks*" {0.0 0.0 l}xyd)96WfksA" {1024 10 /xy AB}xygksC9" {0.0 -24.50002 l}xygksC9" {0.0 0.0 l}xy5PJ>cY?{G+1" {0.0 0.0 l}xyP.rCgdoG+1" {3072 10 /xy AB}xydoG+1" {37.50201 0.0 l}xydoG+1" {0.0 0.0 l}xygoJ>cZ[!{w9asTtypAesetbythe(X9Y 1-picinputlines&ߤN cmtt9\xymatrix{U\ar@/_/[ddr]_y\ar@/^/[drr]^x,\ar@{.>}[dr]|-{(x,y)}8\\ s,&X\times_ZY\ar[d]^q\ar[r]_pPR&X\ar[d]_f!\\ s,&Y\ar[r]^g,&ZK`}Suc9hTdiagramshavethefollowingcharacteristics:`SpAeci edKasamatrixofen9triesthatareautomati-callyTalignedinro9wsandcolumns.`An9yentrymaybAeconnectedtoanyotheren-tryusingav|rariet9yofarrowstylesallrotatedandstretc9hedTasrequired.`Arro9wsmaybAedecoratedwithlabelsthataretiedtoNaspAeci edpoin9talongthearrowandextendinaYparticulardirection;#\andarro9wsmaybAepaired,cross,NandC@visit/bAendaroundotheren9tries\onthew9ay:."Sev9eraln!otherstylesofinputaresuppAorted;ashortsurveyofSthepAossibilitiesisincludedlastattheendalongwithinformationTonho9w(X9Y 1-piccanbAeobtained. (Nff cmbx12Contents)"V cmbx10Preface21t21 3Basics62 g 3K`y cmr101.1#7Loading8.................2 31.2#7Entries|..................2 31.3#7Arrowsҍ..................2 31.4#7LabGels..................3 31.5#7BreaksU ..................3 31.6#7Curvingx.................4 31.7#7SpGeedingUUuptypesetting* ........4Э22 3MoreTArro9wsandLabQelsS4 32.1#7ExplicitUUlabGelpositioning⍍.......4 32.2#7LabGelingUUwithanyob8ject1&........5 32.3#7MoreUUarrowstylesL............5 32.4#7SlidingUUarrowssideways........6 32.5#7MoreUUtargets*?..............6 32.6#7ChangingUUthetarget⍍..........7 32.7#7ArrowsUUpassingunderM.........7 32.8#7MoreUUbGendingarrowsǍ..........8 32.9#7De ningUUnewarrowtypGes.......823 3MoreTEn9tries9 33.1#7ManualUUentryformatting΍........9 33.2#7ExtraUUentriesoutsidethematrix7...9 33.3#7SpacingUUandrotation..........9 33.4#7EntryUUstyleƸ...............10 33.5#7NamingUUforlateruseastargets....10 33.6#7GroupingUUob8jects;􍍑............1024 3Av\railabilit9yTandF urtherInformation11 34.1#7GettingUQXY U-pic#..............11 34.2#7BackwardsUUcompatibilityz........11 34.3#7F*urtherUUreadingTߍ.............12 34.4#7Credits?..................132A 3Answ9ersTtoallexercisesS132ReferencesZ142Indexޕ15ff[ A ß-:!q% cmsy6L|{Ycmr8Lab'ExXfortypGeset-ting#mathematics,*': cmti10e.g.,havestudied[2,ch.16{19],[3,sec.3.3],$Wor[9],andthatXY z-picisinstalledonyourTU>'ExXsystemasdescribGedinthe+ cmmi10AǍ9R." {0.0 20.2825 -8.57004 -20.2825 8.57004 ov}xy(u cmex10P,3; 0ercmmi7m%3;i=nC"=3i^27HR&Bi( Df ^" {-0.02948 0.06422 l}xyE"3" {-1798 10 /xy AB}xyE"3" {-32.95901 24.92227 l}xyE"3" {-0.0483 0.04208 l}xy9~eKwasUUtypGesetbyN8eK\xymatrix{EA?&*+[F]{\sum_{i=n}^m{i^2}}\\e?&?{\bullet}&D\ar[ul]?}eKNoticeUUthefollowing:6CeLeMentriesaretypGesetasmathematics(using\texteMstyle");wentries2shouldnotstartwithamacroeM(asX|illustratedbytheuseof{}0around\bullet(."eLeMallentriesarecenteredandtheseparationbGe-eMtweenQrowsandcolumnsisusuallyquitelargeeMinUUadiagram,eLeMemptykentriesattheendofrowsmaybGeomit-eMted,eLeM\XY -decorations"J(here\ar[ul]) )inentriesal-eMlowdrawingofarrowsandsuchrelativetotheeMentrieswithoutchangingtheoveralllayout,andeLeM\XY -moGdi ers" (here*+[F]O) rstinentriesal-eMlow changingtheformatandshapGeinmanyeMways.deK1.3%KArrowsuTeKAnV\arrow"inanVXY ֋-picdiagramisagenerictermeKforuthedrawndecorationsbGetweentheentriesoftheeKbasic9matrixstructure.[rIn5XY #9-picallarrowsmustbGeeKspGeci edKalongwiththeentryinwhichtheystart;dthiseKisǶcalledtheirb}'aseentry.BEachparticulararrowcom-eKmand|thenrefersexplicitlytoitstar}'getgentry. "5-:2LIfyÎouusetheversion2loadingcommand\inputxypicH(orthexypicdostyle[[Xhop]ᕲ.ȧThiswillbGedescribedinhZmoredetailinsection2.3;YherewejustlistthemostcommonUU@style[s(obviousvqariationsalsowork):N8ps: SDict begin xyc endY퓞" {0.02264 -0.00824 l}xyl" {0.02264 -0.00824 l}xy " {1498 /XT tt}xyY V(" {8.95447 -19.33655 l}xyl V(" {8.95447 -19.33655 l}xy@{=>} N8ps: SDict begin xyc end̞" {0.02264 -0.00824 dt}xy " {1498 10 /xy AB}xy " {10.0 -21.60004 dt}xy " {0.02264 -0.00824 dt}xy @{.>}8 N8ps: SDict begin xyc endY퓞" {0.02264 -0.00824 dt}xyl" {0.02264 -0.00824 dt}xy " {1498 /XT tt}xyY V(" {8.95447 -19.33655 dt}xyl V(" {8.95447 -19.33655 dt}xy, @{:>}\KN8ps: SDict begin xyc end " {1498 10 /xy AB}xy$  " {1498 g}xyw " {1498 g}xy " {1498 g}xyPK@{~>}N8ps: SDict begin xyc end̞" {0.02264 -0.00824 dd}xy " {1498 10 /xy AB}xy " {10.0 -21.60004 dd}xy " {0.02264 -0.00824 dd}xyt@{-->} ПN8ps: SDict begin xyc end̞" {0.02264 -0.00824 l}xy " {10.0 -21.60004 l}xy " {0.02264 -0.00824 l}xy @{-} şN8ps: SDict begin xyc end @{}:ExerciseT2: TypGeset?xps: SDict begin xyc endڪǍ8" {0.0 0.0 dd}xyǍ8" {0.0 -24.0 dd}xyǍ8" {0.0 0.0 dd}xy Q'" {0.0174 -0.01903 l}xy #h" {0.0174 -0.01903 l}xy#Q"" {24.3924 -24.0 l}xy"#" {24.3924 -24.0 l}xy#Q"" {0.0174 -0.01903 l}xy"#" {0.0174 -0.01903 l}xy " {0.0 0.0 l}xy#" {23.99998 0.0 l}xy#" {0.0 0.0 l}xy&ڪǍ(8" {0.0 0.0 dt}xyǍ(8" {0.0 -24.0 dt}xyǍ(8" {0.0 0.0 dt}xy"Lp&"Lp# " {0.0 0.0 l}xy  " {-1024 10 /xy AB}xy  " {-23.99998 0.0 l}xy  " {0.0 0.0 l}xy.B1.4LLab`elsuTY*oucanputlabGelsonarrows.GLabelsareconceptual- izedUassub-andsupGerscriptsonarrowssuchthattheyareKplacedintheusualpGositions(as\limits"),Mi.e.,^reads4\abGove"and_\bGelow"onanarrowpGointingright.ЭNoticeLthatthepGositionsdependonlyɲonthedirectionofthearrow,Ptheabsolutenotionsof\up,"\down,"UUetc.qarenotimpGortant.qF*orexample,N8$\xymatrix@1{X\ar[r]^a_b?&Y&Z\ar[l]^A_B}$hwillXsetps: SDict begin xyc end!ǵXƟ" {0.0 0.0 l}xyǴa ~8b%Ɵ" {3072 10 /xy AB}xy%Ɵ" {22.0 0.0 l}xy%Ɵ" {0.0 0.0 l}xy&ƞ!ǵYH!ZE" {0.0 0.0 l}xy7jPA7B/" {-1024 10 /xy AB}xy/" {-21.99998 0.0 l}xy/" {0.0 0.0 l}xyV{(the@1isaspGecialcodeothatvcanbGeusedfor\one-line"diagramstoimprovetheplacementontheline;M7moresuchspacingcoGdesareUUdescribGedinsection3.3).It]ispGossibletouselabelsthatarenotsinglelet-ters,ídigits,orzhcontrolsequences:ifasimplemathformulaFinthedefaultstyle(scriptstyle)isdesiredthenksimplyenclosein{ ...}꧲. InkpracticeanythingcanUUbGeusedasalabelasdescribedinsection2.2.EachlabGelisplacedperpendiculartothearrowattheUpGointhalfwaybGetweenthecentersofthebaseandtargetSaob8jects.kThisisusuallythemoststhethic,however,inHdiagramswherethesizesoftheentriesvqary?muchitissometimesnicertoplacethelabGelatthecenteroftheactualarrow.ThisbGehaviourisrequestedbyinsertinga-(minus)rightafterthe^卑orUU_R:qps: SDict begin xyc end!ǵA8BQCDJ4" {0.0 0.0 l}xyRlq+`4" {3072 10 /xy AB}xy`4" {22.0 0.0 l}xy`4" {0.0 0.0 l}xya4!ǵBtwasUUtypGesetbygweK$\xymatrix@1{ HA\times?B\timesC\timesD\ar[r]^-{+}&BeK}$<eK(it=bGecomesps: SDict begin xyc end!ǵA8BQCDJ4" {0.0 0.0 l}xyBtq+`4" {3072 10 /xy AB}xy`4" {22.0 0.0 l}xy`4" {0.0 0.0 l}xya4!ǵBp[withoutthe-:). eKIn!fact- ?isinjustoneofthemaypGossibleplacingseKofUUlabGelsdescribedinsection2.1."HۍeKExerciseó3: TypGesetFthesecondaxiomofcategoryeKtheoryUUas9 '?