polynomi_8cpp-source.html

著名的密码库Crypto++的文档 C++语言的杰作。程序员必备。

<a name="l00202"></a>00202 
<a name="l00203"></a>00203 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00204"></a>00204 <span class="keywordtype">bool</span> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;::Equals</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a>&amp; t, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html#f87a6be38193e61c7aecb8c96510583e">Ring</a> &amp;ring)<span class="keyword"> const</span>
<a name="l00205"></a>00205 <span class="keyword"></span>{
<a name="l00206"></a>00206         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count = <a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring);
<a name="l00207"></a>00207 
<a name="l00208"></a>00208         <span class="keywordflow">if</span> (count != t.<a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring))
<a name="l00209"></a>00209                 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00210"></a>00210 
<a name="l00211"></a>00211         <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;count; i++)
<a name="l00212"></a>00212                 <span class="keywordflow">if</span> (!ring.Equal(m_coefficients[i], t.<a class="code" href="class_polynomial_over.html#d669c6670fb313273a4d245eeddb82dc">m_coefficients</a>[i]))
<a name="l00213"></a>00213                         <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00214"></a>00214 
<a name="l00215"></a>00215         <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00216"></a>00216 }
<a name="l00217"></a>00217 
<a name="l00218"></a>00218 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00219"></a>00219 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;::Plus</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a>&amp; t, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html#f87a6be38193e61c7aecb8c96510583e">Ring</a> &amp;ring)<span class="keyword"> const</span>
<a name="l00220"></a>00220 <span class="keyword"></span>{
<a name="l00221"></a>00221         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;
<a name="l00222"></a>00222         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count = <a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring);
<a name="l00223"></a>00223         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> tCount = t.<a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring);
<a name="l00224"></a>00224 
<a name="l00225"></a>00225         <span class="keywordflow">if</span> (count &gt; tCount)
<a name="l00226"></a>00226         {
<a name="l00227"></a>00227                 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> result(ring, count);
<a name="l00228"></a>00228 
<a name="l00229"></a>00229                 <span class="keywordflow">for</span> (i=0; i&lt;tCount; i++)
<a name="l00230"></a>00230                         result.m_coefficients[i] = ring.Add(m_coefficients[i], t.<a class="code" href="class_polynomial_over.html#d669c6670fb313273a4d245eeddb82dc">m_coefficients</a>[i]);
<a name="l00231"></a>00231                 <span class="keywordflow">for</span> (; i&lt;count; i++)
<a name="l00232"></a>00232                         result.m_coefficients[i] = m_coefficients[i];
<a name="l00233"></a>00233 
<a name="l00234"></a>00234                 <span class="keywordflow">return</span> result;
<a name="l00235"></a>00235         }
<a name="l00236"></a>00236         <span class="keywordflow">else</span>
<a name="l00237"></a>00237         {
<a name="l00238"></a>00238                 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> result(ring, tCount);
<a name="l00239"></a>00239 
<a name="l00240"></a>00240                 <span class="keywordflow">for</span> (i=0; i&lt;count; i++)
<a name="l00241"></a>00241                         result.m_coefficients[i] = ring.Add(m_coefficients[i], t.<a class="code" href="class_polynomial_over.html#d669c6670fb313273a4d245eeddb82dc">m_coefficients</a>[i]);
<a name="l00242"></a>00242                 <span class="keywordflow">for</span> (; i&lt;tCount; i++)
<a name="l00243"></a>00243                         result.m_coefficients[i] = t.<a class="code" href="class_polynomial_over.html#d669c6670fb313273a4d245eeddb82dc">m_coefficients</a>[i];
<a name="l00244"></a>00244 
<a name="l00245"></a>00245                 <span class="keywordflow">return</span> result;
<a name="l00246"></a>00246         }
<a name="l00247"></a>00247 }
<a name="l00248"></a>00248 
<a name="l00249"></a>00249 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00250"></a>00250 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;::Minus</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a>&amp; t, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html#f87a6be38193e61c7aecb8c96510583e">Ring</a> &amp;ring)<span class="keyword"> const</span>
<a name="l00251"></a>00251 <span class="keyword"></span>{
<a name="l00252"></a>00252         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;
<a name="l00253"></a>00253         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count = <a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring);
<a name="l00254"></a>00254         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> tCount = t.CoefficientCount(ring);
<a name="l00255"></a>00255 
<a name="l00256"></a>00256         <span class="keywordflow">if</span> (count &gt; tCount)
<a name="l00257"></a>00257         {
<a name="l00258"></a>00258                 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> result(ring, count);
<a name="l00259"></a>00259 
