unx24.htm

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<TR>

<TD>

<P>det</P>

<TD>

<P>exp</P>

<TD>

<P>for</P>

<TD>

<P>if</P>

<TR>

<TD>

<P>Im</P>

<TD>

<P>lim</P>

<TD>

<P>ln</P>

<TD>

<P>log</P>

<TR>

<TD>

<P>max</P>

<TD>

<P>min</P>

<TD>

<P>Re</P>

<TD>

<P>sin</P>

<TR>

<TD>

<P>sinh</P>

<TD>

<P>tan</P>

<TD>

<P>tanh</P>

<TD>

<P><BR></P></TABLE>

<H3 ALIGN="CENTER">

<CENTER><A ID="I7" NAME="I7">

<FONT SIZE=4><B><I>eqn</I></B><B> Operators</B>

<BR></FONT></A></CENTER></H3>

<P>You've already met some of the eqn operators&#151;+, -, =, and &gt;. Table 24.2 lists the other eqn operators.

<BR></P>

<A HREF="tab2402.gif"><B>Table 24.2. Some eqn operators.</B></A>

<BR>

<P>In addition, eqn offers nine diacritical marks, which are listed in Table 24.3.

<BR></P>

<A HREF="tab2403.gif"><B>Table 24.3. Diacritical marks.</B></A>

<BR>

<P>If you need to use a bar with one of the other diacritical marks, use highbar to place the bar correctly. There is also a lowbar. For example, the following code

<BR></P>

<PRE>.EQ

delim ##

.EN

#X highbar#

.sp .5

#x highbar#

.sp .5

#x bar#

.sp .5

#x lowbar#

.sp .5

#x dotdot highbar#

.sp .5

#{x tilde} highbar#</PRE>

<P>produces this output:</P>

<BR><IMG SRC="24unx02.gif"><BR>

<P>To draw a bar over an entire expression, use braces. For example:

<BR></P>

<PRE>{ ( alpha - beta ) * gamma } bar</PRE>

<H3 ALIGN="CENTER">

<CENTER><A ID="I8" NAME="I8">

<FONT SIZE=4><B>Spaces and Braces</B>

<BR></FONT></A></CENTER></H3>

<P>Like most UNIX programs, eqn has to be able to recognize keywords. And, like UNIX, eqn understands that spaces delimit keywords, as do certain operators. For example, UNIX understands

<BR></P>

<PRE>who|grep sally</PRE>

<P>or

<BR></P>

<PRE>who | grep sally</PRE>

<P>The pipe acts as a delimiter, so UNIX can parse your command. Similarly, UNIX understands both the following:

<BR></P>

<PRE>mail sally&lt;myletter

mail sally &lt; myletter</PRE>

<P>In this example, the redirect (less than) sign acts as a delimiter. UNIX does not recognize the hyphen (minus sign) as a delimiter, despite the fact that many options must be preceded by this character. If you type ls-1, UNIX politely responds: ls-1:  
not found.

<BR></P>

<P>eqn behaves the same way. If you write

<BR></P>

<PRE>.EQ

a+b=c

.EN</PRE>

<P>eqn will process this easily because it recognizes + and = as delimiters. The output of this code will be identical to the output from

<BR></P>

<PRE>.EQ

a + b = c

.EN</PRE>

<P>or even

<BR></P>

<PRE>.EQ

a+ b

    =

  c

.EN</PRE>

<P>All of these are output as a+b=c.

<BR></P>

<P>eqn pays no attention to spaces or newlines except as delimiters. Once eqn has determined what you mean (or what it thinks you mean), it throws away spaces and newlines.

<BR></P>

<P>To obtain spaces in your output, use a tilde (~) for a 1-character space, or a circumflex (^) for a half-character space:

<BR></P>

<PRE>.EQ

a~+~b~=~c

a^+^b~=~c

.EN</PRE>

<P>This produces

<BR></P>

<P>a+b=c

<BR></P>

<H4 ALIGN="CENTER">

<CENTER><A ID="I9" NAME="I9">

<FONT SIZE=3><B>Grouping</B>

<BR></FONT></A></CENTER></H4>

<P>If you say, &quot;3 plus 2 times 5&quot; your listener doesn't know whether you mean 25 or 13. eqn has the same problem. Like your listener, eqn makes an assumption about # a + b * c #. If you provide no more information, eqn groups according to the 
order in which you enter information. In other words, it assumes parentheses.

