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<a href="polynomi_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// polynomi.h - originally written and placed in the public domain by Wei Dai</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"></span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">/// \file polynomi.h</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/// \brief Classes for polynomial basis and operations</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"></span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="preprocessor">#ifndef CRYPTOPP_POLYNOMI_H</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="preprocessor">#define CRYPTOPP_POLYNOMI_H</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> </div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="preprocessor">#include "<a class="code" href="cryptlib_8h.html">cryptlib.h</a>"</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#include "<a class="code" href="secblock_8h.html">secblock.h</a>"</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#include "<a class="code" href="algebra_8h.html">algebra.h</a>"</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include "<a class="code" href="misc_8h.html">misc.h</a>"</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include <iosfwd></span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include <vector></span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> NAMESPACE_BEGIN(<a class="code" href="namespace_crypto_p_p.html">CryptoPP</a>)</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">/// represents single-variable polynomials over arbitrary rings</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"></span><span class="comment">/*! \nosubgrouping */</span></div><div class="line"><a name="l00021"></a><span class="lineno"><a class="line" href="class_polynomial_over.html"> 21</a></span> template <class T> class <a class="code" href="class_polynomial_over.html">PolynomialOver</a></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> {</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">public</span>:<span class="comment"></span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> /// \name ENUMS, EXCEPTIONS, and TYPEDEFS</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"></span><span class="comment"> /// division by zero exception</span></div><div class="line"><a name="l00027"></a><span class="lineno"><a class="line" href="class_polynomial_over_1_1_divide_by_zero.html"> 27</a></span> <span class="comment"></span> <span class="keyword">class </span><a class="code" href="class_polynomial_over_1_1_divide_by_zero.html">DivideByZero</a> : <span class="keyword">public</span> <a class="code" href="class_exception.html">Exception</a></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  {</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <a class="code" href="class_polynomial_over_1_1_divide_by_zero.html">DivideByZero</a>() : <a class="code" href="class_exception.html">Exception</a>(OTHER_ERROR, <span class="stringliteral">"PolynomialOver<T>: division by zero"</span>) {}</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  };</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment"></span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"> /// specify the distribution for randomization functions</span></div><div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="class_polynomial_over_1_1_randomization_parameter.html"> 34</a></span> <span class="comment"></span> <span class="keyword">class </span><a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  {</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> coefficientCount, <span class="keyword">const</span> <span class="keyword">typename</span> T::RandomizationParameter &coefficientParameter )</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  : m_coefficientCount(coefficientCount), m_coefficientParameter(coefficientParameter) {}</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> m_coefficientCount;</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">typename</span> T::RandomizationParameter m_coefficientParameter;</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">friend</span> <span class="keyword">class </span><a class="code" href="class_polynomial_over.html">PolynomialOver</a><T>;</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  };</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">typedef</span> T Ring;</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> T::Element CoefficientType;<span class="comment"></span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"> /// \name CREATORS</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"></span><span class="comment"> /// creates the zero polynomial</span></div><div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c"> 53</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c">PolynomialOver</a>() {}</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"></span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> ///</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c">PolynomialOver</a>(<span class="keyword">const</span> Ring &ring, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count)</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  : m_coefficients((size_t)count, ring.<a class="code" href="namespace_name.html#a87f7b89127f1053f118c879e865ab212">Identity</a>()) {}</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"></span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> /// copy constructor</span></div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#a393c8f0c973d431d7e04d3d3682b333d"> 60</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#a393c8f0c973d431d7e04d3d3682b333d">PolynomialOver</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &t)</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  : m_coefficients(t.m_coefficients.size()) {*<span class="keyword">this</span> = t;}</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"></span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> /// construct constant polynomial</span></div><div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#af3f01459e456891391d9650e4b82b8b0"> 64</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#af3f01459e456891391d9650e4b82b8b0">PolynomialOver</a>(<span class="keyword">const</span> CoefficientType &element)</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  : m_coefficients(1, element) {}</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"></span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> /// construct polynomial with specified coefficients, starting from coefficient of x^0</span></div><div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#a7a4e4504a189d1594961879fc10cba43"> 68</a></span> <span