r5rs-z-h-9.html

scheme 标准（r5rs）。Scheme是MIT发布的基于Lambda运算的语言

quantity.  For any Scheme number, precisely one of these predicates
is true.<p>

<p><p>

<p><div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_254"></a>=<i> <em>z</em><sub>1</sub> <em>z</em><sub>2</sub> <em>z</em><sub>3</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_256"></a>&lt;<i> <em>x</em><sub>1</sub> <em>x</em><sub>2</sub> <em>x</em><sub>3</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_258"></a>&gt;<i> <em>x</em><sub>1</sub> <em>x</em><sub>2</sub> <em>x</em><sub>3</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_260"></a>&lt;=<i> <em>x</em><sub>1</sub> <em>x</em><sub>2</sub> <em>x</em><sub>3</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_262"></a>&gt;=<i> <em>x</em><sub>1</sub> <em>x</em><sub>2</sub> <em>x</em><sub>3</sub> <tt>...</tt></i>)</tt>&nbsp;</div>
<p>

These procedures return <tt>#t</tt> if their arguments are (respectively):
equal, monotonically increasing, monotonically decreasing,
monotonically nondecreasing, or monotonically nonincreasing.<p>

These predicates are required to be transitive.<p>

<blockquote><em>Note:&nbsp;&nbsp;</em>
The traditional implementations of these predicates in Lisp-like
languages are not transitive.
</blockquote><p>

<blockquote><em>Note:&nbsp;&nbsp;</em>
While it is not an error to compare inexact numbers using these
predicates, the results may be unreliable because a small inaccuracy
may affect the result; this is especially true of <tt>=</tt> and <tt>zero?</tt>.
When in doubt, consult a numerical analyst.
</blockquote><p>

<p><p>

<p><div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_264"></a>zero?<i> <em>z</em></i>)</tt>&nbsp;</div>

<div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_266"></a>positive?<i> <em>x</em></i>)</tt>&nbsp;</div>

<div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_268"></a>negative?<i> <em>x</em></i>)</tt>&nbsp;</div>

<div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_270"></a>odd?<i> <em>n</em></i>)</tt>&nbsp;</div>

<div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_272"></a>even?<i> <em>n</em></i>)</tt>&nbsp;</div>
<p>

These numerical predicates test a number for a particular property,
returning <tt>#t</tt> or <tt>#f</tt>.  See note above.<p>

<p><p>

<p><div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_274"></a>max<i> <em>x</em><sub>1</sub> <em>x</em><sub>2</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_276"></a>min<i> <em>x</em><sub>1</sub> <em>x</em><sub>2</sub> <tt>...</tt></i>)</tt>&nbsp;</div>
<p>

These procedures return the maximum or minimum of their arguments.<p>

<tt><p>(max&nbsp;3&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;4&nbsp;&nbsp;&nbsp;&nbsp;;&nbsp;exact<br>
(max&nbsp;3.9&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;4.0&nbsp;&nbsp;;&nbsp;inexact<p></tt><p>

<blockquote><em>Note:&nbsp;&nbsp;</em>
If any argument is inexact, then the result will also be inexact (unless
the procedure can prove that the inaccuracy is not large enough to affect the
result, which is possible only in unusual implementations).  If <tt>min</tt> or
<tt>max</tt> is used to compare numbers of mixed exactness, and the numerical
value of the result cannot be represented as an inexact number without loss of
accuracy, then the procedure may report a violation of an implementation
restriction.
</blockquote><p>

<p><p>

<p><div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_278"></a>+<i> <em>z</em><sub>1</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_280"></a>*<i> <em>z</em><sub>1</sub> <tt>...</tt></i>)</tt>&nbsp;</div>
<p>

These procedures return the sum or product of their arguments.

<tt><p>(+&nbsp;3&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;7<br>
(+&nbsp;3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;3<br>
(+)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;0<br>
(*&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;4<br>
(*)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;1<p></tt> <p>

<p><p>

<p><div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_282"></a>-<i> <em>z</em><sub>1</sub> <em>z</em><sub>2</sub></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(-<i> <em>z</em></i>)</tt>&nbsp;</div>

<div align=left><u>optional procedure:</u>&nbsp;&nbsp;<tt>(-<i> <em>z</em><sub>1</sub> <em>z</em><sub>2</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_284"></a>/<i> <em>z</em><sub>1</sub> <em>z</em><sub>2</sub></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(/<i> <em>z</em></i>)</tt>&nbsp;</div>

<div align=left><u>optional procedure:</u>&nbsp;&nbsp;<tt>(/<i> <em>z</em><sub>1</sub> <em>z</em><sub>2</sub> <tt>...</tt></i>)</tt>&nbsp;</div>
<p>

With two or more arguments, these procedures return the difference or
quotient of their arguments, associating to the left.  With one argument,
however, they return the additive or multiplicative inverse of their argument.

