XY-pic User's Guide
Contents
1. amp circ typesets As you see labels are set separately on each segment Exercise 12 Typeset the lambda cube Aw AC 7 a A2 En AP2 Aw APw Z a A gt AP Hint going under an empty entry leaves a small gap at that location The compactness is achieved using a trick described in section 3 3 2 8 More bending arrows Finally arrows can bend around entries just insert dt i e a backquote and a direction d followed by a target t for each turn that starts out in the d direction and ends in a quarter turn towards the tar get t This is different from the curving described earlier in that all turns consist of a straight part end ing in a turn which is a multiple of 1 g circle segments and each segment allows separate labels The possible directions are those of section 1 6 and 2 6 and the possible targets include all those discussed above Actually the direction is only re quired for the first in a series of turns since the final direction of one turn is the obvious choice for the fol lowing turn Furthermore turns can be changed from the default by adding either d for anticlockwise turn to d or _d for clockwise turn to d where d is the exit direction of the turn Finally the turns will have radius 10pt by default but this can be changed to any dimension R from a particular turn and onwards by inserting R imme diately after the of the turn Here is an example2. tips using this form thus it is necessary to include all three of tail shaft and head when using it The ad vantage is that it is possible then to fill with a tip Furthermore the following additional possibilities are available when using this notation HEF oc te ee ee ff eee Pak te SSP sw r ot SLEP g AEP Geet f7 ae ed P 5 AN The even more general form object can be used where object refers to any of the constructions de scribed in section 2 2 Exercise 9 Typeset AaB 2 4 Sliding arrows sideways It is often desirable to have several parallel arrows between two objects This can be done by sliding ei ther or both arrows sideways a distance given as a TX dimension enclosed in lt gt s it specifies how far sideways the arrow should be moved e g xymatrix A ar lt iex gt dr a_ amp B ar lt iex gt ul b ar lt 1ex gt r c amp C ar lt 1ex gt 1 da_ will typeset A nC Beor C d an A positive distance will slide the arrow in the direction e g the two arrows above are slid in the direction of the labels a b c and d respectively a negative distance in the _ direction The dis tance lt 1ex gt is often appropriate since it corresponds roughly to the height of letters like x in the type size being used Exercise 10 Typeset A SB 2 5 More targets The target address can be given in a large number of formats call
3. variant tail shaft head variant head that in describes arrows with the indicated tail shaft and head on the first form the tail and head can be omitted the second style defaults to having no tail and a standard shaft The plain TX command hbox corresponds to mbox in IATFX and text in the A S variants The following possibilities exist for head and tail which we will denote tips here shown as heads lt ave Do eee x x lt lt e gt gt gt F lt PE a gt RSA a lt lt al gt gt A a pac yD o o zl J A and the shaft should be one of the following The variant should be empty or one of the follow ing above variant _ below variant 2 double variant 3 triple variant Here are some standard arrows in this notation all from A to B as usual lt gt A B lt gt A B _ lt gt A B 2 lt gt A4 B 3 lt gt A lt B As a special convenience and are provided as ab breviations for and with variant forced to 2 As it can be seen the variant will affect the entire arrow Sometimes this is not what is wanted In that case a local variant can be used by entering any of the tail shaft and head on the following form variant tip variant shaft Here are some arrows where this is required A gt B A B F gt _ gt Notice that there is no distinction between shafts and
4. 1 A ar gt gt r amp B typesets A B The second argument here can be used to specify a point size 10 11 or 12 if desired the default is 10 5 cm can be replaced by eu and xy to get tips in Euler and the default technical style respectively The declara tion respects T X grouping Exercise 15 Typeset A gt B Hint With the construction objectobject one can typeset an Xy pic object anything that could follow a in section 2 2 in any context 3 More Entries This section explains what can go in an entry and how the general form of the entries is changed 3 1 Manual entry formatting All the entries we have seen thus far have been simple math objects However it is possible to change the format of an individual entry by using the form xobject arrows This allows complete control over what object is placed in the entry overriding any spacing and other conventions for the entry This was how the frame was obtained in the figure in section 1 2 A simple use of this is to insert text in entries us ing txt objects just like labels as described above in section 2 2 xymatrix txt A very long and stupid program ar rr txt weird arrow amp amp txt lt 2pc gt Com pli cated Code will typeset weird Com A very long and stupid arrow pli program cated Code Exercise 16 Typeset 3 2 Extra entries outside the matrix It is possible to