~ps: SDict begin xyc end qA " {0.0 0.0 l}xyMEVf%" {3072 10 /xy AB}xy%" {23.99998 0.0 l}xy%" {0.0 0.0 l}xy Z" {0.02487 -0.02586 l}xy lf;g% q" {2074 10 /xy AB}xy% q" {24.63425 -24.0 l}xy% q" {0.02487 -0.02586 l}xy( qBǍ,j" {0.0 0.0 l}xy/g, q" {1024 10 /xy AB}xyǍ,j" {0.0 -24.0 l}xyǍ,j" {0.0 0.0 l}xy3B" {0.04977 -0.02951 l}xyB^ҟ g@L;hL2 q" {2088 10 /xy AB}xyL2 q" {24.98727 -24.0 l}xyL2 q" {0.04977 -0.02951 l}xy(%ŵC3y"w" {0.0 0.0 l}xy=] *ShK8"w" {3072 10 /xy AB}xyK8"w" {24.11215 0.0 l}xyK8"w" {0.0 0.0 l}xyN8%ŵD9ʟ$HۍeK1.5%KBreaks]ꍒeKItisalsopGossibleto\break"anarrowwithalabelus-eKinghthe|character:$\xymatrix@1{A\ar[r]|f&B}$ eKwillUUsetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xyMaǴfM" {7.80464 0.0 l}xy#" {3072 10 /xy AB}xy#" {9.51126 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB2뎲.#eKIf$youjustwantanemptybreakyoushould PeKusethespGecial\holebreak:thearrowps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy" {7.14668 0.0 l}xy#" {3072 10 /xy AB}xy#" {8.8533 0.0 l}xy#" {0.0 0.0 l}xy$!BeKwasotypGesetbyincluding$\xymatrix@1{eKA\ar[r]|\hole?&B}$UUinthetext. eKA<di erent<useofbreaksistoplacealabGelsome-eKwhere.inadiagramoutsidethenormalmatrixmesh:eKthisisaccomplishedby\breaking"aninvisiblearroweKobtainedUUusingthe@{}arrowstyle:qthesquare ):;ps: SDict begin xyc endK qApd=Ǎ j" {0.0 0.0 l}xy  q" {1024 10 /xy AB}xyǍ j" {0.0 -24.0 l}xyǍ j" {0.0 0.0 l}xy " {0.0 0.0 l}xy&8" {3072 10 /xy AB}xy&8" {24.29338 0.0 l}xy&8" {0.0 0.0 l}xy)8 qBǍ-!Tj" {0.0 0.0 l}xy-!T q" {1024 10 /xy AB}xyǍ-!Tj" {0.0 -24.0 l}xyǍ-!Tj" {0.0 0.0 l}xy%B9"w" {0.0 0.0 l}xy&2"w" {3072 10 /xy AB}xy&2"w" {24.11214 0.0 l}xy&2"w" {0.0 0.0 l}xy)2%C=󵍒eKwasUUtypGesetbyN8eK\xymatrix{\ar?@{}[dr]|{=}HA?\ar[d]\ar[r]&B\ar[d]\\HB?\ar[r])&C}MeKThereUUismoreonbreaksinsection2.7."HۍeKExercise4: TypGeset*|the rstaxiomofcategoryeKtheoryUUasthedisplay 6۵ps: SDict begin xyc end  qAǍ j" {0.0 0.0 l}xyqf  q" {1024 10 /xy AB}xyǍ j" {0.0 -24.0 l}xyǍ j" {0.0 0.0 l}xyo!" {0.0 0.0 l}xybEVf)<" {3072 10 /xy AB}xy)<" {24.29338 0.0 l}xy)<" {0.0 0.0 l}xy,< qB*"" {0.0 -0.0101 l}xyZܞimO \cmmi5B 2 :" {-9.48961 -9.18126 l}xyQ q" {-34 10 /xy AB}xyQ q" {-9.4896 -9.18124 l}xyQ q" {0.0 -0.0101 l}xyǍ0Xj" {0.0 0.0 l}xy3Xg0X q" {1024 10 /xy AB}xyǍ0Xj" {0.0 -24.0 l}xyǍ0Xj" {0.0 0.0 l}xy%ŵB="w" {0.0 0.0 l}xy(zg)"w" {3072 10 /xy AB}xy)"w" {24.11214 0.0 l}xy)"w" {0.0 0.0 l}xy,%ŵC:CLWK3y*tj??X1.6LCurvinguTArrowsDcanbGemadetocurve, forexampletoavoid goingthroughanotherentry*, GusingthespGecialstyle@/ curving}/"z.^TheNsimpleststylesofcurving1;arethefollowing,UUshownappliedtoanarrowfromAtoBq:f͡ps: SDict begin xyc end @/^/D qA@" {mark 89.41823 0.0 70.52153 12.0 51.62483 0.0 1.0 0.17871 q}xyg@ğx" {2668 10 /xy AB}xyD" {mark 89.41823 0.0 70.52153 12.0 51.62483 0.0 0.17871 0.81372 q}xy@" {mark 89.41823 0.0 70.52153 12.0 51.62483 0.0 1.0 0.81366 q}xyj? qB q@/_/DAQ" {mark 89.41823 -20.03339 70.52153 -32.03339 51.62483 -20.03339 1.0 0.17871 q}xyg@ğM" {3476 10 /xy AB}xyU" {mark 89.41823 -20.03339 70.52153 -32.03339 51.62483 -20.03339 0.17871 0.81372 q}xyQ" {mark 89.41823 -20.03339 70.52153 -32.03339 51.62483 -20.03339 1.0 0.81366 q}xyj?B(Q@/_1pc/D)AQ" {mark 89.41823 -40.06677 70.52153 -64.06677 51.62483 -40.06677 1.0 0.15894 q}xyhIT,y" {3953 10 /xy AB}xyU" {mark 89.41823 -40.06677 70.52153 -64.06677 51.62483 -40.06677 0.15894 0.84106 q}xyQ" {mark 89.41823 -40.06677 70.52153 -64.06677 51.62483 -40.06677 1.0 0.84106 q}xyj?)B" {mark 72.5903 0.0 36.29515 12.0 0.0 0.0 0.08081 0.46774 q}xyRt,)" {2854 10 /xy AB}xy=" {mark 72.5903 0.0 36.29515 12.0 0.0 0.0 0.53226 0.8247 q}xy:" {mark 72.5903 0.0 36.29515 12.0 0.0 0.0 1.0 0.82465 q}xyUr!ǵf(x):" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 1.0 0.1753 q}xy3៟ fr 0ncmsy5Zcmr51>" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 0.1753 0.40353 q}xyqi" {-1308 10 /xy AB}xy?" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 0.59647 0.91931 q}xy;" {mark 0.0 0.0 36.29515 -12.0 72.5903 0.0 1.0 0.91931 q}xy1.7Sp`eedinguptypesettinguTOne!thingthatyouwillnoticeisthat!XY -picissome-timesslowintypGesettingdiagrams(thisistobeex-pGectedڳconsideringthenumberڳofdrawingoperationspGerformed@asre ectedbythenumbGerlastineachxymatrix.message).Ifyoufollowtheruleofstart-ing(xallentrieswitha(nonexpandable)characteror{thenUUyoucaninsertthedeclaration ff2 H\CompileMatrices(ff2XinYthepreambleofyourdoGcument:zthiswillcreatetempGorary les^5kmcontainingc}'ompiledversionsofeachXeKmatrixNathatcanbGeloadedveryquickly;Ptheyareau- eKtomaticallyUUrecreatedwhenamatrixischanged. eKIfthiscausessomediagramstonotwork,theneKsuch compilationcanbGeexplicitlyswitchedo byeKusingƄ\xymatrixnocompileinplaceof\xymatrix4i.eKCompilationcanbGeswitchedo completelywitheK\NoCompileMatrices\(whichrespGectsTU>'ExXgroupingeKasUUdoGes\CompileMatrices,bytheway).eKAnd>ifyouarestillnotsatis edwiththespGeedeKthenUUyoucanaddthefollowing:eKgZff2 P̭\OnlyOutlinesff2which|willomitallcompiledpictures;etheadditionalcommand{\ShowOutlineswilladdadottedrectangleoutliningUUthesizeofthepicture.)/Y2LMoreffArrowsandLabs3els⍲InthissectionweexplainanumbGerofvqariationsoftheRarrowcommandsthatareusefulincommutativediagrams.$ˍ2.1Explicitlab`elpositioningNTheh(labGelcommandsexplainedinsection1.4placethelabGeltextnearthepointalongthearrowhalfwaybGetweenvthecentersofthebaseandtargetentries.This,2however,mayןbGechangedbyinsertingaplac}'ebGetweenthe^,;_,or|,andtheactuallabGel(infact-isUUaplac}'e[).qIngeneralyoumayinsertthefollowing:Í<willplacethelabGelatthepointwheretheactualarrowbGegins, i.e.,\appearsfromunder"thebase,Fso$\xymatrix@1{A\ar[r]^<{+}&B}$ɍwillUUtypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy n9q+#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB/9.荍Similarly*,T> vwillplacethelabGelatthe *pGointwheretheactualarrowends,i.e.,\disappGearsbelow"thetarget,so $\xymatrix@1{A\ar[r]^>{+}&B}$willtypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy n8q+#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB/9.荍<< pKand>>willplacethefollowingla-bGelJatapointjustabit^6 $furtherfromthe 7&bGeginningandendofthearrow,so l$\xymatrix@1{A\ar[r]^>>{+}&B}$willtypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xyn8q+#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB/9. *Using^more< ([sor>swill moveUUthelabGelfurtherin.ffff[ J= "5-:5LTheXtemp "5-:6L\AXbit"isinfactaTAEMX\jotwhicÎhisusually3pt.LWK4]*tj??O]w\Afactor$in()s: [e(ba) !indicatesthatthe labGelyshouldbe\tied"tothepointaoftheewayfromthecenterofthebaseen-try(called(0))tothecenterofthetar-get (called(1))insteadofinthemiddle,so,$\xymatrix@1{A\ar[r]^(.3){+}&B}$willɍtypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy ѓq+#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB/9.AUqfactorVcanbGegivenafter jHsome<sor>s,>inwwhichcasetheplaceiscomputedasֳifthebasewasspGeci edbythe<sand$targetspGeci edbythe> !s.4Hence$\xymatrix@1{A\ar[r]^<(0){+}&B}$KUwilltypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy n9q+#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!