67 lines
3.6 KiB
HTML
67 lines
3.6 KiB
HTML
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<TITLE>CLHS: Function GCD</TITLE>
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<A NAME="gcd"><I>Function</I> <B>GCD</B></A> <P>
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<P><B>Syntax:</B><P>
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<P>
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<B>gcd</B> <I><TT>&rest</TT> integers</I> => <I>greatest-common-denominator</I><P>
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<P>
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<P><B>Arguments and Values:</B><P>
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<P>
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<I>integer</I>---an <A REL=DEFINITION HREF="26_glo_i.htm#integer"><I>integer</I></A>. <P>
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<I>greatest-common-denominator</I>---a non-negative <A REL=DEFINITION HREF="26_glo_i.htm#integer"><I>integer</I></A>. <P>
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<P><B>Description:</B><P>
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<P>
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Returns the greatest common divisor of <I>integers</I>. If only one <I>integer</I> is supplied, its absolute value is returned. If no <I>integers</I> are given, <A REL=DEFINITION HREF="#gcd"><B>gcd</B></A> returns <TT>0</TT>, which is an identity for this operation. <P>
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<P><B>Examples:</B><P>
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<P>
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<PRE>
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(gcd) => 0
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(gcd 60 42) => 6
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(gcd 3333 -33 101) => 1
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(gcd 3333 -33 1002001) => 11
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(gcd 91 -49) => 7
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(gcd 63 -42 35) => 7
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(gcd 5) => 5
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(gcd -4) => 4
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</PRE>
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</TT> <P>
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<P><B>Side Effects:</B> None.
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<P>
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<P><B>Affected By:</B> None.
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<P>
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<P><B>Exceptional Situations:</B><P>
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<P>
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Should signal an error of <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <A REL=DEFINITION HREF="e_tp_err.htm#type-error"><B>type-error</B></A> if any <I>integer</I> is not an <A REL=DEFINITION HREF="26_glo_i.htm#integer"><I>integer</I></A>. <P>
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<P><B>See Also:</B><P>
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<P>
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<A REL=DEFINITION HREF="f_lcm.htm#lcm"><B>lcm</B></A> <P>
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<P><B>Notes:</B><P>
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For three or more arguments, <P>
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<PRE>
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(gcd b c ... z) == (gcd (gcd a b) c ... z)
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</PRE>
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