<BR></P>

<P>Although computers do this, mathematicians don't. They believe in precedence, which holds that multiplication always precedes addition. Therefore, 3 + 2 <B>&#180;</B> 5 is 13. Period. Even mathematicians, though, sometimes need parentheses.

<BR></P>

<P>Because parentheses are used so often in mathematical expressions, eqn wants you to use curly braces&#151;{ and }&#151;to indicate grouping in your expressions. Therefore, if you really meant 13, you would write

<BR></P>

<PRE># a + {b * c} #</PRE>

<P>The spaces here are important.

<BR></P>

<P>Because eqn's treatment of spaces is its hardest aspect to get used to, here is a list of rules to memorize. You could have them printed on a tee-shirt or tattooed on your hand if that seems easier.

<BR></P>

<OL>

<LI>eqn throws away all internal spaces once it has used them.

<BR>

<BR></LI>

<LI>eqn uses internal spaces to recognize special words and symbols.

<BR>

<BR></LI>

<LI>You can use circumflexes (^)&#151;eqn calls them hats&#151;or tildes (~) to set off special words and symbols. eqn replaces each tilde with a space in the output. It replaces each circumflex with a half space.

<BR>

<BR></LI>

<HR ALIGN=CENTER>

<NOTE>

<IMG SRC="note.gif" WIDTH = 35 HEIGHT = 35><B>NOTE:</B> Earlier versions of eqn may not replace the circumflex with a half space. They may simply throw the circumflex away.

<BR></NOTE>

<HR ALIGN=CENTER>

<LI>You can use braces or quotation marks to set off parts of an equation, but they have special meanings.

<BR>

<BR>Braces are used for grouping. They force eqn to treat the enclosed term (or terms) as a unit. Braces can be nested.

<BR>

<BR>Quotation marks force eqn to treat the enclosed term literally. For example, to print a brace, enclose it in quotation marks.

<BR>

<BR></LI>

<LI>When in doubt, use a space.

<BR>

<BR></LI>

<LI>eqn ignores newlines, so you can spread your equation over several lines to make it more readable.

<BR>

<BR></LI></OL>

<P>Table 24.4 contains some examples that may help:

<BR></P>

<UL>

<LH><B>Table 24.4. Using spaces and brackets in </B><B>eqn</B><B>.</B>

<BR></LH></UL>

<TABLE BORDER>

<TR>

<TD>

<PRE><I>Desired Output</I>

<BR></PRE>

<TD>

<PRE><I>Code</I>

<BR></PRE>

<TD>

<PRE><I>Actual Output</I>

<BR></PRE>

<TR>

<TD>

<P>a + b = c</P>

<TD>

<P>a~+~b~=~c</P>

<TD>

<P>(as desired)</P>

<TR>

<TD>

<P>a + b = c</P>

<TD>

<P>a + b = c</P>

<TD>

<P>a+b=c</P>

<TR>

<TD>

<P>a=(x<SUP>2</SUP>)+1</P>

<TD>

<P>a=(x sup 2) + 1</P>

<TD>

<P>(as desired)</P>

<TR>

<TD>

<P>a=(x<SUB>2</SUB>)+1</P>

<TD>

<P>a=(x sup 2)+ 1</P>

<TD>

<P>a=(x<SUP>2)+1</SUP></P>

<TR>

<TD>

<P>x<SUB>2</SUB></P>

<TD>

<P>x sub 2</P>

<TD>

<P>(as desired)</P>

<TR>

<TD>

<P>x<SUB>2</SUB></P>

<TD>

<P>x sub2</P>

<TD>

<P>xsub2</P>

<TR>

<TD>

<P>x<SUB>i</SUB><SUP>2</SUP></P>

<TD>

<P>x sub i sup 2</P>

<TD>

<P>(as desired)</P>

<TR>

<TD>

<P>xi<SUP>2</SUP></P>

<TD>

<P>x sup 2 sub i</P>

<TD>

<P>x2i</P></TABLE>

<H3 ALIGN="CENTER">

<CENTER><A ID="I10" NAME="I10">

<FONT SIZE=4><B>Fractions</B>

<BR></FONT></A></CENTER></H3>

<P>Fractions are produced in a straightforward way. Simply use the word over. For example, the code

<BR></P>

<PRE># a over b #</PRE>

<P>produces

<BR></P>

<P><B><IMG SRC="24unx03.gif"></B></P><BR>

<P>More complex fractions present additional problems. Think about the following equation for a moment:

<BR></P>

<PRE>a + b over c</PRE>

<P>This code line could mean # {a+b} over c # or # a + {b over c} #. The most important thing to remember about fractions is to use braces.

