Sophie: php-manual-ro-0:20051028-1 noarch

php-manual-ro-20051028-1.noarch.rpm

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>gmp_gcdext</H1
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>    (PHP 4 &#62;= 4.0.4, PHP 5)</P
>gmp_gcdext&nbsp;--&nbsp;Calculate GCD and multipliers</DIV
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>Description</H2
>array <B
CLASS="methodname"
>gmp_gcdext</B
> ( resource a, resource b)<BR
></BR
><P
>&#13;     Calculates g, s, and t, such that <VAR
CLASS="literal"
>a*s + b*t = g =
     gcd(a,b)</VAR
>, where gcd is the greatest common divisor. Returns
     an array with respective elements g, s and t.
    </P
><P
>&#13;     This function can be used to solve linear Diophantine equations in two
     variables. These are equations that allow only integer solutions and have the form:
     <VAR
CLASS="literal"
>a*x + b*y = c</VAR
>.
      For more information, go to the <A
HREF="http://mathworld.wolfram.com/DiophantineEquation.html"
TARGET="_top"
>"Diophantine 
       Equation" page at MathWorld</A
>
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>Exemplu 1. Solving a linear Diophantine equation</B
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><code><font color="#000000">
<font color="#0000BB">&lt;?php<br /></font><font color="#FF8000">// Solve the equation a*s + b*t = g<br />// where a = 12, b = 21, g = gcd(12, 21) = 3<br /></font><font color="#0000BB">$a </font><font color="#007700">= </font><font color="#0000BB">gmp_init</font><font color="#007700">(</font><font color="#0000BB">12</font><font color="#007700">);<br /></font><font color="#0000BB">$b </font><font color="#007700">= </font><font color="#0000BB">gmp_init</font><font color="#007700">(</font><font color="#0000BB">21</font><font color="#007700">);<br /></font><font color="#0000BB">$g </font><font color="#007700">= </font><font color="#0000BB">gmp_gcd</font><font color="#007700">(</font><font color="#0000BB">$a</font><font color="#007700">, </font><font color="#0000BB">$b</font><font color="#007700">);<br /></font><font color="#0000BB">$r </font><font color="#007700">= </font><font color="#0000BB">gmp_gcdext</font><font color="#007700">(</font><font color="#0000BB">$a</font><font color="#007700">, </font><font color="#0000BB">$b</font><font color="#007700">);<br /><br /></font><font color="#0000BB">$check_gcd </font><font color="#007700">= (</font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$g</font><font color="#007700">) == </font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$r</font><font color="#007700">[</font><font color="#DD0000">'g'</font><font color="#007700">]));<br /></font><font color="#0000BB">$eq_res </font><font color="#007700">= </font><font color="#0000BB">gmp_add</font><font color="#007700">(</font><font color="#0000BB">gmp_mul</font><font color="#007700">(</font><font color="#0000BB">$a</font><font color="#007700">, </font><font color="#0000BB">$r</font><font color="#007700">[</font><font color="#DD0000">'s'</font><font color="#007700">]), </font><font color="#0000BB">gmp_mul</font><font color="#007700">(</font><font color="#0000BB">$b</font><font color="#007700">, </font><font color="#0000BB">$r</font><font color="#007700">[</font><font color="#DD0000">'t'</font><font color="#007700">]));<br /></font><font color="#0000BB">$check_res </font><font color="#007700">= (</font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$g</font><font color="#007700">) == </font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$eq_res</font><font color="#007700">));<br /><br />if (</font><font color="#0000BB">$check_gcd </font><font color="#007700">&amp;&amp; </font><font color="#0000BB">$check_res</font><font color="#007700">) {<br />&nbsp;&nbsp;&nbsp;&nbsp;</font><font color="#0000BB">$fmt </font><font color="#007700">= </font><font color="#DD0000">"Solution: %d*%d + %d*%d = %d\n"</font><font color="#007700">;<br />&nbsp;&nbsp;&nbsp;&nbsp;</font><font color="#0000BB">printf</font><font color="#007700">(</font><font color="#0000BB">$fmt</font><font color="#007700">, </font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$a</font><font color="#007700">), </font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$r</font><font color="#007700">[</font><font color="#DD0000">'s'</font><font color="#007700">]), </font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$b</font><font color="#007700">),<br />&nbsp;&nbsp;&nbsp;&nbsp;</font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$r</font><font color="#007700">[</font><font color="#DD0000">'t'</font><font color="#007700">]), </font><font color="#0000BB">gmp_strval</font><font color="#007700">(</font><font color="#0000BB">$r</font><font color="#007700">[</font><font color="#DD0000">'g'</font><font color="#007700">]));<br />} else {<br />&nbsp;&nbsp;&nbsp;&nbsp;echo </font><font color="#DD0000">"Error while solving the equation\n"</font><font color="#007700">;<br />}<br />&nbsp;&nbsp;&nbsp;&nbsp;<br /></font><font color="#FF8000">// output: Solution: 12*2 + 21*-1 = 3<br /></font><font color="#0000BB">?&gt;</font>
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