ǵB/9.Finally*,there*isasimpleway*todenotetheplace@onanarrowwhereitintersectswithastraight-linebGetweentwopGoints: vtheplace!{ t1|s; pt2|s} ߆places#thelabGelrelativetothepointonthearrowwherethelinefromthetargett1to;-thetargett2crossesit.#NBug:=vOnlyworksforUUstraightarrowsatpresent.S~As;usualmorepGossibilitiescanbefoundintherefer-enceUUmanual[8, g.q2].ލExerciseT6: TypGeset ps: SDict begin xyc end ڪ1" {0.0 0.0 l}xy+DZ1000000xd" {3072 10 /xy AB}xyd" {81.50008 0.0 l}xyd" {0.0 0.0 l}xyk" {0.01772 -0.06744 l}xyp n2000x,eV" {25.61868 -18.70604 l}xy6xڪ" {2326 10 /xy AB}xy6xڪ" {4.35013 -3.21692 l}xy6xڪ" {0.03134 -0.05203 l}xygڪ1000000%Lp1000"" {0.0 0.0 l}xy!Y)e2x2"" {3072 10 /xy AB}xy2"" {24.0 0.0 l}xy2"" {0.0 0.0 l}xy" {0.0 0.01617 l}xy[Kxr2f$ڪ" {3419 10 /xy AB}xyf$ڪ" {76.14337 25.81694 l}xyf$ڪ" {0.0 0.01445 l}xy5%Lp20007ލ2.2LLab`elingwithanyobject XY -piczBsuppGortsageneralformatforenteringanyTU>'ExXtexteZaslabGels(aswellasentriestobGeexplainedlater).The"character* isreservedforthis: #initssimplestform +*{%mathc} will +typGesetthemath͎materialasanob8ject.Thisiislike{ Wfmathc} ɲexceptthatthedefaultstyleUUisignoredandthereisnoaddedblankmargin. ՍHowever,\in[5generalthefollowingformof*obje}'ctisUUavqailable: ff2 9N{?*SegrowUUbydimenw\Q+=Ff,growUUtoenclosingsquare Q-Ff,shrinkQ-<dimenc>Ff,shrinkUUbydimenQ-=Ff,shrinktocontainedsquareQ!Ff,doUUnotcenterQ[o]Ff,roundQ[l]UU[r][u][d]Ff,adjustUUleft,right,...Q[F]UU[F=]Ips: SDict begin xyc endW(" {0.0 15.70836 -6.0 -15.70836 6.0 ov}xyUUfdframeops: SDict begin xyc end'" {0.0 17.77782 -6.0 -17.7778 6.0 ov}xy'" {0.0 15.77782 -4.0 -15.7778 4.0 ov}xyUUfddoublefdQ[F.]UU[F--]Ips: SDict begin xyc endg32328\3232Q썍3232323232323232323232323232323232323232323232323232Q3232  ΟC3232]2323232323232#C3232]232323232323232g32328\3232Q썍3232323232323232323232323232323232323232323232323232Q3232UUfddottedsf/ps: SDict begin xyc endg3232" {3072 F d}xy r" {3072 F d}xy pٍ" {3072 F d}xy p" {3072 F d}xypО3232  ." {1024 F d}xy" {1024 F d}xy.$" {1024 F d}xy$" {1024 F d}xy32g3232" {3072 F d}xy r" {3072 F d}xy pٍ" {3072 F d}xy p" {3072 F d}xypО3232UUfddashedQ[F-,]UU[F-:<3pt>]Ips: SDict begin xyc end\s(" {0.0 18.36115 -6.0 -18.36113 6.0 ov}xy3333$玍$33 33UUfdshadedups: SDict begin xyc end (" {3.0 21.12505 -6.0 -21.12503 6.0 ov}xyUUfdroundedeK mgff2ɍSince[#ob8jectsspGeci edthisway[#startwithnomar- gin,asingle+ isusuallyincludedtogetthedefaultspacing.#`ExerciseT7: TypGesetUUps: SDict begin xyc end!ǵA " {0.0 0.0 l}xyFd(" {5.15277 5.15277 5.85764 5.85764 ox}xyx#" {3072 10 /xy AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!B6@.񩍑There'ecanonlybGeoneb}'oxing.ThiscanbeanybGoxu\generationcommand.'ThefollowingarethemostusefulUUb}'oxing}{"ztext} *combinations: f/ff2 me @variant{2tip}kktipUU(orshaft)ob8ject \txt{?...}kkordinaryUUtext \composite{?...*...}kkcombinedUUob8jects \frm{}kkrepGeatUUlastob8jectff2(thesApGossibilitiesforvariantfandtipٲaregiveninthefollowingsection).~Finally*,n\hbox{?...}꧟^7isaquickway}toensuretext-moGdeinterpretationofasingleob-ject.However,\txtPallowstheuseof\\intextCtocre-ateE>alinebreak,{andthespGecialform\txt<6pc>{6 ...}willQconstrainthetexttoacentered6pGcwidecolumn.Bytheway*,?\txt3CcanbGeusedoutsideof XY -piccon-structions. Finally*,severalob8jectscanbGecombinedusingthelastmform;ythe*sservetoseparatethecompGosedob-ject.1e+ExerciseT8: TypGesetUUps: SDict begin xyc end!ǵA  " {2765 st}xy:High :label= " {2765 st}xy5!+5!Ǹ-!Dz+-!Ǹ%"!Dz+%"!Ǹž!Dz+ž!Ǹb!Dz+b!Ǹ !Dz+ !Ǹ>!ǵBP@.#`2.3Morearrowstyles]TheݧarrowstylesdescribGedinsection1.3areallex-amplesUUofthegeneralarr}'owstyleconstructionsff2 me;@variant{2tail]shaftH-he}'ad};@variant{2he}'ad}ff2ɍthatindescribGesarrowswiththeindicatedtail,shaft,and^xhe}'adg(onthe rstformthetailandheadcanbGeomitted;thesecondstyledefaultstohavingnotailandUUastandardshaft).ff[ J= "5-:7LTheXplainTAEMXcommand\hboxcorrespwC ps: SDict begin xyc endO:" {3328 10 /xy AB}xyO:" {22.76208 5.69052 dt}xyF!xps: SDict begin xyc endO:" {-3686 st}xy|Yu" {-3686 F d}xyO:" {22.76208 5.69052 dt}xy?<<*ps: SDict begin xyc end " {-768 10 /xy AB}xyO:" {-768 10 /xy AB}xyO:" {22.76208 5.69052 dt}xyb>>wC ps: SDict begin xyc end " {3328 10 /xy AB}xyO:" {3328 10 /xy AB}xyO:" {22.76208 5.69052 dt}xyF!+ps: SDict begin xyc endO: " {3328 st}xyV5v" {3328 F d}xyO:" {22.76208 5.69052 dt}xy?|<*ps: SDict begin xyc endO: " {-768 st}xyO:" {-768 10 /xy AB}xyO:" {22.76208 5.69052 dt}xyb>|wC ps: SDict begin xyc endO: " {3328 st}xyO:" {3328 10 /xy AB}xyO:" {22.76208 5.69052 dt}xyF!|ps: SDict begin xyc endO: " {3328 st}xyO:" {22.76208 5.69052 dt}xy|<<*ps: SDict begin xyc endO: " {-768 st}xy " {-768 10 /xy AB}xyO:" {-768 10 /xy AB}xyO:" {22.76208 5.69052 dt}xy]>>|wC ps: SDict begin xyc endO: " {3328 st}xy " {3328 10 /xy AB}xyO:" {3328 10 /xy AB}xyO:" {22.76208 5.69052 dt}xy$||ps: SDict begin xyc endii " {3328 st}xyO: " {3328 st}xyO:" {22.76208 5.69052 dt}xy(*ps: SDict begin xyc endO: " {3328 h}xyO:" {22.76208 5.69052 dt}xyh )wC ps: SDict begin xyc endO: " {-768 h}xyO:" {22.76208 5.69052 dt}xyF!ops: SDict begin xyc endK O!cmsy7O:" {22.76208 5.69052 dt}xy/*ps: SDict begin xyc endO: " {3024 st}xyO:" {22.76208 5.69052 dt}xyb//wC ps: SDict begin xyc endY?K " {3024 st}xyO: " {3024 st}xyO:" {22.76208 5.69052 dt}xy0ff2andUUtheshaftH-shouldbGeoneofthefollowing:+_ff2VY'-6ڤps: SDict begin xyc end%$t" {34.14313 11.38104 l}xy--ps: SDict begin xyc end%$t" {34.14313 11.38104 dd}xya'~6ڤps: SDict begin xyc end@K " {3413 g}xyw5 " {3413 g}xyh " {3413 g}xy ") " {3413 g}xy~~ps: SDict begin xyc end!X " {3413 g}xyRO: " {3413 g}xyq " {3413 g}xy'.6ڤps: SDict begin xyc end%$t" {34.14313 11.38104 dt}xy[3ff2ThevariantshouldbGeemptyoroneofthefollow- ing: ,ff2 [14VN^>K\abGove"UUvqariant4VN_>K\bGelow"UUvqariant4VN2>K\double"UUvqariant4VN3>K\triple"UUvqariantωff2ƍHereHaresomestandardarrowsinthisnotation,DallfromUUAtoBƲasusual:=ps: SDict begin xyc end@{<->}3 qA>?" {-1024 10 /xy AB}xy>?" {0.0 0.0 l}xy\?" {3072 10 /xy AB}xy\?" {29.99998 0.0 l}xy\?" {0.0 0.0 l}xy_? qB@^{<->}3H)A>? " {-1024 10 /xy B}xy>? " {0.0 0.0 l}xy\? " {3072 10 /xy A}xy\? " {29.99998 0.0 l}xy\? " {0.0 0.0 l}xy_?H)BU@_{<->}3A>?7" {-1024 10 /xy A}xy>?7" {0.0 0.0 l}xy\?7" {3072 10 /xy B}xy\?7" {29.99998 0.0 l}xy\?7" {0.0 0.0 l}xy_?B.c)@2{<->}3.A>?+T" {-1024 /XT tt}xy\?