class="comment"></span> <span class="keyword">template</span> <<span class="keyword">typename</span> Iterator> <a class="code" href="class_polynomial_over.html#a7a4e4504a189d1594961879fc10cba43">PolynomialOver</a>(Iterator begin, Iterator end)</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  : m_coefficients(begin, end) {}</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"></span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> /// convert from string</span></div><div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#aef039d41b917e8297e14c050568a37a2"> 72</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#aef039d41b917e8297e14c050568a37a2">PolynomialOver</a>(<span class="keyword">const</span> <span class="keywordtype">char</span> *str, <span class="keyword">const</span> Ring &ring) {FromStr(str, ring);}</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"></span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> /// convert from big-endian byte array</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c">PolynomialOver</a>(<span class="keyword">const</span> byte *encodedPolynomialOver, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> byteCount);</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"></span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> /// convert from Basic Encoding Rules encoded byte array</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"></span> <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c">PolynomialOver</a>(<span class="keyword">const</span> byte *BEREncodedPolynomialOver);</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"></span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> /// convert from BER encoded byte array stored in a BufferedTransformation object</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"></span> <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c">PolynomialOver</a>(<a class="code" href="class_buffered_transformation.html">BufferedTransformation</a> &bt);</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"></span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> /// create a random PolynomialOver<T></span></div><div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#a33a595d1ea6d44eef7ac3636c195a869"> 84</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html#a33a595d1ea6d44eef7ac3636c195a869">PolynomialOver</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a> &parameter, <span class="keyword">const</span> Ring &ring)</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  {Randomize(rng, parameter, ring);}<span class="comment"></span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> /// \name ACCESSORS</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"></span><span class="comment"> /// the zero polynomial will return a degree of -1</span></div><div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="class_polynomial_over.html#a528a5722512381f2d7cb3b705bcbe8bb"> 91</a></span> <span class="comment"></span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_over.html#a528a5722512381f2d7cb3b705bcbe8bb">Degree</a>(<span class="keyword">const</span> Ring &ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> int(CoefficientCount(ring))-1;}<span class="comment"></span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> ///</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> CoefficientCount(<span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;<span class="comment"></span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> /// return coefficient for x^i</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"></span> CoefficientType <a class="code" href="class_polynomial_over.html#a6feeb70252350258e2439f8a864d563f">GetCoefficient</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;<span class="comment"></span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> /// \name MANIPULATORS</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"></span><span class="comment"> ///</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& operator=(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"></span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> ///</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment"></span> <span class="keywordtype">void</span> Randomize(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> RandomizationParameter &parameter, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"></span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"> /// set the coefficient for x^i to value</span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"></span> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_over.html#aac4ab97afda49a151fc9dbd8eaf9aa16">SetCoefficient</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keyword">const</span> CoefficientType &value, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"></span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"> ///</span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"></span> <span class="keywordtype">void</span> Negate(<span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"></span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"> ///</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"></span> <span class="keywordtype">void</span> swap(<a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &t);<span class="comment"></span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"></span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"></span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> /// \name BASIC ARITHMETIC ON POLYNOMIALS</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"></span> <span class="keywordtype">bool</span> Equals(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &t, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordtype">bool</span> IsZero(<span class="keyword">const</span> Ring &ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> CoefficientCount(ring)==0;}</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Plus(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Minus(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Inverse(<span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Times(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> DividedBy(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Modulo(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> MultiplicativeInverse(<span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">bool</span> IsUnit(<span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& Accumulate(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& Reduce(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& t, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"></span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> ///</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Doubled(<span