5. 7 adjust 5 adjusting position 7 apit 12 ar 2 4 arc 12 arrow 2 4 arrow head 5 arrow passing under 7 arrow shaft 5 arrow style 3 5 arrow tail 5 base entry 2 7 bend 8 bpit 12 break 3 centered 5 changing position 7 changing turn radius 8 circle segments 8 circular 10 columns 2 6 combined objects 5 8 commutative diagrams 1 4 compatibility 11 CompileMatrices 4 composite 5 8 computer modern fonts 9 coordinates 3 15 COPYING 11 copyright 11 cover 11 crossing arrows 5 7 cube 7 current direction 7 current entry 6 curve 4 8 d 2 dashed arrow 6 dashed frame 5 default modifier 10 default spacing 5 defining arrows 8 degrees 7 directed graphs 12 direction 4 7 8 directionals 8 dotted arrow 6 dotted frame 5 double arrow 6 double frame 5 elliptical 10 entries outside matrix 9 entries with text 9 entry 2 9 entry format 9 entry outside matrix 3 entry style 10 excursion 9 explicit positioning 4 extra entries 9 format 9 frame 5 free software 11 frm 5 ftp 11 GNU General Public License 11 going around 8 graph 12 grouping 10 grow 5 half arrow 6 hbox 5 head 5 hole 3 hop 2 6 intersects 5 invisible arrow 3 jot 4 knot 12 1 2 label 3 4 8 label centered on arrow 3 label style 10 label with any object 5 labels as targets 10 labels with text 9 labe
6. involving all of these features xymatrix circ ar r d a Crr b 4pt rr c rrr d _dl drrr e arrr f amp circ amp circ amp circ circ amp circ amp circ amp circ typesets a e o o b d c f o o o o The example illustrates the following points e If the segment can not be made as short as re quired then it will point past the target This is useful for going around entries e There is one per turn thus each target ap pears as many times as there are turns towards it except the last target that appears one more time namely both with for each turn towards it and once as an ordinary target to set the final stretch e The sizes of the intermediate targets are ig nored Exercise 13 Typeset A B 1 2 9 Defining new arrow types Last in this treatment of arrows we will explain how new arrows can be defined The crucial fact is that the characters used for tips and shafts are restricted to the following gt lt ox O uo tip characters Senis shaft characters When an arrow is interpreted by Xy pic it is first split into the three components and then each component is looked up in a library of so called directionals It is possible to add new such directionals using the command newdir directional composite where directional should be a sequence either of tip characters or of shaft characte
7. outlining the size of the picture 2 More Arrows and Labels In this section we explain a number of variations of the arrow commands that are useful in commutative diagrams 2 1 Explicit label positioning The label commands explained in section 1 4 place the label text near the point along the arrow halfway between the centers of the base and target entries This however may be changed by inserting a place between the _ or and the actual label in fact is a place In general you may insert the following e lt will place the label at the point where the actual arrow begins i e appears from under the base so xymatrix 1 A ar r lt amp B will typeset AB e Similarly gt will place the label at the point where the actual arrow ends i e disappears below the target so xymatrix 1 A ar r gt amp B will typeset A 3B e lt lt and gt gt will place the following la bel at a point just a bit further from the beginning and end of the arrow so xymatrix 1 A ar r gt gt amp B will typeset A B Using more lt s or gt s will move the label further in 5The temporary files are named the same as your document but tex is replaced by n xyc where n is a sequence number 6A bit is in fact a TEX jot which is usually 3pt e A factor in s a indicates that the label should be tied to the point a of the way from the center of the base en try called 0
8. p 9 The author typed xymatrix 1 A ar r SelectTips cm object gt gt gt SelectTips eu object gt amp B Answer to exercise 16 p 9 The author typed xymatrix 0 bullet ar dr U 1 ar drr U 2 ar drrr U 3 amp F txt x amp F txt x x amp F txt x x x Answer to exercise 17 p 10 The author en tered the display xymatrix dr C 1pc a ar r ar gt gt d amp a ar gt gt a b ar gt gt r amp b Answer to exercise 18 p 10 The author typed xymatrix A ar r a a amp B ar r b b amp C ar 7 Nal Wp Notice the use of both explicit base and target in the arrow between the labels 14 Answer to exercise 19 p 11 The author added the Xy code save dd ddrr rr F frm back restore in the entry with Aw and save dd ddrr rr F frm ar UL back UL ar UR back UR ar DL back DL ar DR back DR restore in the entry with A2 to produce he ee PL coaB A2 in AP2 Aw APw FA Hee aie A AP o References 1 Adobe Systems Incorporated PostScript Lan guage Reference Manual second edition 1990 2 Donald E Knuth The TRXbook Addison Wesley 1984 3 Leslie Lamport ATEX A Document Preparation System Addison Wesley 2nd edition 1994 4 Ross R Moore Typesetting Neural Nets u