+T" {3072 /XT tt}xyY*T" {24.99998 0.0 l}xyY,T" {24.99998 0.0 l}xy_?.B=@3{<->}3=QA>?:" {3072 F d}xy>?:" {-1024 /Xt tT}xyW?:" {-1024 F d}xy\?:" {3072 /Xt tT}xyY 8" {23.59999 0.0 l}xyY <" {23.59999 0.0 l}xyY :" {23.59999 0.0 l}xy_?=QBRAs7aspGecialconvenience7= and7:are7providedasab-breviationsUUfor- ꧲and.withvqariantforcedto2R.As itcanbGeseen,thevqariantwilla ecttheentir}'earrow.GSometimes׭thisisnotwhatiswanted.GInthatcase*alo}'calXovariant˲can*bGeusedbyenteringanyoftheUUtail,shaft,andhe}'ad,onthefollowingform:ff2 [1Rvariant{2tip}Rvariant{2shaft}ωff2ƍHereUUaresomearrowswherethisisrequired:5ps: SDict begin xyc end@{^{(}->}J? qAT " {3072 ha}xyT" {0.0 0.0 l}xyl" {3072 10 /xy AB}xyl" {23.99998 0.0 l}xyl" {0.0 0.0 l}xyo qBܝ@{|-_{>}}J?H)AT  " {3072 st}xyT " {0.0 0.0 l}xyl " {3072 10 /xy B}xyl " {23.99998 0.0 l}xyl " {0.0 0.0 l}xyoH)B%NoticethatthereisnodistinctionbGetweenshaftsandtipseusingthisform,/thusitisnecessarytoincludeallthree[oftail,]shaft,and[he}'ad,whenusingit.mThead-vqantage,MisthatitispGossiblethento\ llwithatip."F*urthermore,JtheXfollowingadditionalpGossibilitiesareavqailableUUwhenusingthisnotation:eKgwff2 ͤ{|-}%ps: SDict begin xyc endO: " {3328 st}xyO:" {3328 F d}xyO:" {22.76208 5.69052 dt}xyN^{|-}s ps: SDict begin xyc endu" {-2816 F d}xyO:" {3328 F d}xyO:" {22.76208 5.69052 dt}xy%_{|-}ps: SDict begin xyc endO:" {1280 F d}xyO:" {3328 F d}xyO:" {22.76208 5.69052 dt}xy T {|=}s ps: SDict begin xyc endV " {3328 st}xyV" {3328 F d}xy/G " {3328 st}xy/G" {3328 F d}xyO:" {22.76208 5.69052 dt}xy%3{|-}ps: SDict begin xyc endF^ " {3328 st}xyF^" {3328 F d}xy?G? " {3328 st}xy?G?" {3328 F d}xyO: " {3328 st}xyO:" {3328 F d}xyF^" {22.76208 5.69052 dt}xy?G?" {22.76208 5.69052 dt}xyO:" {22.76208 5.69052 dt}xy D{*}%ps: SDict begin xyc endKO:" {22.76208 5.69052 dt}xyT ^{`}s ps: SDict begin xyc endO: " {3328 ta}xyO:" {22.76208 5.69052 dt}xy"_{`}ps: SDict begin xyc endO: " {3328 tb}xyO:" {22.76208 5.69052 dt}xyT ^{'}s ps: SDict begin xyc endO: " {-768 tb}xyO:" {22.76208 5.69052 dt}xy"_{'}ps: SDict begin xyc endO: " {-768 ta}xyO:" {22.76208 5.69052 dt}xyHff2The/evenmoregeneralform* oobje}'ct"ֲcanbGeused,whereSobje}'ct+referstoanyoftheconstructionsde-scribGedUUinsection2.2.^ExerciseT9: TypGesetUUps: SDict begin xyc end qA " {-608 10 /xy B}xy9" {mark 37.7934 0.0 18.8967 12.0 0.0 0.0 1.0 0.17871 q}xy%ڟx" {2668 10 /xy B}xy=" {mark 37.7934 0.0 18.8967 12.0 0.0 0.0 0.17871 0.81372 q}xy9" {mark 37.7934 0.0 18.8967 12.0 0.0 0.0 1.0 0.81366 q}xy A[# 2ȟ! " {3608 st}xy N" {3608 F d}xy,A " {3819 st}xy|K" {3819 F d}xy " {4096 st}xyfS" {4096 F d}xy^A" {-3819 st}xylIw" {-3819 F d}xy#V!" {-3608 st}xy!W" {-3608 F d}xy( qB:@.^2.4Slidingarrowssideways ItisoftendesirabletohaveseveralparallelarrowsbGetweenCtwoob8jects.kThiscanbGedonebyslidingei-therZ~orbGotharrowssidewaysadistancegivenasaTU>'ExXr6dimensionenclosedin@<>s:itspGeci eshowfar\sideways"UUthearrowshouldbGemoved,e.g.,N8\xymatrix{?A\ar@<1ex>[dr]^a_{.}\\&?B\ar@<1ex>[ul]^b\ar@<1ex>[r]^c?&?C\ar@<1ex>[l]^d_{.}}kwillUUtypGeset9F3ps: SDict begin xyc end qAYb" {0.02487 -0.02586 l}xy ôa_:(" {2074 10 /xy AB}xy(" {24.63425 -24.0 l}xy(" {0.02487 -0.02586 l}xy(%ŵB"s^" {-0.02487 0.02586 l}xyALnb Us#" {-2022 10 /xy AB}xy Us#" {-24.63425 24.0 l}xy Us#" {-0.02487 0.02586 l}xy39(" {0.0 0.0 l}xy=m(cK8(" {3072 10 /xy AB}xyK8(" {23.99998 0.0 l}xyK8(" {0.0 0.0 l}xyN8%ŵCK8&S" {0.0 0.0 l}xy=s.Ĵd>Wݟ#S:39&S" {-1024 10 /xy AB}xy39&S" {-23.99998 0.0 l}xy39&S" {0.0 0.0 l}xyCGA3pGositive֖distancewillslidethearrowinthe\^?-direction,"-e.g.,the5twoarrowsabGoveareslidinthedirectionDŽofthelabGelsa,$b,c,andDŽd,respectively;anegativedistanceinthe\_?-direction." :Thedis-tanceU<@1ex>$+isUoftenappropriatesinceitcorrespGondsroughlytotheheightofletterslike\x,"3inthetypGesizeUUbGeingused.^ExerciseT10: TypGesetUUps: SDict begin xyc end!ǵA8" {mark 33.7934 0.0 16.8967 12.0 0.0 0.0 1.0 0.1997 q}xy#" {2566 10 /xy AB}xy<" {mark 33.7934 0.0 16.8967 12.0 0.0 0.0 0.1997 0.85083 q}xy9" {mark 33.7934 0.0 16.8967 12.0 0.0 0.0 1.0 0.85077 q}xyE" {mark 33.7934 -4.30554 16.8967 7.69446 0.0 -4.30554 1.0 0.1997 q}xy#7" {2564 10 /xy AB}xyI" {mark 33.7934 -4.30554 16.8967 7.69446 0.0 -4.30554 0.1997 0.85083 q}xyF" {mark 33.7934 -4.30554 16.8967 7.69446 0.0 -4.30554 1.0 0.85077 q}xy$!B6@.2.5Moretargets The targetaddresscanbGegiveninalargenumbGerofformatsccalledp}'ositions.ThefullrangeofpGossibili-tiesisdescribGedinthereferencemanual[8,N g.1];hereisanumbGerofusefulonesinadditiontothehopformatUUdescribGedinsection1.3:V[?rG,c]?,;where5]r;careintegers,denotesther}'ela-tive1entrymfoundr1 rowsbGelowandccolumnstotherightofthecurrententry(thecurrententryitselfisthus[0,0]/).@ThisalwayscorrespGondstoma[ hop]ᕲ,e.g.,[1,2]#aismthesameas[drr]andUU[-2,0]&*isUUthesameas[uu]UI.LWK6b*tj??gw"rG,c"?,ţwhere-r;carepGositiveintegers,ţdenotes the6absolute entryfoundintherGthrowandcthcolumnNofthediagram.]Thetopleftentryis"1,1" .t^09;6t,Dnwheret^0ղisanytarget,changesthebaseentryofthepresentarrowtot^0andthensetsthe,targettotrelativetotheoriginalbaseen-try*.qForUUexample,N8\xymatrix{?A\\6KB?&C\ar@<1ex>[ul]U\ar@<1ex>[ul];[]?}ƍtypGesets ՍH1ps: SDict begin xyc endK qA%B)8%C#b" {-0.02628 0.03304 l}xy #" {-2017 10 /xy AB}xy #" {-24.75284 24.0 l}xy #" {-0.02628 0.03304 l}xy8" {0.02628 -0.03304 l}xy)g" {2079 10 /xy AB}xy)g" {24.75284 -24.0 l}xy)g" {0.02628 -0.03304 l}xy8ai.e., the<^second\ar[ul]/8arrowstartsatthel]dentryUUandendsinthecurrententry*.ՍSeeUUsection3.5forhowtousealabGelasatarget.pg2.6LChangingthetargetɍIt.?ispGossibletooverwrite.?atargetwithanotherbyappGendingtsomethingoftheform*obje}'ctgutoit.ϞThishasthee ectoftypGesettingtheobje}'ct atthecurrentpGosition, thusOe ectivelyontopofthetarget, andthenUUusewhatwastypGesetasthetarget. GAfstargetfmayalsohaveitspGositionchangedbyoneUUofthefollowingconstructions:+ve}'ctorpuor\-vectorwhich\changesthetargettobGeLazero-sizedoneatthepositionobtainedbyaddingorsubtractingtheve}'ctor-toitscenter,or!ve}'ctorwhichTmovesthecenterofthetargetbytheUUve}'ctor;whereUUave}'ctorhshouldhaveUUtheform<Dx, HDy·> ۲,wherexWDx;DyF޲areTU>'ExXdimensions,isUUthevectorwiththosecoGordinates,the>following\cornero sets"ofatargetarevec-torsUUasshown:.R3Ӆps: SDict begin xyc endu$32323232:z32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:k3232")č(֍3232j32323232323232323232323232323232323232323232323232323232Nq@(֍3232j3232323232323232323232323232323232323232323232323232323232$32323232:z32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:k3232ؽ" {0.0 0.0 dt}xyNq?" {0.0 0.0 dt}xyǍ/$R" {0.0 0.0 dt}xyǍ/$" {0.0 0.0 dt}xyؽ" {-31.29787 0.0 l}xyؽ" {-1024 10 /xy AB}xy8LNq?" {31.29787 0.0 l}xyNq?" {3072 10 /xy AB}xyWARǍ/$R" {0.0 -17.07156 l}xy/$" {1024 10 /xy AB}xy,RDǍ/$" {0.0 17.07156 l}xy/$u" {-3072 10 /xy AB}xy,㝮Uؽ" {-31.29787 -17.07156 l}xyؽ" {-465 10 /xy AB}xycDLNq?" {31.29787 -17.07156 l}xyNq?" {2513 10 /xy AB}xySbcDRؽu" {-31.29787 17.07156 l}xyؽu" {-1583 10 /xy AB}xyULNq?u" {31.29787 17.07156 l}xyNq?u" {3631 10 /xy AB}xySbUR1(theyUUmustbGespeci edinuppercase),andgweLeM/ddimenc/߲istheve}'ctor goingdimen_inthepar- eMticulardirectiondwhichcanbGeeithertheeighteMsimpleonesinsection1.6,emptytodenotethateMthe\curr}'entpdirection!X(thelastdirectionofaneMarrow)UUshouldbGeused,oroneofthefollowing: eMff0 va(#@õ z);6fabsoluteUUangle̵d:a( z);6frelativeUUangleindegrees̵d:( x,y[);6frelativeUUvector̵d^UU/d_;6fshort-for:a(90)thedinthelastfourmaybGeemptytoeMdenoteUUthe\currentdirection."neLeM0UUisthezerovector.ReKMany*,omanyWmorepGossibilitiesaredescribedintheeKreferenceUUmanual[8].