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3/29/17, 10*20 AMLaTeX Math Symbols

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LaTeX Math Symbols

The following tables are extracted from The Not So Short Introduction to LaTeX2e, aka. LaTeX2e in 90 minutes, by Tobias Oetiker, Hubert

Partl, Irene Hyna, and Elisabeth Schlegl. It can be located here.

3/29/17, 10*20 AMLaTeX Math Symbols

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3/29/17, 10*20 AMLaTeX Math Symbols

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Last modified: Wed May 31 14:04:55 CDT 2000

X Y -picUser'sGuide

Kristo!erH.R ose !krisrose@ens-lyon.fr"

Version3.7,February 16,1999

Abstract

X Y -picisapack agefort ypesetting graphsanddiagrams usingKnuth's T E

Xtyp esettingsystem.X

Y -picworkswith mostofthe manyformats available; e.g.,plainT E X, L A T E

X,andA

M S-T E

X.Severalstyles ofinputforvarious

diagramtyp esaresupported;theyallshareamnemonic notationbasedon thelogicalcomposition ofvisualcom- ponents.Thisguide concentrateson howto typeset "matrix-like"diagrams,suchascomm utativediagrams, inthefollo wingstyle: U y x (x,y)##X!ZY q p%% X f Yg Z wastypesetb ytheX Y -picinputlines \xymatrix{

U\ar@/_/[ddr]_y\ar@/^/[drr]^x

\ar@{.>}[dr]|-{(x,y)}\\ &X\times_Z Y\ar[d]^q\ar[r]_p &X\ar[d]_f \\ &Y\ar[r]^g &Z}

Suchdiagramshave thefollo wingcharacteristics:

•Specifiedasamatrixof entriesthat areautomati- callyalignedin rowsand columns. •Anyentrymaybe connectedtoanyother en- tryusinga variety ofarro wstylesallrotatedand stretchedasrequired. •Arrowsmaybedecoratedwith labelsthataretied toasp ecifiedpoin talongthearrow andextendin aparticulardirection; andarrows may bepaired, cross,andvisit/b endaroundother entries"onthe way." Severalotherstylesof inputare supported;ashortsurvey ofthep ossibilitiesisincluded lastattheendalong with informationonho wX Y -piccanbeobtained.

Contents

Preface2

1Basics 2

1.1Loading. ... .. ... ... ... ..2

1.2Entrie s........ ... ... .. ..2

1.3Arrows ...... ... ... ... .. .2

1.4Labe ls........ ... ... .. ..3

1.5Bre aks........ ... ... .. ..3

1.6Curving. ... ... ... ... .. ..4

1.7Spe edinguptypesetting.. ... ...4

2MoreA rrowsand Labels4

2.1Explicit labelpos itioning.......4

2.2Labe lingwithanyobject ... .....5

2.3Morearro wst yles.... ........5

2.4Slidingarro wsside ways.. ......6

2.5Moretarge ts.. ..... ... ... .6

2.6Changingthe target. ... ...... 7

2.7Arrows passingunder ......... 7

2.8Moreb endingarro ws....... ...8

2.9Defining newarrowtyp es.... ...8

3MoreEn tries9

3.1Manual entryformatting ........9

3.2Extrae ntries outsidethematrix...9

3.3Spacing androtation... ... ... .9

3.4Entry style.. ......... ... .10

3.5Naming forlateruse astargets ....10

3.6Groupingob jec ts........... .10

4Av ailabilityandFurtherInformation11

4.1Getting X

Y -pic.. ... .. ... ... .11

4.2Bac kwardscompatibility..... ...11

4.3Furthe rreading...... ...... .12

4.4Credits ..... ... ... ... ... .13

AAnsw erstoallexercises13

References14

Index15

Laboratoiredel'InformatiqueduP arall´elisme, EcoleNormaleSup ´erieure deLyon;46,All´eed'Italie;F-69364Lyon7, France.

1

Preface

Thisguidee xplainssom efeaturesof X

Y -picthatare relevanttotypesettingof"matrix-lik ediagrams "as usedin,forexample, cate gorytheory; pleasereferto therefe rencemanual[8]forcompleteinformationon thedes cribedconstructions.Theguideassumesthat youhaves omeexperiencein usingT E

Xfort ypes et-

tingmathe matics,e.g.,hav estudied[2,ch.16-19], [3, sec.3.3],or[9],andthatX Y -picisins talledon your T E

Xsys temasdescribedinthe INSTALLfileacc om-

panyingthedistribution.

Thefirst sectiondes cribeswhatyouneedto get

started,inparticularallthatis neede dtotypes et thediagramin theabstrac t.Se ction2 and3explain advanceduseofarrowsande ntries,res pec tively.Fi- nally,section 4explainswhereandunderwhatcondi- tionsX Y -picisa vailable, givestherelationofversion

3.7topre viousve rsions,andlis tsfurthersourcesof

information.

Throughoutwe giveexerc isesthatyou shouldbe

abletos olveas yougoalong;allexerc ises arean- sweredattheendjustpriortothere ferenc esand index.