9. to the center of the tar get called 1 instead of in the middle so xymatrix 1 A ar r 3 amp B will typeset A eee e A factor can be given after some lt or gt s in which case the place is computed as if the base was specified by the lt s and target specified by the gt s Hence xymatrix 1 A ar r lt 0 amp B will typeset A gt B e Finally there is a simple way to denote the place on an arrow where it intersects with a straight line between two points the place t t2 places the label relative to the point on the arrow where the line from the target t to the target t crosses it Bug Only works for straight arrows at present As usual more possibilities can be found in the refer ence manual 8 fig 2 Exercise 6 Typeset 1000000x 1 1000000 a S 1000 E 2000 2 2 Labeling with any object Xy pic supports a general format for entering any TEX text as labels as well as entries to be explained later The character is reserved for this in its simplest form math will typeset the math material as an object This is like math except that the default style is ignored and there is no added blank margin However in general the following form of object is available modifiers text where modifiers can be used to change the shape and size of the constructed object The following are the most common the full list of possibilities can be found in the reference manua
10. 1 Basics EL Leading rss amp ade eetaega a amp amp Eat U2 Entries ad fx ee ey epee Gs WE ee 123 MATEOWSxe 4 eae TE wet set ee dae es ee Be A TA Dabelsits 4 2 6 2 4 of bee ee dad L5 Breaks 3 xcveya ete a a Bae EN 6 CUTIE a eoon eins 4 ay alae doadeder ah 1 7 Speeding up typesetting 2 More Arrows and Labels 2 1 Explicit label positioning 2 2 Labeling with any object 2 3 More arrow styles 2 4 Sliding arrows sideways 2 5 More targets 0 2 6 Changing the target 2 7 Arrows passing under 2 8 More bending arrows 2 9 Defining new arrow types 3 More Entries 3 1 Manual entry formatting 3 2 Extra entries outside the matrix 3 3 Spacing and rotation 3 4 Entry style 3 5 Naming for later use as targets 3 6 Grouping objects 4 Availability and Further Information 4 1 Getting Xy pic 2 4 2 Backwards compatibility 4 3 Further reading oaoa FA Credits a 4 ee oer decks R E A A Answers to all exercises References Index 2 oNN DA AA KK rR Wwwnnnw WN ooo 10 10 11 11 11 12 13 13 14 15 Laboratoire de l Informatique du Parall lisme Ecole Normale Sup rieure de Lyon 46 All e d Italie F 69364 Lyon 7 France Preface This guide explains some features of Xy pic that are relevant to typesetting of matrix like diagrams a
11. Xy pic User s Guide Kristoffer H Rose krisrose ens lyon fr Version 3 7 February 16 1999 Abstract Xy pic is a package for typesetting graphs and diagrams using Knuth s TEX typesetting system Xy pic works with most of the many formats available e g plain Tex ISTeX and AMS T X Several styles of input for various diagram types are supported they all share a mnemonic notation based on the logical composition of visual com ponents This guide concentrates on how to typeset matrix like diagrams such as commutative diagrams in the following style was typeset by the Xy pic input lines xymatrix U ar _ ddr _y ar drr x ar gt dr x y amp X times_Z Y ar d q ar r _p amp X ar d _f amp Y ar r l g amp Z Such diagrams have the following characteristics e Specified as a matrix of entries that are automati cally aligned in rows and columns e Any entry may be connected to any other en try using a variety of arrow styles all rotated and stretched as required e Arrows may be decorated with labels that are tied to a specified point along the arrow and extend in a particular direction and arrows may be paired cross and visit bend around other entries on the way Several other styles of input are supported a short survey of the possibilities is included last at the end along with information on how Xy pic can be obtained Contents Preface 2
12. a tail is not supported Fiz Use the supported lt notation Finally note that sometimes the spacing with ver sion 3 7 is improved relative to earlier versions Please report all other things that do not work the same in version 2 6 and 3 7 to the author 4 3 Further reading The reference manual 8 describes several more in put modes that are useful when the diagram is not organised as a matrix We ll give some examples of such diagrams but refer to the reference manual for the details e The graph feature allows input of data struc tured as directed graphs to make it easy to pro duce such pictures as cas Cm ta e The knot feature allows drawing of mathe matical knots and links like simple link figure 8 knot cinquefoil e The 2cell feature provides special support for 12 categorical twocells like B lt 2 Q e The poly feature allows polygon like struc e The web feature allows composition in lat tices such as a8 gt o e The arc feature is suitable for effects like In each case the figure is produced with relatively few lines using techniques documented in the respective sections of the reference manual together with the de tails of the Xy pic kernel and extensions arrow and matrix features as used in this guide further exten sions provide support for use of colour POSTSCRIPT effects a
