.SC "Size and Font Changes".PPBy default, equations are set in 10-point type (the same size as this guide),with standard mathematical conventionsto determine what characters are in roman and what in italic.Although .UC EQNmakes a valiant attempt to useesthetically pleasing sizes and fonts,it is not perfect.To change sizes and fonts, use.ulsize nand.ulroman, italic, .ulboldand.ulfat.Like.ulsuband.ulsup,sizeand font changes affect only the thing that followsthem, and revert to the normal situationat the end of it. Thus.P1bold x y.P2is.EQbold x y.ENand.P1size 14 bold x = y +   size 14 {alpha + beta}.P2gives.EQsize 14 bold x = y +   size 14 {alpha + beta}.ENAs always, you can use braces if you want to affect somethingmore complicated than a single letter.For example, you can change the size of an entire equation by.P1size 12 { ... }.P2.PPLegal sizes which may follow .ulsizeare6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 28, 36.You can also change the size.ulbya given amount;for example, you can say.ulsize~+2to make the size two points bigger,or.ulsize~\(mi3to make it three points smaller.This has the advantage that you don't haveto know what the current size is..PPIf you are using fonts other than roman, italic and bold,you can say.ulfont Xwhere .ulXis a one character.UC TROFFname or number for the font.Since.UC EQNis tuned for roman, italic and bold,other fonts may not give quite as good an appearance..PPThe.ulfat operation takes the current font and widens it by overstriking:.ulfat\ gradis$fat grad$ and.ulfat {x sub i}is$fat {x sub i}$..PPIf an entire document is to be in a non-standard sizeor font, it is a severe nuisanceto have to write out a size and font change for eachequation.Accordingly, you can set a ``global'' size or fontwhich thereafter affects all equations.At the beginning of any equation, you might say, for instance,.P1^EQgsize 16gfont R ...^EN.P2to set the size to 16 and the font to roman thereafter.In place of R, you can use any of the.UC TROFFfont names.The size after.ulgsizecan be a relative change with + or \(mi..PPGenerally,.ulgsizeand.ulgfontwill appear at the beginning of a documentbut they can also appearthoughout a document: the global font and sizecan be changed as often as needed.For example, in a footnote\(dd.FS\(ddLike this one, in which we have a$gsize -2$few randomexpressions like $x sub i$ and $pi sup 2$.The sizes for these were set by the command.ulgsize~\(mi2..FE $gsize +2$you will typically want the size of equations to matchthe size of the footnote text, which is two points smallerthan the main text.Don't forget to reset the global sizeat the end of the footnote..SC "Diacritical Marks".PPTo get funny marks on top of letters,there are several words:.P1.tr ^^.tr ~~.ta 1ix dot	$x dot$x dotdot	$x dotdot$x hat	$x hat$x tilde	$x tilde$x vec	$x vec$x dyad	$x dyad$x bar	$x bar$x under	$x under$.P2The diacritical mark is placed at the right height.The .ulbarand.ulunderare made the right length for the entire construct,as in $x+y+z bar$;other marks are centered..SC "Quoted Text".PPAny input entirely within quotes (\|"..."\|)is not subject to any of the font changes and spacingadjustments normally done by the equation setter.This provides a way to do your own spacing and adjusting if needed:.P1italic "sin(x)" + sin (x).P2is.EQitalic "sin(x)" + sin (x).EN.PPQuotes are also used to get braces and other.UC EQNkeywords printed:.P1"{ size alpha }".P2is.EQ"{ size alpha }".ENand.P1roman "{ size alpha }".P2is.EQroman "{ size alpha }".EN.PPThe construction "" is often used as a place-holderwhen grammatically.UC EQNneeds something, but you don't actually want anything in your output.For example, to make$"" sup 2 roman He$,you can't just type.ulsup 2 roman Hebecause a.ulsuphas to be a superscript.ulonsomething.Thus you must say.P1"" sup 2 roman He.P2.PPTo get a literal quoteuse ``\\"''..UC TROFF characters like.ul\e(bscan appear unquoted, but more complicated things likehorizontal and vertical motions with.ul\ehand.ul\evshouldalwaysbe quoted.