/usr/share/doc/axiom-doc/hypertex/numbasicfunctions.xhtml

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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Basic Functions</div>
  <hr/>
The size of an integer in Axiom is only limited by the amount of computer
storage you have available. The usual arithmetic operations are available.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="2^(5678-4856+2*17)" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
There are a number of ways of working with the sign of an integer. Let's
use the x as an example.
<ul>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="makeRequest('p2');"
    value="x:=-101" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
First of all, there is the absolute value function.
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" 
    onclick="handleFree(['p2','p3']);"
    value="abs(x)" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
The <a href="dbopsign.xhtml">sign</a> operation returns -1 if its argument
is negative, 0 if zero and 1 if positive.
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" 
    onclick="handleFree(['p2','p4']);"
    value="sign(x)" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
You can determine if an integer is negative in several other ways.
<ul>
 <li>
  <input type="submit" id="p5" class="subbut" 
    onclick="handleFree(['p2','p5']);"
    value="x &lt; 0" />
  <div id="ansp5"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p6" class="subbut" 
    onclick="handleFree(['p2','p6']);"
    value="x &lt;= -1" />
  <div id="ansp6"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p7" class="subbut" 
    onclick="handleFree(['p2','p7']);"
    value="negative?(x)" />
  <div id="ansp7"><div></div></div>
 </li>
</ul>
Similarly, you can find out if it is positive.
<ul>
 <li>
  <input type="submit" id="p8" class="subbut" 
    onclick="handleFree(['p2','p8']);"
    value="x > 0" />
  <div id="ansp8"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p9" class="subbut" 
    onclick="handleFree(['p2','p9']);"
    value="x >= 1" />
  <div id="ansp9"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p10" class="subbut" 
    onclick="handleFree(['p2','p10']);"
    value="positive?(x)" />
  <div id="ansp10"><div></div></div>
 </li>
</ul>
This is the recommended way of determining whether an integer is zero.
<ul>
 <li>
  <input type="submit" id="p11" class="subbut" 
    onclick="handleFree(['p1','p11']);"
    value="zero?(x)" />
  <div id="ansp11"><div></div></div>
 </li>
</ul>
<hr/>
Use the <a href="dbopzeroq.xhtml">zero?</a> whenever you are testing any
mathematical object for equality with zero. This is usually more efficient
than using <a href="dbopequal.xhtml">=</a> (think of matrices: it is easier
to tell if a matrix is zero by just checking term by term than constructing
another "zero" amtrix and comparing the two matrices term by term) and also
avoids the problem that <a href="dbopequal.xhtml">=</a> is usually used
for creating equations.
<hr/>
This is the recommended way of determining whether an integer is equal to one.
<ul>
 <li>
  <input type="submit" id="p12" class="subbut" 
    onclick="handleFree(['p2','p12']);"
    value="one?(x)" />
  <div id="ansp12"><div></div></div>
 </li>
</ul>
This syntax is used to test equality using <a href="dbopequal.xhtml">=</a>.
It says that you want a <a href="db.xhtml?Boolean">Boolean</a> (true or false)
answer rather than an equation.
<ul>
 <li>
  <input type="submit" id="p13" class="subbut" 
    onclick="handleFree(['p2','p13']);"
    value="(x=-101)@Boolean" />
  <div id="ansp13"><div></div></div>
 </li>
</ul>
The operations <a href="dbopoddq.xhtml">odd?</a> and 
<a href="dbopevenq.xhtml">even?</a> determine whether an integer is odd
or even, respectively. They each return a 
<a href="db.xhtml?Boolean">Boolean</a>
object.
<ul>
 <li>
  <input type="submit" id="p14" class="subbut" 
    onclick="handleFree(['p2','p14']);"
    value="odd?(x)" />
  <div id="ansp14"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p15" class="subbut" 
    onclick="handleFree(['p2','p15']);"
    value="even?(x)" />
  <div id="ansp15"><div></div></div>
 </li>
</ul>
The operation <a href="dbopgcd.xhtml">gcd</a> computes the greatest common
divisor of two integers.
<ul>
 <li>
  <input type="submit" id="p16" class="subbut" 
    onclick="makeRequest('p16');"
    value="gcd(56788,43688)" />
  <div id="ansp16"><div></div></div>
 </li>
</ul>
The operation <a href="dboplcm.xhtml">lcm</a> computes their least common
multiple.