<BR></P>

<P>You can, of course, produce an expression with a fraction like this:

<BR></P>

<P><B><IMG SRC="24unx04.gif"></B></P><BR>

<H3 ALIGN="CENTER">

<CENTER><A ID="I11" NAME="I11">

<FONT SIZE=4><B>Square Roots</B>

<BR></FONT></A></CENTER></H3>

<P>The keyword sqrt produces the root sign. Consider these expressions:

<BR></P>

<P><B><IMG SRC="24unx05.gif"></B></P>

<P>They are produced with the following code:

<BR></P>

<PRE>sqrt a+b=x

sqrt {X bar}

y= sqrt {a-b}

y = sigma over {sqrt N}</PRE>

<P>You can also produce large root signs. For example,

<BR></P>

<PRE>sqrt {{a sup x} over b sub y}</PRE>

<P>When you do this, however, the root sign doesn't just get bigger; it gets thicker&#151;and uglier. In cases like this, you're better off using a fractional power. For example,

<BR></P>

<PRE>{( a sup x /b sub y ) } sup half</PRE>

<P>produces

<BR></P>

<P><B><IMG SRC="24unx06.gif"></B></P>

<H3 ALIGN="CENTER">

<CENTER><A ID="I12" NAME="I12">

<FONT SIZE=4><B>Sums, Integrals, and Limits</B>

<BR></FONT></A></CENTER></H3>

<P>In their simplest form, sums, integrals, and limits are produced by sum, int, and lim. Of course, you never see them in their simplest form. Usually included is a from or even a from and a to. For example,

<BR></P>

<PRE>sum from 1=0 to {i=inf} x sup i

int from a to b

lim from {n -&gt; inf} sum from i=0 to m c sup i</PRE>

<P>produces

<BR></P>

<P><B><IMG SRC="24unx07.gif"></B></P>

<P>In addition, you can use prod, union, and inter to produce the symbols used with sets.

<BR></P>

<H3 ALIGN="CENTER">

<CENTER><A ID="I13" NAME="I13">

<FONT SIZE=4><B>Brackets, Braces, and Piles</B>

<BR></FONT></A></CENTER></H3>

<P>You can create big braces and brackets by enclosing expressions that require them. Consider the following code:

<BR></P>

<PRE>#left [ {a over b} + {c over d} right ]#

#left { {s over t} - {r over q} right }#</PRE>

<P>The expression that this code produces is

<BR></P>

<P><B><IMG SRC="24unx08.gif"></B></P>

<P>You can specify floor and ceiling characters. For example,

<BR></P>

<PRE>left floor a over b right floor =&gt;

left ceiling x over y right ceiling</PRE>

<P>produces

<BR></P>

<P><B><IMG SRC="24unx09.gif"></B></P>

<P>Although piles look like big brackets, they are actually different. Piles line up in three ways: left, right, and centered. For example,

<BR></P>

<PRE>A= left [

pile { a above b above c }

pile { x above y above z }

right ]</PRE>

<P>produces

<BR></P>

<P><B><IMG SRC="24unx10.gif"></B></P>

<P>If you require only one brace, you must include a null argument for the missing side. Consider

<BR></P>

<PRE>left &quot;&quot;

lpile

{SIGMA X sub 3 above SIGMA X sub 1

X sub 3 above SIGMA X sub 2 X sub 3}

right )</PRE>

<P>which produces

<BR></P>

<P><B><IMG SRC="24unx11.gif"></B></P>

<H3 ALIGN="CENTER">

<CENTER><A ID="I14" NAME="I14">

<FONT SIZE=4><B>Arrays and Matrices</B>

<BR></FONT></A></CENTER></H3>

<P>To create an array or a matrix, use the keyword matrix, as in