<a name="l00260"></a>00260                 <span class="keywordflow">for</span> (i=0; i&lt;tCount; i++)
<a name="l00261"></a>00261                         result.m_coefficients[i] = ring.Subtract(m_coefficients[i], t.m_coefficients[i]);
<a name="l00262"></a>00262                 <span class="keywordflow">for</span> (; i&lt;count; i++)
<a name="l00263"></a>00263                         result.m_coefficients[i] = m_coefficients[i];
<a name="l00264"></a>00264 
<a name="l00265"></a>00265                 <span class="keywordflow">return</span> result;
<a name="l00266"></a>00266         }
<a name="l00267"></a>00267         <span class="keywordflow">else</span>
<a name="l00268"></a>00268         {
<a name="l00269"></a>00269                 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> result(ring, tCount);
<a name="l00270"></a>00270 
<a name="l00271"></a>00271                 <span class="keywordflow">for</span> (i=0; i&lt;count; i++)
<a name="l00272"></a>00272                         result.m_coefficients[i] = ring.Subtract(m_coefficients[i], t.m_coefficients[i]);
<a name="l00273"></a>00273                 <span class="keywordflow">for</span> (; i&lt;tCount; i++)
<a name="l00274"></a>00274                         result.m_coefficients[i] = ring.Inverse(t.m_coefficients[i]);
<a name="l00275"></a>00275 
<a name="l00276"></a>00276                 <span class="keywordflow">return</span> result;
<a name="l00277"></a>00277         }
<a name="l00278"></a>00278 }
<a name="l00279"></a>00279 
<a name="l00280"></a>00280 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00281"></a><a class="code" href="class_polynomial_over.html#037a72b82d5acfcacbb94a73784b0d85">00281</a> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> <a class="code" href="class_polynomial_over.html#037a72b82d5acfcacbb94a73784b0d85">PolynomialOver&lt;T&gt;::Inverse</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html#f87a6be38193e61c7aecb8c96510583e">Ring</a> &amp;ring)<span class="keyword"> const</span>
<a name="l00282"></a>00282 <span class="keyword"></span>{
<a name="l00283"></a>00283         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count = <a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring);
<a name="l00284"></a>00284         <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> result(ring, count);
<a name="l00285"></a>00285 
<a name="l00286"></a>00286         <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;count; i++)
<a name="l00287"></a>00287                 result.<a class="code" href="class_polynomial_over.html#d669c6670fb313273a4d245eeddb82dc">m_coefficients</a>[i] = ring.Inverse(m_coefficients[i]);
<a name="l00288"></a>00288 
<a name="l00289"></a>00289         <span class="keywordflow">return</span> result;
<a name="l00290"></a>00290 }
<a name="l00291"></a>00291 
<a name="l00292"></a>00292 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00293"></a>00293 <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;::Times</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a>&amp; t, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html#f87a6be38193e61c7aecb8c96510583e">Ring</a> &amp;ring)<span class="keyword"> const</span>
<a name="l00294"></a>00294 <span class="keyword"></span>{
<a name="l00295"></a>00295         <span class="keywordflow">if</span> (<a class="code" href="class_polynomial_over.html#de0983f77089c32d1f7ce07738ea4619">IsZero</a>(ring) || t.<a class="code" href="class_polynomial_over.html#de0983f77089c32d1f7ce07738ea4619">IsZero</a>(ring))
<a name="l00296"></a>00296                 <span class="keywordflow">return</span> <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;</a>();
<a name="l00297"></a>00297 
<a name="l00298"></a>00298         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count1 = <a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring), count2 = t.<a class="code" href="class_polynomial_over.html#65c6004a42608f31008ff066f2eba3e2">CoefficientCount</a>(ring);
<a name="l00299"></a>00299         PolynomialOver&lt;T&gt; result(ring, count1 + count2 - 1);
<a name="l00300"></a>00300 
<a name="l00301"></a>00301         <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;count1; i++)
<a name="l00302"></a>00302                 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;count2; j++)
<a name="l00303"></a>00303                         ring.Accumulate(result.m_coefficients[i+j], ring.Multiply(m_coefficients[i], t.<a class="code" href="class_polynomial_over.html#d669c6670fb313273a4d245eeddb82dc">m_coefficients</a>[j]));
<a name="l00304"></a>00304 
<a name="l00305"></a>00305         <span class="keywordflow">return</span> result;
<a name="l00306"></a>00306 }
<a name="l00307"></a>00307 
<a name="l00308"></a>00308 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00309"></a>00309 PolynomialOver&lt;T&gt; <a class="code" href="class_polynomial_over.html" title="represents single-variable polynomials over arbitrary rings">PolynomialOver&lt;T&gt;::DividedBy</a>(<span class="keyword">const</span> PolynomialOver&lt;T&gt;&amp; t, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html#f87a6be38193e61c7aecb8c96510583e">Ring</a> &amp;ring)<span class="keyword"> const</span>
<a name="l00310"></a>00310 <span class="keyword"></span>{
<a name="l00311"></a>00311         PolynomialOver&lt;T&gt; remainder, quotient;
<a name="l00312"></a>00312         <a class="code" href="class_polynomial_over.html#e4e0b0beb7bfab492d6f7343630c2df9" title="calculate r and q such that (a == d*q + r) &amp;&amp; (0 &lt;= degree of r &lt; degree...">Divide</a>(remainder, quotient, *<span class="keyword">this</span>, t, ring);