13. an put labels on arrows Labels are conceptual ized as sub and superscripts on arrows such that they are placed in the usual positions as limits i e reads above and _ below on an arrow pointing right Notice that the positions depend only on the direction of the arrow the absolute notions of up down etc are not important For example xymatrix if X ar r 7a_b amp Y amp Z ar 1 7A_B will set X lt y gt Z the 1 is a special code that can be used for one line diagrams to improve the placement on the line more such spacing codes are described in section 3 3 It is possible to use labels that are not single let ters digits or control sequences if a simple math formula in the default style script style is desired then simply enclose in In practice anything can be used as a label as described in section 2 2 Each label is placed perpendicular to the arrow at the point halfway between the centers of the base and target objects This is usually the most sthethic however in diagrams where the sizes of the entries vary much it is sometimes nicer to place the label at the center of the actual arrow This behaviour is requested by inserting a minus right after the or_ Ax BxCx D B was typeset by xymatrix 1f A times B times C times D ar r amp B it becomes Ax B x C x D gt B without the In fact is in just one of the may possible placing
14. declaring the default modifiers to be applied to all entries that do not override them cf section 2 2 entrymodifiers o F SelectTips cm xymatrix l1pc txt start ar r amp 0 ar r u b ar r _a amp 1 ar r b ar r d _a amp 2 ar r b ar dr_1 1 amp o F 3 ar ur71 111 drf 111 b 111 ar dr_1 11 _ur 11 11 ur 1 _a 1 will typeset Notice how we obtain the double ring using the xobject form which then has to include all the desired modifiers and how the use of computer modern tips is nice for diagrams as these 3 5 Naming for later use as targets If you build an entry with a long and complicated excursion then you might wish to be able to refer to it later Xy pic provides a mechanism for this there is a special target form which we haven t discussed yet t name This will introduce the new target name which will refer to the target just before the This is particu larly useful inside excursions of course and can also be used after labels a AS b Exercise 18 Typeset A gt B gt C 3 6 Grouping objects Sometimes you wish to frame or otherwise treat a rectangle of objects as a single object This is pos sible with the last two target position forms that we will mention t s merge t with simple s t make t simple The first will enlarge t to also cover the simple s simp
15. documents but if you distribute any part of Xy pic including modified versions to someone then you are obliged to ensure that the full source text of Xy pic is available to them the full text of the license in the file COPYING explains this in somewhat more detail 4 2 Backwards compatibility The first widely distributed version of Xy pic was ver sion 2 from release 1 40 to release 2 6 A special compatibility mode is used automatically if the old style of loading is used using files named xypic tex and xypic sty You can also mix old and new di agrams in a document if you load as described in section 1 1 and add the declaration xyoption v2 This provides almost full backwards compatibility the following are the only known exceptions e Automatic shortening of arrow tails by lt lt break was a bug and has been fixed so it does not work any more Fiz Put a lt hole break before it as described in section 2 3 e The release 2 6 position operator is not avail able Fix Use the and operators de scribed in detail in the reference manual 8 e Using t t2 x y as the target of an arrow command does not work Fir Enclose it in braces i e write ty t2 x y e The old pit apit and bpit commands are not defined Fix Use gt or tip with variants and rotation e The even older notation where an argument in braces to rto and the others was automati cally taken to be
16. e of the following directions u ul ur d y dr d In this case the curving is computed such that the curve begins at the base entry in the in direction and ends at the target entry from the out direction this means that d d2 and d2 d1 are mirror images See section 2 6 for more directions Exercise 5 Typeset anaes 1 7 Speeding up typesetting One thing that you will notice is that Xy pic is some times slow in typesetting diagrams this is to be ex pected considering the number of drawing operations performed as reflected by the number last in each xymatrix message If you follow the rule of start ing all entries with a nonexpandable character or then you can insert the declaration CompileMatrices in the preamble of your document this will create temporary files containing compiled versions of each matrix that can be loaded very quickly they are au tomatically recreated when a matrix is changed If this causes some diagrams to not work then such compilation can be explicitly switched off by using xymatrixnocompile in place of xymatrix Compilation can be switched off completely with NoCompileMatrices which respects TeX grouping as does CompileMatrices by the way And if you are still not satisfied with the speed then you can add the following OnlyOutlines which will omit all compiled pictures the additional command ShowQutlines will add a dotted rectangle