ꍒeKExerciseA11: Whatisthedi erencebGetweenatar-eKgetUUtandthetargett+0 ?ꍍeK2.7%KArrowspassingunderʍeKArrowscanpassunder(orvia)anyotherentry:AJusteKinsert_,'t,hi.e.,aquote(apGostrophe)characterfollowedeKbyEatarget,HJforeachentrythatshouldbGevisitedex-eKceptUUthelast,\ordinary& nal"entry:N8eK\xymatrix{H{\circ}E\ar@{|-->}?'[dr]^a%$'[rr]+D*{\bullet}?^b*![drrr]?^c0&?{\circ}&{\circ}&{\circ}\\H{\circ}?&{\circ}&{\circ}&{\circ}}iߍeKtypGesets R􍍒Qps: SDict begin xyc endڪ Ɵڪ " {2064 st}xy :߉" {0.0174 -0.01903 dd}xyT ڪa#2:ڪ" {24.3924 -24.0 dd}xyI4CwbI " {26.99998 22.54253 dd}xy_4wci}M" {2217 10 /xy AB}xyi}M" {26.99998 -22.55034 dd}xyi}M" {0.02907 -0.03276 dd}xy&ڪIڪlڪ"Lp&"LpI"Lpl"Lp3+eKAs:yousee,labGelsaresetseparatelyoneachsegment.eKExerciseT12: TypGesetUUthe\lambGdacube"7M$Nps: SDict begin xyc endW!, " {0.0 0.0 l}xyI" {28.94374 0.0 l}xyI" {0.0 0.0 l}xyǍ"꬟x" {0.0 0.0 l}xyǍ"꬟" {0.0 -14.52779 l}xyǍ"꬟( " {0.0 -13.52783 l}xyǍ"꬟( " {0.0 0.0 l}xyLCǍR꬟x" {0.0 0.0 l}xyǍR꬟( " {0.0 -34.05562 l}xyǍR꬟( " {0.0 0.0 l}xy2Ǎc" {0.0 0.0 l}xyǍqɟx" {11.05557 11.05557 l}xyǍqɟx" {0.0 0.0 l}xyUX" {0.0 0.0 l}xy.r" {27.26212 0.0 l}xy.r" {0.0 0.0 l}xyǍ ꬟x" {0.0 0.0 l}xyǍ ꬟A" {0.0 -35.05557 l}xyǍ ꬟A" {0.0 0.0 l}xy1rPc2ǍAc" {0.0 0.0 l}xyǍLqɟx" {11.05557 11.05557 l}xyǍLqɟx" {0.0 0.0 l}xyǍ:꬟x" {0.0 0.0 l}xyǍ:꬟A" {0.0 -35.05557 l}xyǍ:꬟A" {0.0 0.0 l}xyW0!feT, -" {0.0 0.0 l}xy7꬟-" {11.79166 0.0 l}xyEȟ-" {7.88715 0.0 l}xyEȟ-" {0.0 0.0 l}xyHȟ0Pc!cfeTI!XE" {0.0 0.0 l}xy1rE" {27.26212 0.0 l}xy1rE" {0.0 0.0 l}xyǍcA" {0.0 0.0 l}xyǍq̟7x" {10.05562 10.05562 l}xyǍq̟7x" {0.0 0.0 l}xy4rIPǍAcA" {0.0 0.0 l}xyǍKq̟7x" {10.05562 10.05562 l}xyǍKq̟7x" {0.0 0.0 l}xy^CeKHintز:\goingmunder"anemptyentryleavesasmalleKgaphatthatloGcation.ThecompactnessisachievedeKusingUUatrickdescribGedinsection3.3.LWK7*tj??gw2.8LMoreb`endingarrowsuTFinally*,arrowscanbGendaroundentries:justinsert `dt,i.e.,abackquoteandadirectiondfollowedbyawtargett,)foreach\turn"thatstartsoutinthed-directionandendsinaquarterturntowardsthetar-getqt.&Thisisdi erentfromthecurvingdescribGedearlierinthatallturnsconsistofastraightpartend-ingwinaturnwhichisamultipleofw1Z/8Ncirclesegments,andUUeachsegmentallowsseparatelabGels.ThepGossibledirectionsarethoseofsection1.6and2.6,@#andthepGossibletargetsincludeallthosediscussedabGove.Actuallythedirectionisonlyre-quiredhlforthe rstinaseriesofturnssincethe naldirection!ofoneturnistheobviouschoiceforthefol-lowingo8turn.%F*urthermore,>turnscanbGechangedfromthedefaultbyaddingeither^dforanticloGckwiseturntodor_dforcloGckwiseturntod,wheredisthe\exitdirection"UUoftheturn.Finally*,(theturnswillhaveradius10ptbydefault,butthiscanbGechangedtoanydimensionRݲfromaparticularIturnandonwardsIbyinserting/R imme-diately4afterthe``boftheturn.mdHereisanexampleinvolvingUUallofthesefeatures:N8\xymatrix{{\circ}?\ar`r[d]^aK`[rr]?^bK`/4pt[rr]?^cK`[rrr]^dK`_dl[drrr]^e"[drrr]^f&?{\circ}&{\circ}&{\circ}\\{\circ}?&{\circ}&{\circ}&{\circ}}typGesetsӤps: SDict begin xyc endڪ " {10.0 0 90 o}xy " {0.0 0.0 l}xy˟Ǵa " {0.00008 0.0 l}xy" {10.0 -180 -90 o}xy bǍ " {0.0 -0.00008 l}xyG " {4.0 -90 0 o}xy1vcG" {40.49991 -0.0009 l}xyO" {4.0 90 180 o}xyDV.  dǍK" {-0.00098 12.00098 l}xyJH" {4.0 -45 90 o}xyiIeJH" {55.79048 0.00194 l}xyO! fsڪ" {0 10 /xy AB}xyǍs8" {-22.39572 -22.39572 l}xyǍs8" {0.0 0.0 l}xy&ڪIڪlڪ"Lp&"LpI"Lpl"Lp3 TheUUexampleillustratesthefollowingpGoints: wIffthesegmentcannotbGemadeasshortasre-quiredthenitwillpGoint\past"thetarget.0ThisisUUusefulfor\goingaround"entries.ThereisoneW`p}'erWturnQthuseachtargetap-pGears#asmanytimesasthereareturnstowardsit,exceptܐthelasttargetthatappGearsonemoretime xnamelybGothwith` foreachturntowardsitandUonceasan\ordinary"targettosetthe nalUUstretch.TheBsizesoftheintermediatetargetsareig-nored.daExerciseT13: TypGesetUUps: SDict begin xyc end!ǵA" {12.0 -180 -90 o}xyǍ" {0.0 0.0 l}xyǍ" {0.0 -0.00008 l}xyG" {12.0 -90 0 o}xyG" {13.7934 0.00203 l}xy*̟%" {-3065 10 /xy AB}xyǍ*̟" {-0.02466 2.48291 l}xyǍ*̟" {-0.01012 0.0 l}xy" {8.0 -180 -90 o}xyǍ" {0.0 0.0 l}xyǍ" {0.0 -0.00008 l}xyG" {8.0 -90 0 o}xy G" {13.7934 0.00203 l}xy&%" {-3079 10 /xy AB}xyǍ&" {0.0188 2.48315 l}xyǍ&" {0.00183 0.0 l}xy$!B98.gweK2.9%KDe ningnewarrowtyp`esڐeKLasteinthistreatmentofarrowswewillexplainhow eKnewarrowscanbGede ned.ThecrucialfactisthateKtheocharactersusedfortipsAandshaftsarerestrictedeKtoUUthefollowing:eK ff2 &Wv_> ev}{%?!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}}+de nesUUanewtipthatmakes\xymatrix{?A\ar@{=|>}[r]&B}typGesetps: SDict begin xyc end qA " {0.0 0.0 l}xy " {0.0 0.0 l}xy#@ " {3072 st}xy'" {2867 10 /xy A}xy'" {3277 10 /xy B}xy#@" {21.74998 0.0 l}xy#@" {21.74998 0.0 l}xy( qB<.0aNoticehowthe\relativedi- rection"8isusedheretorotatesomeofthecompGosedcompGonents.Exercise14: Oftentipsusedas\tails"havetheirinkonthewrongsideofthepGointwheretheyareplaced. F*ortunatelyspace( )isalsoatipcharac-terPsowecande nethedirectional >togeneratea\tail-spaced"UUarrow.qDothissuchthat\xymatrix{?A\ar@{>->} @<2pt>[r]D?\ar?@{>->}@<-2pt>[r]&B}+typGesets?ٍY!}ps: SDict begin xyc end qA " {3072 10 /xy AB}xy " {0.0 0.0 l}xy%" {3072 10 /xy AB}xy%" {23.99998 0.0 l}xy%" {0.0 0.0 l}xy" {3072 10 /xy AB}xy%" {3072 10 /xy AB}xy%" {21.49998 0.0 l}xy%" {0.0 0.0 l}xy( qB?َLWK8 Dc*tj??O]w\Finally*,MwhenXYh-picdiagramsareusedincon- junctionFwithKnuth'sc}'omputerqmodernfontsвthentheUUdeclaration Eff2 ӍC\SelectTips?{cm}{}Yqff2willUUchangethetipstosomethatloGoksimilar,e.g.,N8$\SelectTips{cm}{}?\xymatrix@1{A\ar@{->>|}[r]&B}$>čtypGesetsps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy# " {3072 st}xy!" {3072 10 /cm AB}xy#" {3072 10 /cm AB}xy#" {21.99998 0.0 l}xy#" {0.0 0.0 l}xy$!B2.]Thesecondargument(here{} ܲ) canebGeusedtospecifyapointsize{10}Y,{11}ݲ,or{12},'ifdesired(thedefaultis{10}^8y);Q{cm}NcanbGereplacedby{eu}and{xy}togettipsin\Euler"andthe.defaulttechnicalstyle,6respGectively*.UeThedeclara-tionUUrespGectsTU>'ExXgrouping.