1Basics

Thisse ctionexplainstheX

Y -diagramcons truction conceptsneededtoget startedwithtypesetting matrix-likediagrams.

1.1Loading

TheX Y -picse tupusedinthisguideis loadedbyin- sertingthelines \inputxy \xyoption{all} inthede finitionspartof yourdocume nt.1

Ifyou wish

toloadonly thefeature syou use, oryouwishtouse non-standardfacilitieslik ethev2backwardscompat- ibilitymode 2 orthepsPostScript 3 backendthen thisisals opos sibleasdes cribedinthereferencem an- ual[8].

1.2Entries

Adiagramis create db ythecommand

\xymatrix{...}wherethe"... "should bereplacedbyentriestobe alignedinrowsandcolumnswhere •entriesinarowarese paratedb y&, 4 and •entirerowsareseparate dby\\.

Forexample,

A m i=n i 2 D wastypes etby \xymatrix{

A&*+[F]{\sum_{i=n}^m{i^2}} \\

&{\bullet}& D\ar[ul]}

Noticethefollowing:

•entriesaretypeset asmathe matics(using"text style");entriesshouldnots tartwithamacro (asillustrate dbytheuseof{}around\bullet. •allen triesarecenteredandthe separation be- tweenrowsandcolumnsisusuallyquite large inadiagram , •emptyentriesatthee ndofrowsmaybeomit- ted, •"X Y -decorations"(here\ar[ul])ine ntries al- lowdrawingofarro wsandsuch relative tothe entrieswithoutchangingtheove ralllay out,and •"X Y -modifiers"(here*+[F])first inentriesal- lowchangingtheform atandshape inman y ways.

1.3Arrows

An"arrow" inanX

Y -picdiagramis agene ricte rm forthedra wndec orationsbetw eentheentriesof the basicmatrixstruc ture.InX Y -picallarro wsmus tbe specifiedalongwiththeentryinwhichthey start;this iscalle dtheirbaseentry.Each particulararrowcom - mandthenrefe rsexplicitlytoits targetentry.This isobtained usingthe\arcommandwhichaccepts manyoptionsofwhichwe willde scrib eafewhere andsom emoreinsection2. Initssimples tform an arrowisente red as\ar[hop]wherehopisas equenc e ofsingle letters:uforup,dfordown, lforleft, and rforright, e.g.,thearro w\ar[ur]reads"types etan arrowfromthecurre nt entry tothatoneupandone right." 1 L A T E X2 [3]userscan use\usepackage[all]{xy}. 2

Ifyou usetheversion2loading command\inputxypic(orthexypicdocumentstyleoption)thenthe v2optiondescribed in

section4.2will beloaded automatically. 3 PostScriptisaregistered Trademarkof Adobe, Inc.[1]. 4

ThuswhenusingX

Y -constructionsinv olving&insideothertabular constructionsthenenclose theX Y -picconstructionin anextra pairofbraces! 2

Exercise1:Whichentrydo es[]referto?

Therelativ ecoordinatesspec ifiedinthiswayare

purelylogical,e.g.,ifthe diagramcon tainsv erywide entriesthen"diagonal"arrowswillbe nearlyhorizon- tal.Thec onstructe darrowsarealignedalongtheline betweenthecentersofthebaseandtarget entrie s; theywillnotautomatic allydisapp ear underentries thatthey cross(wedis cusshowthisisac hievedin section2.7).

Thearrow stylekan bechangedbywritingthe

commandas\ar@style[hop].Thiswill bede sc ribed inmore detailinsec tion2.3;herewe justlis tthemost common@styles(obvious variationsalsow ork):

Exercise2:Typeset

1.4Labels

Youcanputlab elsonarrows .Labe lsareconceptual-

izedassub-andsup ersc riptsonarrowssuc hthat they areplace dintheusualpositions (as"limits "),i.e.,^ reads"above "and_"below"onanarrowpointing right.Noticethatthe positionsdepe ndonlyonthe directionofthearrow,theabs olutenotionsof "up," "down,"etc.are notimportant.Forexam ple, $\xymatrix@1{

X\ar[r]^a_b&Y &Z\ar[l]^A_B}$

willse tX a b YZ A B (the@1isas pec ialcode thatcan beused for"one-line"diagrams toimprove theplace mentontheline;moresuchspacingco des aredes cribedinsection3.3).

Itisp ossible touselabelsthatarenotsingle let-

ters,digits,orcontrol sequences :ifa simplemath formulainthedefault st yle(sc riptstyle)is desired thensimplye nclosein{...}.Inprac ticean ything canbeuse dasalabe lasdescribedin sec tion2.2.

Eachlabelis placedperpendic ulartothe arrowat

thepoin thalfwaybetwe enthecenters ofthebaseand targetobjects .Thisisusuallythemostaesthethic, however,indiagramswherethesizesof theen tries varymuchit issometimesnic erto placethe label atthec ente roftheactualarrow.Thisbehaviouris or_:A#B#C#D

Bwastypes etby$\xymatrix@1{

A\timesB\timesC\times D\ar[r]^-{+} &B

(itbe comesA#B#C#D

Bwithoutthe-).

