[PDF] [PDF] LaTeX Math Symbols - UCI Mathematics

[PDF] Notes on Writing Mathematics - MIT OpenCourseWare

But a recap is never part of a mathematics paper B Mathematical style There is a highly developed standard international style of writing math ematics, which this 

Math symbol tables

Setting up MathTlme Looking at a mathematical artide typeset with the Times text font, you may find that the Computer Modern math symbols look too thin

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This edition of the Braille Mathematics Notation has been prepared by the Mathemat- ics Committee of the letters standing alone or starting a mathematical expression in ordinary text now require a letter sign as an apostrophe ) 5 gm ;1

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A Mathematical symbols B Horrible Mathematical Examples to Study sometimes resembles a grave accent or back-quote) and ' (apostrophe)

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Typesetting Mathematical Formulae placement of \bar for a variable with subscript The apostrophe mark ' gives a prime: 3 8 List of Mathematical Symbols 63

[PDF] LaTeX Math Symbols - UCI Mathematics

31 mai 2000 · entries are typeset as mathematics (using “text style”); entries insert 't, i e , a quote (apostrophe) character followed by a target, for each entry 

AMS Style Guide - American Mathematical Society

sives and indicating contractions, the apostrophe is used in mathematics to form the plural of a single character variable Consult The Chicago Manual of Style 

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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.

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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 )aremirrorquotesdbs_dbs47.pdfusesText_47