17. ed positions The full range of possibili ties is described in the reference manual 8 fig 1 here is a number of useful ones in addition to the hop format described in section 1 3 e r c where r c are integers denotes the rela tive entry found r rows below and c columns to the right of the current entry the current entry itself is thus 0 0 This always corresponds to a hop e g 1 2 is the same as drr and 2 0 is the same as uu e r c where r c are positive integers denotes the absolute entry found in the rth row and cth column of the diagram The top left entry is 1 5 1 e t t where t is any target changes the base entry of the present arrow to t and then sets the target to t relative to the original base en try For example xymatrix A B amp C ar lt 1ex gt ul ar lt 1ex gt ul typesets A n i e the second ar ul arrow starts at the ul entry and ends in the current entry See section 3 5 for how to use a label as a target 2 6 Changing the target It is possible to overwrite a target with another by appending something of the form object to it This has the effect of typesetting the object at the current position thus effectively on top of the target and then use what was typeset as the target A target may also have its position changed by one of the following constructions e vector or vector which changes the target to be a zero sized one a
18. f sec tion 2 2 with the same meaning i e replace set with increase increase to at most decrease and decrease to at least respectively For exam ple xymatrix 1 Opt M Opt A amp B C amp D in the text typesetsAB CD In case uniform spacing is desired several alter native forms exist force all spaces equal 0 and ignore entry sizes R force equal row spacing C force equal column spacing Finally a special notation allows rotation of an entire matrix d rotate towards d Only the matrix grid will rotate however not the actual contents Exercise 17 Typeset the strip lemma a ra 3 al b Eg b 3 4 Entry style As mentioned above the entries of a diagram are set in math mode in text style You may change this by redefinining the macro objectstyle and the la bel style by redefining labelstyle We can combine this with the above to get small diagrams e g typ ing left def objectstyle scriptstyle def labelstyle scriptstyle vcenter xymatrix 1 2pc Our A ar r a amp B ar d b A ar u a amp B ar 1 b right in a paragraph will typeset A You can even abandon the use of math mode en tirely the command def objectstyle hbox will change the format of entries to plain text 10 Similarly all entries are rectangular by default but it is possible to change this to round by
19. l 8 fig 3 grow lt dimen gt grow by dimen grow to enclosing square E shrink lt dimen gt shrink by dimen shrink to contained square do not center o round 1 r u a adjust left right F F frame double F F dotted dashed F F lt 3pt gt shaded rounded Since objects specified this way start with no mar gin a single is usually included to get the default spacing Exercise 7 Typeset 4p There can only be one bosing This can be any box generation command The following are the most useful boxing text combinations variant tip tip or shaft object txt ordinary text composite combined objects frm repeat last object the possibilities for variant and tip are given in the following section Finally hbox is a quick way to ensure text mode interpretation of a single ob ject However txt allows the use of in teat to cre ate a line break and the special form txt lt 6pc gt will constrain the text to a centered 6pc wide column By the way txt can be used outside of Xy pic con structions Finally several objects can be combined using the last form the s serve to separate the composed ob ject High label Exercise 8 Typeset AAKXKKKHB 2 3 More arrow styles The arrow styles described in section 1 3 are all ex amples of the general arrow style constructions
20. l describe a few here and some more in section 2 In its simplest form an arrow is entered as ar hop where hop is a sequence of single letters u for up d for down 1 for left and r for right e g the arrow ar ur reads typeset an arrow from the current entry to that one up and one right If you use the version 2 loading command input xypic or the xypic document style option then the v2 option described in section 4 2 will be loaded automatically 3PosTScRIPT is a registered Trademark of Adobe Inc 1 4Thus when using Xy constructions involving amp inside other tabular constructions then enclose the Xy pic construction in an extra pair of braces Exercise 1 Which entry does refer to The relative coordinates specified in this way are purely logical e g if the diagram contains very wide entries then diagonal arrows will be nearly horizon tal The constructed arrows are aligned along the line between the centers of the base and target entries they will not automatically disappear under entries that they cross we discuss how this is achieved in section 2 7 The arrow style kan be changed by writing the command as ar style hop This will be described in more detail in section 2 3 here we just list the most common styles obvious variations also work gt gt gt gt gt f 5 l _ R N K q y Exercise 2 5 Typeset 4 1 4 Labels You c