<tt><p>(-&nbsp;3&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-1<br>
(-&nbsp;3&nbsp;4&nbsp;5)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-6<br>
(-&nbsp;3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-3<br>
(/&nbsp;3&nbsp;4&nbsp;5)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;3/20<br>
(/&nbsp;3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;1/3<p></tt><p>

<p><p>

<p><div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_286"></a>abs<i> x</i>)</tt>&nbsp;</div>
<p>

<tt>Abs</tt> returns the absolute value of its argument.  
<tt><p>(abs&nbsp;-7)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;7<br>
<p></tt>
<p><p>

<p><div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_288"></a>quotient<i> <em>n</em><sub>1</sub> <em>n</em><sub>2</sub></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_290"></a>remainder<i> <em>n</em><sub>1</sub> <em>n</em><sub>2</sub></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_292"></a>modulo<i> <em>n</em><sub>1</sub> <em>n</em><sub>2</sub></i>)</tt>&nbsp;</div>
<p>

These procedures implement number-theoretic (integer)
division.  <em>n</em><sub>2</sub> should be non-zero.  All three procedures
return integers.  If <em>n</em><sub>1</sub>/<em>n</em><sub>2</sub> is an integer:
<tt><p>&nbsp;&nbsp;&nbsp;&nbsp;(quotient&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;<em>n</em><sub>1</sub>/<em>n</em><sub>2</sub><br>
&nbsp;&nbsp;&nbsp;&nbsp;(remainder&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;0<br>
&nbsp;&nbsp;&nbsp;&nbsp;(modulo&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;0<br>
<p></tt>
If <em>n</em><sub>1</sub>/<em>n</em><sub>2</sub> is not an integer:
<tt><p>&nbsp;&nbsp;&nbsp;&nbsp;(quotient&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;<em>n</em><sub><em>q</em></sub><br>
&nbsp;&nbsp;&nbsp;&nbsp;(remainder&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;<em>n</em><sub><em>r</em></sub><br>
&nbsp;&nbsp;&nbsp;&nbsp;(modulo&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;<em>n</em><sub><em>m</em></sub><br>
<p></tt>
where <em>n</em><sub><em>q</em></sub> is <em>n</em><sub>1</sub>/<em>n</em><sub>2</sub> rounded towards zero,
0 &lt; |<em>n</em><sub><em>r</em></sub>| &lt; |<em>n</em><sub>2</sub>|, 0 &lt; |<em>n</em><sub><em>m</em></sub>| &lt; |<em>n</em><sub>2</sub>|,
<em>n</em><sub><em>r</em></sub> and <em>n</em><sub><em>m</em></sub> differ from <em>n</em><sub>1</sub> by a multiple of <em>n</em><sub>2</sub>,
<em>n</em><sub><em>r</em></sub> has the same sign as <em>n</em><sub>1</sub>, and
<em>n</em><sub><em>m</em></sub> has the same sign as <em>n</em><sub>2</sub>.<p>

From this we can conclude that for integers <em>n</em><sub>1</sub> and <em>n</em><sub>2</sub> with
<em>n</em><sub>2</sub> not equal to 0,
<tt><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(=&nbsp;<em>n</em><sub>1</sub>&nbsp;(+&nbsp;(*&nbsp;<em>n</em><sub>2</sub>&nbsp;(quotient&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>))<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(remainder&nbsp;<em>n</em><sub>1</sub>&nbsp;<em>n</em><sub>2</sub>)))<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;<tt>#t</tt><p></tt>
provided all numbers involved in that computation are exact.<p>

<tt><p>(modulo&nbsp;13&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;1<br>
(remainder&nbsp;13&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;1<br>
<br>
(modulo&nbsp;-13&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;3<br>
(remainder&nbsp;-13&nbsp;4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-1<br>
<br>
(modulo&nbsp;13&nbsp;-4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-3<br>
(remainder&nbsp;13&nbsp;-4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;1<br>
<br>
(modulo&nbsp;-13&nbsp;-4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-1<br>
(remainder&nbsp;-13&nbsp;-4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-1<br>
<br>
(remainder&nbsp;-13&nbsp;-4.0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;-1.0&nbsp;&nbsp;;&nbsp;inexact<p></tt>
<p><p>

<p><div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_294"></a>gcd<i> <em>n</em><sub>1</sub> <tt>...</tt></i>)</tt>&nbsp;</div>

<div align=left><u>library procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_296"></a>lcm<i> <em>n</em><sub>1</sub> <tt>...</tt></i>)</tt>&nbsp;</div>
<p>

These procedures return the greatest common divisor or least common
multiple of their arguments.  The result is always non-negative.

<tt><p>(gcd&nbsp;32&nbsp;-36)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;4<br>
(gcd)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;0<br>
(lcm&nbsp;32&nbsp;-36)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;288<br>
(lcm&nbsp;32.0&nbsp;-36)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;288.0&nbsp;&nbsp;;&nbsp;inexact<br>
(lcm)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;1<p></tt><p>

<p><p>

<p><div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_298"></a>numerator<i> <em>q</em></i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_300"></a>denominator<i> <em>q</em></i>)</tt>&nbsp;</div>
<p>

These procedures return the numerator or denominator of their
argument; the result is computed as if the argument was represented as
a fraction in lowest terms.  The denominator is always positive.  The
denominator of 0 is defined to be 1.

<tt><p>(numerator&nbsp;(/&nbsp;6&nbsp;4))&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;3<br>
(denominator&nbsp;(/&nbsp;6&nbsp;4))&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;&nbsp;2<br>
(denominator<br>
&nbsp;&nbsp;(exact-&gt;inexact&nbsp;(/&nbsp;6&nbsp;4)))&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;===&gt;&nbsp;2.0<p></tt><p>

<p><p>

<p><div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_302"></a>floor<i> x</i>)</tt>&nbsp;</div>

<div align=left><u>procedure:</u>&nbsp;&nbsp;<tt>(<a name="%_idx_304"></a>ceiling<i> x</i>)</tt>&nbsp;</div>