.SC "Shorthand for In-line Equations".PPIn a mathematical document,it is necessary to follow mathematical conventionsnot just in display equations,but also in the body of the text,for example by making variable names like $x$ italic.Although this could be done by surrounding the appropriate partswith.UC .EQand.UC .EN ,the continual repetition of.UC .EQand.UC .ENis a nuisance.Furthermore, with `\(mims',.UC .EQand.UC .ENimply a displayed equation..PP.UC EQNprovides a shorthand for short in-line expressions.You can define two characters to mark the left and right endsof an in-line equation, and then type expressions right in the middle of textlines.To set both the left and right characters to dollar signs, for example,add to the beginning of your document the three lines.P1 .EQ delim %% .EN.P2Having done this, you can then say things like.P1.fiLet %alpha sub i% be the primary variable,and let %beta% be zero.Then we can show that %x sub 1% is %>=0%..P2This works asyou might expect _spaces, newlines, and so on are significantin the text, but not in the equation part itself.Multiple equations can occur in a single input line..PPEnough room is left before and after a line that containsin-line expressionsthat something like$sum from i=1 to n x sub i$does not interfere with the lines surrounding it..PPTo turn off the delimiters,.P1 .EQ delim off .EN.P2Warning: don't use braces, tildes, circumflexes, or double quotes as delimiters _chaos will result..SC "Definitions".PP.UC EQNprovides a facility so you can givea frequently-used string of characters a name,and thereafter just type the name instead of thewhole string.For example, if the sequence.P1x sub i sub 1 + y sub i sub 1.P2appears repeatedly throughout a paper,you can save re-typing it each time by defining it like this:.P1 2define  xy  'x sub i sub 1 + y sub i sub 1'.P2This makes.ulxya shorthand for whatever characters occur between the single quotesin the definition.You can use any character instead of quote to mark the ends of the definition,so long as it doesn't appear inside the definition..PPNow you can use.ulxylike this:.P1^EQf(x) = xy ...^EN.P2and so on.Each occurrence of.ulxywill expand into what it was defined as.Be careful to leave spaces or their equivalentaround the namewhen you actually use it, so.UC EQNwill be able to identify it as special..PPThere are several things to watch out for.First, although definitions can use previous definitions,as in.P1 .EQ define  xi  ' x sub i ' define  xi1  ' xi sub 1 ' .EN.P2.uldon't define something in terms of itself'A favorite error is to say.P1define  X  ' roman X '.P2This is a guaranteed disaster,since X.ulisnow defined in terms of itself.If you say.P1define  X  ' roman "X" '.P2however, the quotesprotect the second X,and everything works fine..PP.UC EQNkeywords can be redefined.You can make/ mean.uloverby saying.P1define  /  ' over '.P2or redefine.uloveras /with.P1define  over  ' / '.P2.PPIf you need different thingsto print on a terminal and on the typesetter, it is sometimes worthdefining a symbol differently in.UC NEQNand.UC EQN .This can be done with.ulndefineand.ultdefine.A definition made with.ulndefineonly takes effect if you are running.UC NEQN ;if you use.ultdefine,the definition only applies for.UC EQN .Names defined with plain.uldefineapply to both.UC EQN and.UC NEQN ..SC "Local Motions".PPAlthough.UC EQNtries to get most things at the right place on the paper,it isn't perfect, and occasionally you will need to tunethe output to make it just right.Small extra horizontal spaces can be obtained withtilde and circumflex.You can also say.ulback nand.ulfwd nto move small amounts horizontally..ulnis how far to move in 1/100's of an em (an em is about the widthof the letter`m'.)Thus.ulback 50moves back about half the width of an m.Similarly you can move things up or down with.ulup nand.uldown n.As with .ulsubor.ulsup,the local motions affect the next thing in the input,and this can be something arbitrarily complicated if it is enclosedin braces.