^ Exercise*15: TypGesetps: SDict begin xyc end!ǵA " {0.0 0.0 l}xy" {3072 10 /cm AB}xy" {3072 10 /cm AB}xy" {10.99998 0.0 l}xy#" {3072 10 /eu AB}xy#" {11.0 0.0 l}xy#" {3072 10 /xy AB}xy#" {0.0 0.0 l}xy#" {0.0 0.0 l}xy$!B4m.- Hintز: Withtheconstruction0\objectobje}'ctonecantypGesetan,XY !0-picobje}'ct5(anythingC&thatcouldfollowa* Iinsection2.2)inUUanycontext."D3LMoreffEntriesThissectionexplainswhatcangoinanentryandhowUUthegeneralformoftheentriesischanged.ض3.1ManualentryformattingƍAlltheentrieswehaveseenthusfarhavebGeensimplemathob8jects.However,itispGossibletochangetheformatUUofanindividualentrybyusingtheform: ff2 ӍR,*obje}'ctH-arrowsYqff2This allowscompletecontroloverwhatob8jectisplaced,intheentry*,!4overriding,anyspacingandotherconventionsCfortheentry*.=ThiswashowtheframewasUUobtainedinthe gureinsection1.2. YoAsimpleuseofthisistoinserttextinentriesus-ing\txtob8jectsjustlikelabGelsasdescribedaboveinsectionUU2.2:N8\xymatrix{?*\txt{Averylongandstupid\\program} \ar[rr]^-{\txt{weird\\arrow}}?&&*\txt<2pc>{Com\-pli\-cated\\Code}}willUUtypGeset'Sps: SDict begin xyc endōAUUverylongandstupid  etUU\restore‰ff2dwheretshouldbGeatargetinoneoftheformatsde-scribGedinsections2.5-2.6.MtcandoanykindoftypGe-settingUUdesired,forexample,N8\xymatrix{?A\ar@{-}[dr]?&{}\save[]+<3cm,0cm>*\txt<8pc>{%?This?isaverybigcommentary?but?itdoesnototherwiseaffect?the?diagram.}?\ar[l]?\ar[d]\restore\\?&B\ar@{-}[r]&C\ar@{-}[r]&D}willUUtypGeset#0ps: SDict begin xyc end qA Z" {0.02487 -0.02586 l}xy% q" {24.63425 -24.0 l}xy% q" {0.02487 -0.02586 l}xy͍[oThisU>isaverybig XcommentaryU>butitY#XdoGesU>nototherwiseXVa ectU>thediagram.Qӟ" {0.0 0.0 l}xy " {-1024 10 /xy AB}xy " {-68.40164 0.0 l}xy " {0.0 0.0 l}xyQY" {-0.01466 0.0 l}xy39l" {-582 10 /xy AB}xy39l" {-30.31485 -13.07434 l}xy39l" {-0.00333 0.0 l}xy(%ŵB39"w" {0.0 0.0 l}xyK8"w" {23.99998 0.0 l}xyK8"w" {0.0 0.0 l}xyN8%CYs"w" {0.0 0.0 l}xyqs"w" {24.0 0.0 l}xyqs"w" {0.0 0.0 l}xyts%D:FMItLillustrateshowa\down"arrowdoGesnotnecessar-ilyc.havetopGointparticularlystraightdown{inthiscasebGecauseitisbasedinthedisplacedpseudoentry*.㍍3.3SpacingandrotationuTThe7* wobje}'ct*ֲform7describGedabove7canbeusedtospaceindividualob8jectsdi erently*,however,itisalsopGossibleBtochangetheoverallspacingofamatrixbyinserting!thefollowingcoGdesb}'etweenׄ\xymatrix6*andtheUUfollowing{R: ff2 J$!j0@=dimenQisetUUspacing!j0@R=dimenQisetUUrowspacing!j0@C=dimenQisetUUcolumnspacing!j0@M=dimenQisetUUentrydefaultmargin!j0@W=dimenQisetUUentrydefaultwidthff[ J= "5-:8LExceptXwhenXs0`Y O-picisloadedasaL#A TAEMXFd2"B(pacÎkagewherethedefaultsizeisused.LWK9 bK*tj??gwI@H=dimen5setUUentrydefaultheight I@L=dimen5setUUlabGelmarginGff2m=canbGereplacedbyanyof+,կ+=,-,and-=ofsec-tion}2.2withthesamemeaning, i.e.,replace}\set"with\increase,"\increasetoatmost,"\decrease,"and<_\decreasetoatleast,"v!respGectively*.&For<_exam-ple, $\xymatrix@1@=0pt@M=0pt{A&B\\C&D}$ninthetextUUtypGesetsps: SDict begin xyc end.f!ǵA!B !C̟ !Dk`.Incaseuniformsp}'acing!isdesired, severalalter-nativeUUformsexist.ᾉff2 /Q@!CHforceUUallspacesequal/Q@!0CH|UUandignoreentrysizes/Q@!RCHforceUUequalrowspacing/Q@!CCHforceZequalcolumnspacingff2mFinally=aspGecialnotationallowsr}'otationofanentirematrix:ᾉff2 0@dB۲rotateUUtowardsdff2mOnly thematrixgridwillrotate,however,not theactualUUcontents.GExerciseT17: TypGesetUUthe\striplemma"{XS$ps: SDict begin xyc end Şa(hˉ" {0.0204 -0.01035 l}xy1 ›" {2048 10 /xy AB}xy1 ›" {8.9871 -8.97546 l}xy1 ›" {0.02042 -0.0072 l}xyǍ{A'" {0.0 0.0 l}xy ik" {0 10 /xy AB}xy Jz" {0 10 /xy AB}xyǍ JW" {-20.1898 -20.1898 l}xyǍ JW" {0.0 0.0 l}xy4yşG+a^0Ǎ11d" {0.0 0.0 dt}xy"(Vj" {0 10 /xy AB}xy *uy" {0 10 /xy AB}xyǍ ,Ӳ" {-17.18088 -17.18088 dt}xyǍ ,Ӳ" {0.0 0.0 dt}xyb MP!H" {0.01035 -0.02042 dt}xy\(X" {2048 10 /xy AB}xy|*w" {2048 10 /xy AB}xy|*w" {9.19272 -9.20416 dt}xy|*w" {0.00761 -0.02042 dt}xy|43b^0A?G3.4EntrystyleuTAs)QmentionedabGove,2theentriesofadiagramaresetinmathmoGdeintextstyle.썒eKwillUUtypGeset(Ops: SDict begin xyc endstart" {0.0 0.0 l}xy " {3072 10 /cm AB}xy " {11.99998 0.0 l}xy " {0.0 0.0 l}xyn)# " {9.22221 9.22221 8.5 8.5 ox}xy&ګ0 QȟM" {mark 30.81946 0.0 66.81946 0.0 30.81946 36.0 30.81946 0.0 1.0 0.0957 bz}xy0L8b*>i" {716 10 /cm AB}xy QȟQ" {mark 30.81946 0.0 66.81946 0.0 30.81946 36.0 30.81946 0.0 0.0957 0.89294 bz}xy QȟN" {mark 30.81946 0.0 66.81946 0.0 30.81946 36.0 30.81946 0.0 1.0 0.89294 bz}xy5xXUa=" {3072 10 /cm AB}xy=" {11.99998 0.0 l}xy=" {0.0 0.0 l}xynF# " {9.22221 9.22221 8.5 8.5 ox}xyCګ1RnǴbZ" {3072 10 /cm AB}xyZ" {11.99998 0.0 l}xyZ" {0.0 0.0 l}xy QȟN" {mark 59.81946 0.0 95.81946 0.0 59.81946 -36.0 59.81946 0.0 1.0 0.0957 bz}xyLM !aG>" {-2764 10 /cm AB}xy QȟR" {mark 59.81946 0.0 95.81946 0.0 59.81946 -36.0 59.81946 0.0 0.0957 0.89294 bz}xy QȟO" {mark 59.81946 0.0 95.81946 0.0 59.81946 -36.0 59.81946 0.0 1.0 0.89294 bz}xync# " {9.22221 9.22221 8.5 8.5 ox}xy`ګ2onǴbw" {3072 10 /cm AB}xyw" {11.99998 0.0 l}xyw" {0.0 0.0 l}xybQ A" {10.0 -90 45 o}xyic֟ " {0.00612 -0.00612 l}xyic؟" {0.00615 -0.00615 l}xyF " {10.0 135 270 o}xyRx!xaF " {-27.36172 -0.00168 l}xy?K " {-4096 10 /cm AB}xyǍ?K@E" {0.00172 0.00172 l}xyǍ?K@E" {0.0 0.0 l}xyn# " {9.22221 9.22221 8.5 8.5 ox}xyn# " {7.22221 7.22221 6.5 6.5 ox}xy}ګ3QOM" {10.0 -45 90 o}xyǍc՟" {0.00002 0.00002 l}xyǍc؟" {0.00005 0.00005 l}xy) N" {10.0 90 225 o}xyR7+b) N" {-85.36172 0.00168 l}xy"Ka" {2048 10 /cm AB}xy"ܟc" {0.00784 -0.00784 l}xy"Ka" {0.00002 -0.00002 l}xyQ A" {10.0 -90 45 o}xyc֟ " {0.00612 -0.00612 l}xyc؟" {0.00615 -0.00615 l}xyF " {10.0 135 270 o}xyF " {-56.36172 -0.00168 l}xy?K " {-4096 10 /cm AB}xyǍ?K@E" {0.00172 0.00172 l}xyǍ?K@E" {0.0 0.0 l}xy(ݍeKNotice howweobtainthedoubleringusingtheeK*Hobje}'ctformwhichthenhastoincludeallthedesiredeKmoGdi ersHx(andhowtheuseofcomputermoderntipseKisUUnicefordiagramsasthese). DeK3.5%KNamingforlateruseastargets5LeKIfDyoubuildanentrywithalongandcomplicatedeKexcursionw!thenyoumightwishtobGeabletorefertoeKitlater._fXYj-picprovidesamechanismforthis:3thereeKis5aspGecialtargetformwhichwehaven'tdiscussedeKyet:eK9ff2 W[r%tUU="?name["ff2.ThiswillintroGducethenewtarget"name["3whichwillreferitothetargetjustbGeforethe=ɲ.+Thisisparticu-larlyB-usefulinsideexcursions,Fofcourse,andcanalsobGeUUusedafterlabels.!5ExerciseT18: TypGesetUUps: SDict begin xyc end qA " {0.0 0.0 l}xyzVǴa%" {3072 10 /xy AB}xy%" {23.99998 0.0 l}xy%" {0.0 0.0 l}xy( qB39" {0.0 0.0 l}xy=ŻǴbK8" {3072 10 /xy AB}xyK8" {23.99998 0.0 l}xyK8" {0.0 0.0 l}xyN8 qCJ" {mark 56.78072 5.43054 37.4637 16.96288 18.8967 4.50694 1.0 0.13892 q}xy:4b" {2637 10 /xy AB}xyN" {mark 56.78072 5.43054 37.4637 16.96288 18.8967 4.50694 0.13892 0.87659 q}xyJ" {mark 56.78072 5.43054 37.4637 16.96288 18.8967 4.50694 1.0 0.87659 q}xy\Y.3.6Groupingobjects5LSometimesyouwishtoframeorotherwisetreatarectangle Uofob8jectsasasingleobject.ThisispGos-siblepwiththelasttwoptargetpGositionformsthatwewillUUmention: G͉ff2 W/t.?sCmergeUUtwithsimples/{5(t}CmakeUUtsimpleff2LWeJ10 *tj??gwThe rstwillenlargettoalso\cover"the\simple" sd(simplemeansthatitcannothavedchangesetc.at-tachedmunlessencapsulatedin{} gs).VzHereisanexam-pleUUwherewemergeandframe:N8\xymatrix?