Infact -isinjus toneof themayp ossible placings

oflabe lsdescribedin section2.1. theoryas A f f;g B g g;h C h D

1.5Breaks

Itisals opos sibleto"break" anarrowwithalabelus-

willse tAf %%B.

Ifyou justwantan emptybre akyoushould

usethespe cial\holebreak:thearrowA %%B wastypes etbyincluding$\xymatrix@1{

A\ar[r]|\hole&B }$inthete xt.

Adi erentuseofbreaksisto placealabel some - whereinadiagramouts idethenorm alm atrixme sh: thisisac complis hedby"breaking"aninvisiblearrow obtainedusingthe@{}arrowstyle: thesquare A %%B B%% C wastypes etby \xymatrix{\ar@{}[dr] |{=}

A\ar[d]\ar[r] &B\ar[d] \\

B\ar[r]& C}

Thereismoreon breaks insection2.7.

Exercise4:Typesetthefirstaxiomofcategory

theoryasthedispla y A f f B i B g B g C 3

1.6Curving

Arrowscanbe madetocurve ,forexampleto avoid

goingthroughanothe ren try,usingthe specialstyle @/curving/.Thes imples tstylesofcurvingarethe following,shownapplie dtoanarrowfromAtoB: @/^/A B @/_/A-- B @/_1pc/ A B

Asthelas texam pleshowsadim ensioncanbein-

sertedjustafter^or_ifmore orlesscurving isde - sired.

Incas eitiseasierto spe cifythe in-andout-going

directionsofthecurvingthen thatisals opos sible: use @(in,out)whereinandoutareoneof thefollowing directions: dl d $$dr r %%ur 00 u 11 ul 22
l

Inthisc asethe curvingiscomputeds uchthat the

curvebeginsatthebas eentryintheindirection andends atthetargeten tryfromthe outdirection (thisme ansthat@(d 1 ,d 2 )and@(d 2 ,d 1 )aremirror images.Seesection2.6for moredirections).

Exercise5:Typeset

xid

33f44f(x)

f !1

551.7Speedinguptyp esetting

Onethingthat youwill noticeis thatX

Y -piciss ome- timesslowintyp esettingdiagrams(thisis tobe ex- pectedconsideringthenumber ofdrawingoperations performedasreflectedbythe numb erlastineach ingalle ntries witha(nonexpandable)characteror{ thenyoucan insertthede claration \CompileMatricesinthepre ambleof yourdocument:this willcre ate temporaryfiles 5 containingcompiledversionsofeach matrixthatcanb eloade dveryquickly; theyareau- tomaticallyrecreatedwhe namatrixischanged.

Ifthisc auses somediagramstonotwork,then

suchcompilationcanb eexplicitlyswitched o by using\xymatrixnocompileinplace of\xymatrix.

Compilationcanbe switchedo

completelywith \NoCompileMatrices(whichrespe ctsT E

Xgrouping

asdoe s\CompileMatrices,by theway).

Andify ouares tillnotsatisfied withthes peed

thenyoucan addthefollowing: \OnlyOutlineswhichwillomitall compile dpictures;the additional command\ShowOutlineswilladda dottedre ctangle outliningthes izeof thepicture.

2More ArrowsandLab els

Inthiss ection weexplainanumberofv ariationsof

thearrow commandsthatare usefulincommutative diagrams.

2.1Explicitlab elpositioning

Thelabe lcommandsexplainedin section1.4place

thelabe ltextnearthepoin talongthearrowhalfw ay betweenthecentersofthebaseandtargete ntrie s.

This,howev er,maybechangedbyinsertingaplace

betweenthe^,_,or|,andthe actuallab el(in fact- isaplace).Inge neraly oumayinsertthefollo wing: •willplace thelabelat thepoin twheretheactualarrow ends, i.e.,"disapp earsbelow"thetarget, so$\xymatrix@1{A\ar[r]^>{+}&B}$will typesetA B. •<>willplace thefollowingla- belatapointjus ta bit 6 furtherfrom thebe ginningandendofthearrow, so$\xymatrix@1{A\ar[r]^>>{+}&B}$will typesetA

B.Using moreswill

movethelabelfurtherin. 5

Thetemporary filesarenamedthesame asyour document but.texisreplacedb y-n.xycwherenisasequence numb er.

6 "Abit"is infacta T E

X\jotwhichisusually3pt.

4 •Afactor in()s:(a)indicatesthatthe labelshouldbe"tied" tothepoint aof thewa yfromthecenter ofthebas een- try(calle d(0))tothe cen ter ofthetar- get(called(1))inste adofinthemiddle, so$\xymatrix@1{A\ar[r]^(.3){+}&B}$will typesetA B. •Afactor canbegiv enaftersomes,inwhichc asethe placeiscom puted asifthe basew ass pecifiedb ythes.Hence $\xymatrix@1{A\ar[r]^<(0){+}&B}$will typesetA B. •Finally,thereisa simplewa ytode notethe placeonanarrow where itinte rsectswitha straightlinebetwe en twopoints:theplace !{t 1 ;t 2 }placesthelabelrelativ eto thepointquotesdbs_dbs9.pdfusesText_15