21. le means that it cannot have changes etc at tached unless encapsulated in s Here is an exam ple where we merge and frame xymatrix R 1pc 1 1 1 2 1 3 1 4 amp 1 5 2 1 amp 2 2 amp 2 3 amp 2 4 amp 2 5 save 1 2 2 4 F frm ar 1 1 ar 2 1 ar 1 5 ar 2 5 restore will typeset iie 1 9 1 3 1 4 1 5 2 2 2 3 2 4 2 5 As you can see the center of the merged object is the same as the one of the target before the Finally a more advanced example where we create two merged objects with center in their real center name them and then connect to them It also shows how macros can be used inside diagrams they should always expand to commands like ar etc A gt B A age bB l C D C lt D can be typeset by def g 1 save dr C g 1 F frm restore xymatrix g1 A ar r amp B ar d amp g2 A ar r amp B ar d C ar u amp D ar 1 amp C ar u amp D ar 1 ar gt g1 1 4 ar gt 2 1 g2 Then we can make arrows from to the two frames by using the two new targets g1 and g2 as shown Exercise 19 Change the lambda cube of exer cise 12 such it is enclosed in a transparent i e dot ted cube 4 Availability and Further In formation Below we describe how to and the conditions for ob taining Xy pic version 3 7 the compatibility with pre vious versions and we conclude with a few appe
22. lstyle 10 TATRX 2 2 license 11 line break 5 links 12 loading 2 merge 11 moving target 7 name 11 new arrows 8 newdir 8 NoCompileMatrices 4 0 6 object 5 object 9 object modifier 5 8 10 objectstyle 10 old style of loading 11 OnlyOutlines 4 overwrite 7 parallel 6 pit 12 plain text entries 10 poly 12 polygon like 12 position 6 7 ps 2 quarter turn 8 r 2 radius 8 relative angle 7 relative entry 6 relative vector 7 repeat last object 5 retrieving Xy pic 11 rotation 8 10 round 10 round shape 5 rounded frame 5 rows 2 6 segment 7 SelectTips cm 9 shaded frame 5 shaft 5 8 shaft as tip 6 shaft characters 8 shape 5 ShowOutlines 4 shrink 5 sideways 6 size 5 sliding 6 spacing 9 square 5 squiggly arrow 6 tail 5 target 6 7 10 16 target entry 2 text 5 text in entries 9 text label 5 text style 2 tip 5 8 tip characters 8 tip in shaft 6 triple arrow 6 turn 8 twocells 12 txt 5 9 u 2 uniform spacing 10 usepackage 2 v2 2 va 7 variant 5 8 vector 7 vector coordinates 7 vector in direction 7 vector to corner 7 version 2 11 warranty 11 web 12 World Wide Web 11 x 6 xymatrix 2 xymatrixnocompile 4 xyoption 2 11 xypic sty 11 xypic tex 11
23. nce man ual 8 1 2 Entries A diagram is created by the command xymatrix TIATEX 2e 3 users can use usepackage a11 xy where the should be replaced by entries to be aligned in rows and columns where e entries in a row are separated by amp and e entire rows are separated by For example was typeset by xymatrix A amp F sum_ i n m i72 amp bullet amp D ar ul Notice the following e entries are typeset as mathematics using text style entries should not start with a macro as illustrated by the use of around bullet e all entries are centered and the separation be tween rows and columns is usually quite large in a diagram e empty entries at the end of rows may be omit ted e Xy decorations here ar ul in entries al low drawing of arrows and such relative to the entries without changing the overall layout and e Xy modifiers here F first in entries al low changing the format and shape in many ways 1 3 Arrows An arrow in an Xy pic diagram is a generic term for the drawn decorations between the entries of the basic matrix structure In Xy pic all arrows must be specified along with the entry in which they start this is called their base entry Each particular arrow com mand then refers explicitly to its target entry This is obtained using the ar command which accepts many options of which we wil
24. nd much more Finally the following documents might prove use ul How to Typeset Pretty Diagram Arrows with TEX 6 presents some of the design decisions be hind Xy pic Xy pic and Notation for Categorical Di agrams 7 explains how the modularity of Xy pic can be used to obtain complex effects with commuta tive diagrams and Typesetting Neural Nets using X pic 4 explains how neural networks can be typeset eR using the package Finally a collection of complex examples is maintained on the Xy pic home page and the ftp servers discussed above 4 4 Credits Xy pic version 2 was a small package created by the author The present version 3 7 is the result of more than three years of continued collaboration with Ross Moore and would never have been developed with out his support and T X nical expertise This in cludes many of the modes mentioned above which were created for use within specialised branches of mathematics however the notations are designed to fit quite naturally within the framework of Xy pic and are useful more generally Finally we are grateful to Y amp Y Inc for making very nicely done POSTSCRIPT versions of the Xy pic fonts available A Answers to all exercises Answer to exercise 1 p 2 The target is the current entry itself Answer to exercise 2 p 3 The author did xymatrix bullet ar d ar dr ar r amp bullet ar a bullet amp bullet a
25. put extra entries in your diagrams that are not part of any entry of the matrix cre ated by amp and This is done with the excursion command save t restore where t should be a target in one of the formats de scribed in sections 2 5 2 6 can do any kind of type setting desired for example xymatrix A ar dr amp save lt 3cm Ocm gt txt lt 8pc gt This is a very big commentary but it does not otherwise affect the diagram ar 1 ar d restore amp B ar r amp C ar r amp D will typeset x It illustrates how a down arrow does not necessar ily have to point particularly straight down in this case because it is based in the displaced pseudo entry This is a very big commentary but it does not otherwise affect the diagram A B C D 3 3 Spacing and rotation The object form described above can be used to space individual objects differently however it is also possible to change the overall spacing of a matrix by inserting the following codes between xymatrix and the following dimen set spacing R dimen set row spacing C dimen set column spacing M dimen set entry default margin W dimen set entry default width 8Except when Xy pic is loaded as a IAT FX 2e package where the default size is used H dimen set entry default height L dimen set label margin can be replaced by any of and o