<ul>
 <li>
  <input type="submit" id="p17" class="subbut" 
    onclick="makeRequest('p17');"
    value="lcm(56788,43688)" />
  <div id="ansp17"><div></div></div>
 </li>
</ul>
To determine the maximum of two integers, use <a href="dbopmax.xhtml">max</a>.
<ul>
 <li>
  <input type="submit" id="p18" class="subbut" 
    onclick="makeRequest('p18');"
    value="max(678,567)" />
  <div id="ansp18"><div></div></div>
 </li>
</ul>
To determine the minimum, use <a href="dbopmin.xhtml">min</a>.
<ul>
 <li>
  <input type="submit" id="p20" class="subbut" 
    onclick="makeRequest('p20');"
    value="min(678,567)" />
  <div id="ansp20"><div></div></div>
 </li>
</ul>
The <a href="dbopreduce.xhtml">reduce</a> operation is used to extend
binary operations to more than two arguments. For example, you can use
<a href="dbopreduce.xhtml">reduce</a> to find the maximum integer in a
list or compute the least common multiple of all integers in a list.
<ul>
 <li>
  <input type="submit" id="p21" class="subbut" 
    onclick="makeRequest('p21');"
    value="reduce(max,[2,45,-89,78,100,-45])" />
  <div id="ansp21"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p22" class="subbut" 
    onclick="makeRequest('p22');"
    value="reduce(min,[2,45,-89,78,100,-45])" />
  <div id="ansp22"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p23" class="subbut" 
    onclick="makeRequest('p23');"
    value="reduce(gcd,[2,45,-89,78,100,-45])" />
  <div id="ansp23"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p24" class="subbut" 
    onclick="makeRequest('p24');"
    value="reduce(lcm,[2,45,-89,78,100,-45])" />
  <div id="ansp24"><div></div></div>
 </li>
</ul>
The infix operator "/" is not used to compute the quotient of integers.
Rather , it is used to create rational numbers as described in
<a href="numintegerfractions.xhtml">Fractions</a>.
<ul>
 <li>
  <input type="submit" id="p25" class="subbut" 
    onclick="makeRequest('p25');"
    value="13/4" />
  <div id="ansp25"><div></div></div>
 </li>
</ul>
The infix operator <a href="dbopquo.xhtml">quo</a> computes the integer
quotient.
<ul>
 <li>
  <input type="submit" id="p26" class="subbut" 
    onclick="makeRequest('p26');"
    value="13 quo 4" />
  <div id="ansp26"><div></div></div>
 </li>
</ul>
The infix operation <a href="dboprem.xhtml">rem</a> computes the integer
remainder.
<ul>
 <li>
  <input type="submit" id="p27" class="subbut" 
    onclick="makeRequest('p27');"
    value="13 rem 4" />
  <div id="ansp27"><div></div></div>
 </li>
</ul>
One integer is evenly divisible by another if the remainder is zero.
The operation <a href="dbopexquo.xhtml">exquo</a> can also be used. See
<a href="axbook/section-2.5.xhtml">Unions</a> for an example.
<ul>
 <li>
  <input type="submit" id="p28" class="subbut" 
    onclick="makeRequest('p28');"
    value="zero?(167604736446952 rem 2003644)" />
  <div id="ansp28"><div></div></div>
 </li>
</ul>
The operation <a href="dbopdivide.xhtml">divide</a> returns a record of
the quotient and remainder and thus is more efficient when both are needed.
<ul>
 <li>
  <input type="submit" id="p29" class="subbut" 
    onclick="makeRequest('p29');"
    value="d:=divide(13,4)" />
  <div id="ansp29"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p30" class="subbut" 
    onclick="handleFree(['p29','p30']);"
    value="d.quotient" />
  <div id="ansp30"><div></div></div>
 </li>
</ul>
Records are discussed in detail in 
<a href="axbook/section-2.4.xhtml">Records</a>.
<ul>
 <li>
  <input type="submit" id="p31" class="subbut" 
    onclick="handleFree(['p29','p31']);"
    value="d.remainder" />
  <div id="ansp31"><div></div></div>
 </li>
</ul>
 </body>
</html>
axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / numbasicfunctions.xhtml