(If you've never heard of.ul\\hand.ul\\v,ignore this section.).SC "Lining Up Equations".PPSometimes it's necessary to line up a series of equationsat some horizontal position, often at an equals sign.This is done with two operations called.ulmarkand.ullineup..PPThe word.ulmarkmay appear once at any place in an equation.It remembers the horizontal position where it appeared.Successive equations can contain one occurrence of the word.ullineup.The place where.ullineupappears is made to line upwith the place marked by the previous.ulmarkif at all possible.Thus, for example,you can say.P1^EQ Ix+y mark = z^EN^EQ Ix lineup = 1^EN.P2to produce.EQ Ix+y mark = z.EN.EQ Ix lineup = 1.ENFor reasons too complicated to talk about,when you use.UC EQNand`\(mims',use either.UC .EQ\ Ior.UC .EQ\ L .markand.ullineupdon't work with centered equations.Also bear in mind that .ulmarkdoesn't look ahead;.P1x mark =1 ...x+y lineup =z.P2isn't going to work, because there isn't roomfor the.ulx+ypart after the.ulmarkremembers where the.ulxis..SC "Big Brackets, Etc.".PP.tr ~To get big brackets [~],braces {~}, parentheses (~), and bars |~|around things, use the.ulleft and.ulrightcommands:.tr ~~.P1left { a over b + 1 right } ~=~ left ( c over d right ) + left [ e right ].P2is.EQleft { a over b + 1 right } ~=~ left ( c over d right ) + left [ e right ].ENThe resulting brackets are made big enough to cover whatever they enclose.Other characters can be used besides these,but the are not likely to look very good.One exception is the.ulfloorand.ulceiling characters:.P1left floor x over y right floor <= left ceiling a over b right ceiling.P2produces.EQleft floor x over y right floor <= left ceiling a over b right ceiling.EN.PPSeveral warnings about brackets are in order.First, braces are typically bigger than brackets and parentheses,because they are made up of three, five, seven, etc., pieces,while brackets can be made up of two, three, etc.Second, big left and right parentheses often look poor,because the character set is poorly designed..PPThe.ulrightpart may be omitted:a ``left something'' need not have acorresponding ``rightsomething''.If the.ulrightpart is omitted,put braces around the thing you want the left bracketto encompass.Otherwise, the resulting brackets may be too large..PPIf you want to omit the.ulleftpart, things are more complicated,because technically you can't have a.ulrightwithout a corresponding.ulleft.Instead you have to say.P1left "" ..... right ).P2for example.The.ulleft ""means a ``left nothing''.This satisfies the rules without hurting your output..SC "Piles".PPThere is a general facility for making vertical pilesof things; it comes in several flavors.For example:.P1.tr ~~A ~=~ left [  pile { a above b above c }  ~~ pile { x above y above z }right ].P2will make.EQA ~=~ left [pile { a above b above c } ~~ pile { x above y above z }right ].ENThe elements of the pile (there can be as many as you want)are centered one above another, at the right height formost purposes.The keyword.ulaboveis used to separate the pieces;braces are used around the entire list.The elements of a pile can be as complicated as needed, even containing more piles..PPThree other forms of pile exist:.ullpilemakes a pile with the elements left-justified;.ulrpilemakes a right-justified pile;and.ulcpilemakes a centered pile, just like.ulpile.The vertical spacing between the piecesis somewhat larger for.ull-,.ulr-and.ulcpilesthan it is for ordinary piles..P1 2roman sign (x)~=~ left {   lpile {1 above 0 above -1}    ~~ lpile    {if~x>0 above if~x=0 above if~x<0}.P2makes.EQroman sign (x)~=~ left {   lpile {1 above 0 above -1}    ~~ lpile    {if~x>0 above if~x=0 above if~x<0}.ENNotice the left bracewithout a matching right one..SC Matrices.PPIt is also possible to make matrices.For example, to makea neat array like.EQmatrix {  ccol { x sub i above y sub i }  ccol { x sup 2 above y sup 2 }}.ENyou have to type.P1matrix {  ccol { x sub i above y sub i }  ccol { x sup 2 above y sup 2 }}.P2This produces a matrix withtwo centered columns.The elements of the columns are then listed just as for a pile,each element separated by the word.ulabove.You can also use.ullcolor.ulrcolto left or right adjust columns.Each column can be separately adjusted,and there can be as many columns as you like..PPThe reason for using a matrix instead of two adjacent piles, by the way,is that if the elements of the piles don't all have the same height,they won't line up properly.A matrix forces them to line up,because it looks at the entire structure before deciding whatspacing to use..PPA word of warning about matrices _.uleach column must have the same number of elements in it.The world will end if you get this wrong.