26. r 1 Notice how e has been enclosed in since it is an expandable entity i e a defined macro this is rec ommended Answer to exercise 3 p 3 The author used xymatrix A ar r f ar dr _ f g amp B ar d g ar dr g h amp C ar r _h amp D Answer to exercise 4 p 3 The author entered xymatrix A ar d _f ar r f amp B ar d1 i_B ar d g B ar r _g amp C Answer to exercise 5 p 4 The author did xymatrix x ar ul dl id ar rr f amp amp f x ar 11 f 1 Note that both arrows are curved above relative to their direction Answer to exercise 6 p 5 The author used the display xymatrix 1 ar rr 1000000x ar dr _ 2 2000x d rr hole amp amp 1000000 1000 ar r _ 2x ar urr _ gt gt gt gt x72 amp 2000 In particular notice how the break was specified to happen exactly where the two arrows cross For an easier but not so general method see exercise 12 last in section 2 7 Answer to exercise 7 p 5 The author typed xymatrix 1 A ar r o F x amp B Answer to exercise 8 p 5 The author did xymatrix 1 A ar composite times rr txt High label amp amp B Answer to exercise 9 p 6 The author entered xymatrix A ar f lt _ gt r ar _ O x r amp B Answer to exercise 10 p 6 The author typed x
27. rs and composite should be a list of objects separated with just like the argument to composite described in section 2 2 If arrows of a particular variant always one of the let ters _23 needs an alternate definition then another declaration can be given with the variant inserted be tween newdir and the first There is one object modifier which is very useful in this context in addition to those of section 2 2 vector shift object vector where the possibilities for vector are described in section 2 6 Combined with the direction code this is very powerful for example newdir gt 1 4 5pt O 1 2 gt 1 2 _ gt defines a new tip that makes xymatrix A ar gt r amp B typeset A gt B Notice how the relative di rection is used here to rotate some of the composed components Exercise 14 Often tips used as tails have their ink on the wrong side of the point where they are placed Fortunately space is also a tip charac ter so we can define the directional u gt to generate a tail spaced arrow Do this such that xymatrix A ar gt gt lt 2pt gt r ar gt gt lt 2pt gt r amp B typesets A B Finally when Xy pic diagrams are used in con junction with Knuth s computer modern fonts then the declaration SelectTips cm will change the tips to some that look similar e g SelectTips cm xymatrix
28. s of labels described in section 2 1 Exercise 3 Typeset the second axiom of category theory as A B a 1 5 Breaks It is also possible to break an arrow with a label us ing the character xymatrix 1 A ar r f amp B will set A f B If you just want an empty break you should use the special hole break the arrow A B was typeset by including xymatrix 1 A ar r hole amp B in the text A different use of breaks is to place a label some where in a diagram outside the normal matrix mesh this is accomplished by breaking an invisible arrow obtained using the arrow style the square _ _ gt I nn was typeset by xymatrix ar dr A ar d ar r amp B ar d B ar r amp c There is more on breaks in section 2 7 Exercise 4 Typeset the first axiom of category theory as the display f gt F Bo N QA lt bw 1 6 Curving Arrows can be made to curve for example to avoid going through another entry using the special style curving The simplest styles of curving are the following shown applied to an arrow from A to B 7 A B _ A B _1pc A B Saa As the last example shows a dimension can be in serted just after or _ if more or less curving is de sired In case it is easier to specify the in and out going directions of the curving then that is also possible use Cin out where in and out are on
29. s used in for example category theory please refer to the reference manual 8 for complete information on the described constructions The guide assumes that you have some experience in using TX for typeset ting mathematics e g have studied 2 ch 16 19 3 sec 3 3 or 9 and that Xy pic is installed on your TEX system as described in the INSTALL file accom panying the distribution The first section describes what you need to get started in particular all that is needed to typeset the diagram in the abstract Section 2 and 3 explain advanced use of arrows and entries respectively Fi nally section 4 explains where and under what condi tions Xy pic is available gives the relation of version 3 7 to previous versions and lists further sources of information Throughout we give exercises that you should be able to solve as you go along all exercises are an swered at the end just prior to the references and index 1 Basics This section explains the Xy diagram construction concepts needed to get started with typesetting matrix like diagrams 1 1 Loading The Xy pic setup used in this guide is loaded by in serting the lines input xy xyoption all in the definitions part of your document If you wish to load only the features you use or you wish to use non standard facilities like the v2 backwards compat ibility mode or the ps POSTSCRIPT backend then this is also possible as described in the refere