@R=1pc{1,1?&1,2&1,3&1,4&1,5\\2,1?&2,2&2,3&2,4&2,5\save?"1,2"."2,4"*[F.]\frm{} \ar"1,1"?\ar"2,1"\ar"1,5"\ar"2,5"\restore?}^willUUtypGesetK\Cps: SDict begin xyc end1;1/qƞ1;2[㌞1;3UR1;41;5EU2;1/qƟEU2;2[㌟EU2;3UREU2;4EU2;5l,Q3232-93232:+32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:3232(<,7xn3232323232323232323232323232323232323232323232323232323232323232323232323232n323232323232323232323232323232323232323232323232323232323232323232323232323232,Q3232-93232:+32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232:3232,j" {0.0 0.0 l}xyqǟ" {-1024 10 /xy AB}xyqǟ" {-23.97221 0.0 l}xyqǟ" {0.0 0.0 l}xy,j" {0.0 -0.00002 l}xyqǟ" {-416 10 /xy AB}xyqǟ" {-23.97221 -14.23352 l}xyqǟ" {0.0 -0.00002 l}xy" {0.0 0.0 l}xy" {3072 10 /xy AB}xy" {24.02776 0.0 l}xy" {0.0 0.0 l}xyC" {0.0 -0.08682 l}xy" {2869 10 /xy AB}xy" {24.02776 -4.82668 l}xy" {0.0 -0.08684 l}xy4'.Asyoucansee,thecenterofthemergedob8jectisthesameUUastheoneofthetargetb}'eforetheUU\.?." &Finallyamoreadvqancedexamplewherewecreatetwo#mergedob8jectswithcenterintheir\real"center,namegthemandthenconnecttothem.ItalsoshowshowmacroscanbGeusedinsidediagrams:ltheyshouldalwaysUUexpandto\commands"like\arL...,UUetc.:?ps: SDict begin xyc end.f qAdL0" {0.0 26.1191 -25.17557 -26.1191 25.17557 ov}xy g" {0.0 0.0 l}xy&" {3072 10 /xy AB}xy&" {24.4163 0.0 l}xy&" {0.0 0.0 l}xy) qBǍ-$j" {0.0 0.0 l}xy-$" {1024 10 /xy AB}xyǍ-$" {0.0 -24.68451 l}xyǍ-$" {0.0 0.0 l}xyOşdA^0di{2" {0.0 28.92465 -25.51782 -28.92465 25.51782 ov}xy\" {0.0 0.0 l}xyuR" {3072 10 /xy AB}xyuR" {24.41629 0.0 l}xyuR" {0.0 0.0 l}xyxRdBq^0Ǎ}ʟH" {0.0 0.0 l}xy}ʟd" {1024 10 /xy AB}xyǍ}ʟH" {0.0 -24.0 l}xyǍ}ʟH" {0.0 0.0 l}xy&CǍf" {0.0 0.0 l}xyf q" {-3072 10 /xy AB}xyǍfj" {0.0 24.68451 l}xyǍfj" {0.0 0.0 l}xy(̟&D%̟#&W" {0.0 0.0 l}xy ̟#&W" {-1024 10 /xy AB}xy ̟#&W" {-24.0 0.0 l}xy ̟#&W" {0.0 0.0 l}xyOk`&C^0ǍTH" {0.0 0.0 l}xyTd" {-3072 10 /xy AB}xyǍTH" {0.0 24.0 l}xyǍTH" {0.0 0.0 l}xyxd&蟵DG^0ud#&W" {0.0 0.0 l}xy]e#&W" {-1024 10 /xy AB}xy]e#&W" {-23.99998 0.0 l}xy]e#&W" {0.0 0.0 l}xy4k` t" {0.0 0.01146 dt}xyuR9N" {3265 10 /xy AB}xyuR9N" {64.90309 12.24417 dt}xyuR9N" {0.0 0.01146 dt}xyLş"" {3267 10 /xy AB}xyLş"" {62.73817 11.93091 dd}xyLş"" {0.02504 0.0 dd}xy>رcanUUbGetypesetbyN8\def\g#1{\save[].[dr]!C="g#1"*[F]\frm{}\restore}%\xymatrix{\g1?A\ar[r]&B\ar[d]&\g2A'\ar[r]&B'\ar[d]\\ C\ar[u]&D\ar[l]&C'\ar[u]&D'\ar[l]\ar?@{.>} "g1";"1,4"\ar?@{-->}"2,1";"g2"}^Thenwecanmakearrowsfrom/tothetwoframesbyusingUUthetwoUUnewtargets"g1"and"g2"asshown.!Exercisew19: Change]thelambGdacubeofexer-ciseg12suchitisenclosedinatransparent(i.e.,lXdot-ted)UUcubGe.)4AvailabilityandFfurtherIn-formation-BelowXwedescribGehowtoandtheconditionsforob-tainingXY 6-picversion3.7,֜thecompatibilitywithpre-viousversions,andweconcludewithafewappGetiserstoUUlurethereaderintoreadingmoreabGoutUQXY 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-pichomepageandtheUUftpserversdiscussedabGove.t64.4LCreditsXY -pic'ExX-nicalexpertise.^10AThisin-cludesmanyofthemoGdesmentionedabGovewhichwere%createdforusewithinspGecialisedbranchesofmathematics,Ghowever,theD:notationsaredesignedto tquitenaturallywithintheframeworkofXY ,-picandaredusefulmoregenerally*.Finally,hwedaregratefultoY&YInc.formakingverynicelydonePostScriptversionsUUoftheUQXY U-picfontsavqailable."čAAnswersfftoallexercisesjLAnsw9erStoexercise1(p.2): Thetarget[]HisthecurrentUUentryitself.t6Answ9erTtoexercise2(p.3): TheUUauthordidN8\xymatrix{{\bullet}?\ar@{--}[d]\ar@{=}[dr]\ar@{-}[r]K&?{\bullet}\ar@{.}[d]\\{\bullet}?&{\bullet}\ar[l]}Notice ehowhasbGeenenclosedin{}IJsinceitisan\expandable"entity*,#i.e.,ade nedmacro:thisisrec-ommended.Answ9erTtoexercise3(p.3): TheUUauthorusedN8\xymatrix{A?\ar[r]^f\ar[dr]_{f;g} &?B\ar[d]^g\ar[dr]^{g;h}\\ &?C\ar[r]_h&D9}nAnsw9ertoexercise4(p.3): The7 authorentered\xymatrix{A?\ar[d]_f\ar[r]^f"&?B\ar[dl]|{i_B}\ar[d]^g\\B?\ar[r]_g&C}nAnsw9erTtoexercise5(p.4): TheUUauthordid\xymatrix{x?\ar@(ul,dl)[]|{id}\ar@/^/[rr]|f&&?f(x)\ar@/^/[ll]|{f^{-1}}}fXeKNotexthatbGotharrowsarecurved\abGove"relativeto eKtheirUUdirection.퍒eKAnsw9er)toexercise6(p.5): TheauthorusedtheeKdisplayN8eK\xymatrix{H1?\ar[rr]^-{1000000x}%B\ar[dr]?_(.2){2000x}|!{[d];[rr]}\hole_e&&?1000000\\H1000?\ar[r]_{2x}9\ar[urr]?_>>>>{x^2}_e&?2000}keKInLparticularnoticehowthebreakwasspGeci edtoeKhappGenexactlywherethetwoarrowscross.CF*oraneKeasierfXbutnotsogeneralmethoGdseeexercise12lasteKinUUsection2.7.eKAnsw9erTtoexercise7(p.5): TheUUauthortypGedN8eK\xymatrix@1{?A\ar[r]^*+[o][F-]{x}&B}%eKAnsw9erTtoexercise8(p.5): TheUUauthordideK\xymatrix@1{ HA?\ar@{/*\composite{{+}*{\times}}/}[rr]%6^*+\txt{High\\label}H&&?B}eKAnsw9ertoexercise9(p.6): The7 authorenteredN8eK\xymatrix{HA?\ar@/^/@{^{<}-_{>}}[r]%B\ar?@/_/@{{*}{x}{*}}[r]&B}eKAnsw9erTtoexercise10(p.6): TheUUauthortypGedN8eK\xymatrix@1{HA?\ar@/^/[r]\ar@/^/@<-1ex>[r]&B}eKAnsw9er(toexercise11(p.7): Thesize:!t+0al-eKwaysUUhaszerosize.퍒eKAnsw9er|toexercise12(p.7): Theiauthorcon-eKstructedN8eK\xymatrix@!0{H&?\lambda\omega\ar@{-}[rr]\ar@{-}'[d][dd]%B&?&\lambdaC\ar@{-}[dd]eK\\H\lambda2?\ar@{-}[ur]\ar@{-}[rr]\ar@{-}[dd]H&?&\lambdaP2\ar@{-}[ur]\ar@{-}[dd]eK\\H&?\lambda\underline\omega\ar@{-}'[r][rr]Jff[ J= "5-:9LMathematicsXDepartmenÎt,MacquarieUniversityJ,Sydney,Australia2109;e-mail: ross@mpw-:10LPÎartial_ fundingforthiscollab`d[r]`[r][r]L\ar@<+2pt>?`d[r]`[r][r]&B}ՍAnsw9erTtoexercise14(p.8): TheUUauthorused\newdir{?>}{{}*!/-5pt/@{>}}Answ9erTtoexercise15(p.9): TheUUauthortypGed\xymatrix@1{ A?\ar[r]|-{\SelectTips{cm}{}\object@{>>}} |>{\SelectTips{eu}{}\object@{>}}&?B}ՍAnsw9erTtoexercise16(p.9): TheUUauthortypGed\xymatrix{*=0{\bullet}\ar@/^/[dr]!U|1\ar@/^/[drr]!U|2\ar@/^/[drrr]!U|3\\&*+[F]\txt{x}&*+[F]\txt{x\\x}&*+[F]\txt{x\\x\\x}}ՍAnsw9ertoexercise17(p.10): TheLauthoren-teredUUthedisplay\xymatrix@dr@C=1pc{a?\ar[r]\ar@{->>}[d]&a'\ar@{.>>}[d]\\b?\ar@{.>>}[r]$&b'}ՍAnsw9ertoexercise18(p.10): TheFauthortypGed\xymatrix{A?\ar[r]^a="a"&B\ar[r]^b="b"&C \ar?@/^/"a";"b"}NoticetheuseofbGothexplicitbaseandtargetinthearrowUUbGetweenthelabGels.gweKAnsw9ertoexercise19(p.11): The\gauthoradded eKtheUQXY U-coGdeN8eK\save?[].[dd].[ddrr].[rr]*[F.]\frm{}="back"H\restoreeKinUUtheentrywith![ٲ,andH\save?[].[dd].[ddrr].[rr]*[F.]\frm{}E\ar@{.}?+UL;"back"+UL\ar@{.}+UR;"back"+URE\ar@{.}?+DL;"back"+DL\ar@{.