30. sing Xy pic 1994 Available through 5 5 Kristoffer H Rose The Xy pic home page URL http www ens lyon fr krisrose Xy pic html 6 Kristoffer H Rose How to typeset pretty dia gram arrows with TRmX design decisions used in Xy pic In Ji Zlatu ka editor EuroTpx 92 Proceedings of the 7th European TEX Conference pages 183 190 Prague Czechoslovakia Septem ber 1992 Czechoslovak TREX Users Group Kristoffer H Rose Xy pic and notation for cate gorical diagrams Invited talk at ECCT 94 July 1994 Available through 5 Kristoffer H Rose and Ross R Moore Ay pic Ref erence Manual DIKU University of Copenhagen Universitetsparken 1 DK 2100 K benhavn 3 0 edition June 1995 Michael D Spivak The Joy of TEX A Gourmet Guide to Typesetting with the AMS TEX Macro Package American Mathematical Society second edition 1990 Index 1 5 7 8 5 amp 2 EST 6 0 5 0 5 1 5 6 5 7 9 12 5 7 10 5 10 3 5 7 10 6 5 10 6 6 8 6 Osh a 7 Ti lt 4 6 lt lt 4 6 10 gt 4 6 gt gt 4 6 gt gt 6 gt 6 3 5 10 10 4 4 _ 4 1 3 lt gt 6 9 ec 9 H 10 L 10 M 9 R 9 W 9 3 F 5 F 5 F lt 3pt gt 5 F 5 F 5 F 5 3 6 a 5 1 5 0 5 r 5 2cell 12 3 1 6 0 7 absolute angle 7 absolute entry
31. t the position obtained by adding or subtracting the vector to its center or e vector which moves the center of the target by the vector where a vector should have the form e lt D D gt where Dz Dy are TEX dimensions is the vector with those coordinates e the following corner offsets of a target are vec tors as shown U UL UR L R DL DR D they must be specified in upper case and e d dimen is the vector going dimen in the par ticular direction d which can be either the eight simple ones in section 1 6 empty to denote that the current direction the last direction of an arrow should be used or one of the following va a absolute angle d a a relative angle in degrees d x y relative vector d d_ short for a 90 a 90 where the d in the last four may be empty to denote the current direction e 0 is the zero vector Many many more possibilities are described in the reference manual 8 Exercise 11 What is the difference between a tar get t and the target t 0 2 7 Arrows passing under Arrows can pass under or via any other entry Just insert t i e a quote apostrophe character followed by a target for each entry that should be visited ex cept the last ordinary amp final entry xymatrix circ ar gt dr a gt rr D bullet b drrr c amp circ amp circ amp circ circ amp circ amp circ
32. tisers to lure the reader into reading more about Xy pic 11 4 1 Getting Xy pic The easiest way to retrieve the latest version of Xy pic is through the Xy pic home page 5 on the World Wide Web it is also available by Inter net ftp from URL ftp ftp diku dk diku users kris TeX as well as URL ftp ftp mpce mq edu au pub maths TeX in files starting with xy Finally Xy pic has been contributed to the CTAN archives where it is located in the directory macros generic diagrams xypic License Xy pic is free software in the sense that it is available under the following license conditions Xy pic Graphs and Diagrams with T X 1991 1997 Kristoffer H Rose 1994 1997 Ross Moore The Xy pic package is free software you can redis tribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version The Xy pic package is distributed in the hope that it will be useful but without any warranty without even the implied warranty of merchantability or fit ness for a particular purpose See the GNU General Public License for more details You should have received a copy of the GNU Gen eral Public License along with this package if not write to the Free Software Foundation Inc 675 Mass Ave Cambridge MA 02139 USA In practice this means that you are free to use Xy pic for your
33. ymatrix 1 A ar r ar lt 1lex gt r amp B Answer to exercise 11 p 7 The size t 0 al ways has zero size Answer to exercise 12 p 7 The author con structed xymatrix 0f amp lambda omega ar rr ar d dd amp amp lambda C ar dd lambda2 ar ur ar rr ar dd amp amp lambda P2 ar ur ar dd amp lambda underline omega ar r rr Mathematics Department Macquarie University Sydney Australia 2109 e mail ross mpce mq edu au 10Partial funding for this collaboration has been provided by a Macquarie University Research Grant MURG by the Australian Research Council ARC and through a research agreement with the Digital Equipment Corporation DEC amp amp lambda P underline omega lambda to ar rr ar ur amp amp lambda P ar ur A special thing is added forces rows and columns to be equally spaced as discussed in sec tion 3 3 0 furthermore makes the spacing ignore the entry sizes giving a completely fixed grid The gaps could also be made with the crossing nota tion of exercise 6 last in section 2 1 but the above is shorter Answer to exercise 13 p 8 The author typed xymatrix 1 A ar lt 2pt gt d r r r ar lt 2pt gt d r r r amp B Answer to exercise 14 p 8 The author used newdir gt 5pt gt Answer to exercise 15
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