}+DR;"back"+DRE\restoreeKinUUtheentrywith2toproGduce:$MSps: SDict begin xyc endW!, " {0.0 0.0 l}xyI" {28.94374 0.0 l}xyI" {0.0 0.0 l}xyǍ"꬟x" {0.0 0.0 l}xyǍ"꬟" {0.0 -14.52779 l}xyǍ"꬟( " {0.0 -13.52783 l}xyǍ"꬟( " {0.0 0.0 l}xy(čQ3232h3232C32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232C3232=㍍KZ32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232` $KZ3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232Q3232h3232C32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232C3232LCǍR꬟x" {0.0 0.0 l}xyǍR꬟( " {0.0 -34.05562 l}xyǍR꬟( " {0.0 0.0 l}xy2Ǎc" {0.0 0.0 l}xyǍqɟx" {11.05557 11.05557 l}xyǍqɟx" {0.0 0.0 l}xyUX" {0.0 0.0 l}xy.r" {27.26212 0.0 l}xy.r" {0.0 0.0 l}xyǍ ꬟x" {0.0 0.0 l}xyǍ ꬟A" {0.0 -35.05557 l}xyǍ ꬟A" {0.0 0.0 l}xy% hX3232荍3232332323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323{3232<捍NB׍32323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232D؟B׍3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232hX3232荍3232332323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323{3232Ǎ8" {0.0 0.008 dt}xyǍ" {23.20692 23.98546 dt}xyǍ" {0.0 0.008 dt}xyD`% " {0.00209 0.0 dt}xy` #(" {27.29022 23.98546 dt}xy` #(" {0.00209 0.0 dt}xyL{" {0.0 0.00522 dt}xy5" {23.20692 22.9855 dt}xy5" {0.0 0.00522 dt}xyDןL" {0.0 0.0127 dt}xy` #5" {27.29022 22.9855 dt}xy` #5" {0.0 0.0127 dt}xy1rPc2ǍAc" {0.0 0.0 l}xyǍLqɟx" {11.05557 11.05557 l}xyǍLqɟx" {0.0 0.0 l}xyǍ:꬟x" {0.0 0.0 l}xyǍ:꬟A" {0.0 -35.05557 l}xyǍ:꬟A" {0.0 0.0 l}xyW0!feT, -" {0.0 0.0 l}xy7꬟-" {11.79166 0.0 l}xyEȟ-" {7.88715 0.0 l}xyEȟ-" {0.0 0.0 l}xyHȟ0Pc!cfeTI!XE" {0.0 0.0 l}xy1rE" {27.26212 0.0 l}xy1rE" {0.0 0.0 l}xyǍcA" {0.0 0.0 l}xyǍq̟7x" {10.05562 10.05562 l}xyǍq̟7x" {0.0 0.0 l}xy4rIPǍAcA" {0.0 0.0 l}xyǍKq̟7x" {10.05562 10.05562 l}xyǍKq̟7x" {0.0 0.0 l}xyoEeKReferenceseK[1]AdobGeN SystemsIncorporated. NPostScriptd;L}'an-guageR}'eferenceManual,UUsecondedition,1990.eK[2]DonaldE.Knuth.1TheTKß'E-Xb}'ook.Addison-W*esley,1984.eK[3]LeslieoLampGort.L雍Q1t}\cmti7ATKß'E-X|AdDo}'cumentPreparationSystem.nAddison-W*esley,UU2ndedition,1994.eK[4]RossbR.MoGore.؃T;yp}'esettingNeuralNetsusingXY2-pic,UU1994.nAvqailablethrough[5].eK[5]Kristo erbDH.Rose.zTheb@XY D-pichomepage.hurl:http://www.ens-lyon.fr/~krisr}'ose/Xy-pic.htmli.eK[6]Kristo erH.Rose.8HowtotypGesetprettydia-gramFarrowswithTU>'ExX|designdecisionsusedinXYs-pic.In;JiuUrqZlatuxskqa,ɵeditor,Eur}'oTKß'E-X'92|Pr}'oceedingsSofthe7thEur}'opeanSTKß'E-XConfer}'ence,pages183{190,Prague,Czechoslovqakia,Septem-bGerUU1992.CzechoslovqakUUTU>'ExXUsersGroup.eK[7]Kristo er-H.Rose.tXY-picandnotationforcate-goricaldiagrams.%InvitedtalkatECCT-94,July1994.nAvqailableUUthrough[5].eK[8]Kristo erH.RoseandRossR.MoGore.XY Y-picDR}'ef-er}'enceManual.DIKU,nUniversityofCopGenhagen,Universitetsparken1,dDK{2100KbGenhavn,3.0UUedition,June1995.eK[9]MichaelD.Spivqak.TheUJoyofTKß'E-X|AUGourmetGuidetoT;yp}'esettingwiththeAU>'M S-TKß'E-XMacroPackage.bPAmericanMathematicalSoGciety*,рsecondedition,UU1990.LWeJ14c*tj??gwIndexT}w!,UU5,7,8 !{;},UU5&,UU2',UU7(,UU6(),UU5(0),UU5(1),UU5),UU6*,UU5,7{9,12+,UU5{7,10+=,UU5,10-,UU3,5{7,10--,UU6-=,UU5,10.,UU6/,UU6{8//,UU6:(),UU7:a(),UU7;,UU7<,UU4,6<<,UU4,6=,UU10>,UU4,6>>,UU4,6>>|,UU6>|,UU6@,UU3,5,10@!,UU10@(,UU4@/^/,UU4@/_/,UU4@1,UU3@<>,UU6@=,UU9@C=,UU9@H=,UU10@L=,UU10@M=,UU9@R=,UU9@W=,UU9@{},UU3[F-,],UU5[F--],UU5[F-:<3pt>],UU5[F.],UU5[F=],UU5[F],UU5[],UU3,6[d],UU5[l],UU5[o],UU5[r],UU5}wr:[u],UU5 tr:\\,UU2,5r:^,UU3,4,6{8r:^{'},UU6r:^{`},UU6r:^{|-},UU6r:_,UU3,4,6{8r:_{'},UU6r:_{`},UU6r:_{|-},UU6r:`,UU8r:{*},UU6r:{|-},UU6r:{|=},UU6r:|,UU3,4,6r:|<,UU6r:|<<,UU6,11r:||,UU6r:~,UU6r:~~,UU6r:2cell,UU12r:3{|-},UU6Sr:0,UU7r:absoluteUUangle,7 tr:absoluteUUentry*,7r:adjust,UU5r:adjustingUUpGosition,7r:\apit?,UU12r:\ar?,UU2,4r:arc,UU12r:arrow,UU2,4r:arrowUUhead,5r:arrowUUpassingunder,7r:arrowUUshaft,5r:arrowUUstyle,3,5r:arrowUUtail,5Sr:baseUUentry*,2,7r:bGend,UU8r:\bpit?,UU12r:break,UU3r:centered,UU5r:changingUUpGosition,7r:changingUUturnradius,8r:circleUUsegments,8r:circular,UU10r:columns,UU2,6r:combinedUUob8jects,5,8r:commutativeUUdiagrams,1,4r:compatibility*,UU11r:\CompileMatrices?,UU4r:\composite?,UU5,8r:computerUUmoGdernfonts,9r:coGordinates,UU3}w=X[COPYING,UU11 ?=X[copyright,UU11=X[cover,UU11=X[crossingUUarrows,5,7=X[cubGe,UU7=X[currentUUdirection,7=X[currentUUentry*,6=X[curve,UU4,8ꍒ=X[d,UU2=X[dashedUUarrow,6=X[dashedUUframe,5=X[defaultUUmoGdi er,10=X[defaultUUspacing,5=X[de ningUUarrows,8=X[degrees,UU7=X[directedUUgraphs,12=X[direction,UU4,7,8=X[directionals,UU8=X[dottedUUarrow,6=X[dottedUUframe,5=X[doubleUUarrow,6=X[doubleUUframe,5=X[elliptical,UU10=X[entriesUUoutsidematrix,9=X[entriesUUwithtext,9=X[entry*,UU2,9=X[entryUUformat,9=X[entryUUoutsidematrix,3=X[entryUUstyle,10=X[excursion,UU9=X[explicitUUpGositioning,4=X[extraUUentries,9=X[format,UU9=X[frame,UU5=X[freeUUsoftware,11=X[\frm?,UU5=X[ftp,UU11=X[GNU+General+PublicLicense, eX[11=X[goingUUaround,8=X[graph,UU12=X[grouping,UU10=X[grow,UU5=X[halfUUarrow,6=X[\hbox?,UU5=X[head,UU5=X[\hole?,UU3=X[hop,UU2,6=X[intersects,UU5=X[invisibleUUarrow,3=X[\jot?,UU4LWeJ15*tj??2px荑knot,UU12čl,UU2 1labGel,UU3,4,8labGelUUcenteredonarrow,3labGelUUstyle,10labGelUUwithanyob8ject,5labGelsUUastargets,10labGelsUUwithtext,9\labelstyle?,UU10L5ffA͉TU>'ExX2")Ʋ,UU2license,UU11lineUUbreak,5links,UU12loading,UU2merge,UU11movingUUtarget,7name,UU11newUUarrows,8\newdir?,UU8\NoCompileMatrices?,UU4o,UU6ob8ject,UU5\object?,UU9ob8jectUUmoGdi er,5,8,10\objectstyle?,UU10oldUUstyleofloading,11\OnlyOutlines?,UU4overwrite,UU7parallel,UU6\pit?,UU12plainUUtextentries,10pGoly*,UU12px荒r:pGolygon-like,UU12 r:pGosition,UU6,7r:ps,UU2N8r:quarterUUturn,8r:r,UU2 r:radius,UU8r:relativeUUangle,7r:relativeUUentry*,6r:relativeUUvector,7r:repGeatUUlastob8ject,5r:retrievingUQXY U-pic,UU11r:rotation,UU8,10r:round,UU10r:roundUUshapGe,5r:roundedUUframe,5r:rows,UU2,6N8r:segment,UU7r:\SelectTips?{cm}{},UU9r:shadedUUframe,5r:shaft,UU5,8r:shaftUUastip,6r:shaftUUcharacters,8r:shapGe,UU5r:\ShowOutlines?,UU4r:shrink,UU5r:sideways,UU6r:size,UU5r:sliding,UU6r:spacing,UU9r:square,UU5r:squigglyUUarrow,6r:tail,UU5r:target,UU6,7,10px荒=X[targetUUentry*,2 U=X[text,UU5=X[textUUinentries,9=X[textUUlabGel,5=X[textUUstyle,2=X[tip,UU5,8=X[tipUUcharacters,8=X[tipUUinshaft,6=X[tripleUUarrow,6=X[turn,UU8=X[twoGcells,UU12=X[\txt?,UU5,9S=X[u,UU2=X[uniformUUspacing,10=X[\usepackage?,UU2=X[v2,UU2=X[va(),UU7=X[vqariant,UU5,8=X[vector,UU7=X[vectorUUcoGordinates,7=X[vectorUUindirection,7=X[vectorUUtocorner,7=X[versionUU2,11=X[warranty*,UU11=X[web,UU12=X[W*orldUUWideWeb,11=X[x,UU6=X[\xymatrix?,UU2=X[\xymatrixnocompile?,UU4=X[\xyoption?,UU2,11=X[xypic.sty,UU11=X[xypic.tex,UU11LWeJ16;>}1t}\cmti7.- cmcsc10-- cmcsc10,N cmbx12+ cmmi10 0ercmmi7O \cmmi5K`y cmr10ٓRcmr7Zcmr5u cmex10