class="keyword">const</span> Ring &ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> Plus(*<span class="keyword">this</span>, ring);}<span class="comment"></span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> ///</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"></span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> Squared(<span class="keyword">const</span> Ring &ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> Times(*<span class="keyword">this</span>, ring);}</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  CoefficientType EvaluateAt(<span class="keyword">const</span> CoefficientType &x, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> </div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& ShiftLeft(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a>& ShiftRight(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"></span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> /// calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d)</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_over.html#aaa1a0b9d2470af2a01ae1c01d743b042">Divide</a>(<a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &r, <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &q, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<Ring></a> &d, <span class="keyword">const</span> Ring &ring);<span class="comment"></span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> /// \name INPUT/OUTPUT</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"></span> std::istream& Input(std::istream &in, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  std::ostream& Output(std::ostream &out, <span class="keyword">const</span> Ring &ring) <span class="keyword">const</span>;<span class="comment"></span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"></span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">private</span>:</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordtype">void</span> FromStr(<span class="keyword">const</span> <span class="keywordtype">char</span> *str, <span class="keyword">const</span> Ring &ring);</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  std::vector<CoefficientType> m_coefficients;</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> };</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"></span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment">/// Polynomials over a fixed ring</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"></span><span class="comment">/*! Having a fixed ring allows overloaded operators */</span></div><div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html"> 163</a></span> <span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance> <span class="keyword">class </span><a class="code" href="class_polynomial_over_fixed_ring.html">PolynomialOverFixedRing</a> : <span class="keyword">private</span> <a class="code" href="class_polynomial_over.html">PolynomialOver</a><T></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> {</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keyword">typedef</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<T></a> <a class="code" href="class_polynomial_over.html">B</a>;</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keyword">typedef</span> <a class="code" href="class_polynomial_over_fixed_ring.html">PolynomialOverFixedRing<T, instance></a> <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a>;</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keyword">typedef</span> T Ring;</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> T::Element CoefficientType;</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="class_polynomial_over_1_1_divide_by_zero.html">B::DivideByZero</a> <a class="code" href="class_polynomial_over_1_1_divide_by_zero.html">DivideByZero</a>;</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">B::RandomizationParameter</a> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a>;</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"></span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"> /// \name CREATORS</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"></span><span class="comment"> /// creates the zero polynomial</span></div><div class="line"><a name="l00177"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a8e10a57bab595f53a2055bcfb03fb66e"> 177</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over_fixed_ring.html#a8e10a57bab595f53a2055bcfb03fb66e">PolynomialOverFixedRing</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count = 0) : <a class="code" href="class_polynomial_over.html">B</a>(ms_fixedRing, count) {}</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"></span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> /// copy constructor</span></div><div class="line"><a name="l00180"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#ad63e985a7c37535ea710b7779ecfb3aa"> 180</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over_fixed_ring.html#ad63e985a7c37535ea710b7779ecfb3aa">PolynomialOverFixedRing</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a> &t) : <a class="code" href="class_polynomial_over.html">B</a>(t) {}</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over_fixed_ring.html#a8e10a57bab595f53a2055bcfb03fb66e">PolynomialOverFixedRing</a>(<span class="keyword">const</span> B &t) : B(t) {}</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"></span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> /// construct constant polynomial</span></div><div class="line"><a name="l00185"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#adbff44242557cef909c01a74d75d181e"> 185</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over_fixed_ring.html#adbff44242557cef909c01a74d75d181e">PolynomialOverFixedRing</a>(<span class="keyword">const</span> CoefficientType &element) : <a class="code" href="class_polynomial_over.html">B</a>(element) {}</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"></span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment"> /// construct polynomial with specified coefficients, starting from coefficient of x^0</span></div><div class="line"><a name="l00188"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#af1e2af7d588db8db85d7f55df99c59eb"> 188</a></span> <span class="comment"></span> <span class="keyword">template</span> <<span class="keyword">typename</span> Iterator> <a class="code" href="class_polynomial_over_fixed_ring.html#af1e2af7d588db8db85d7f55df99c59eb">PolynomialOverFixedRing</a>(Iterator first, Iterator last)</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  : <a class="code" href="class_polynomial_over.html">B</a>(first, last) {}</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"></span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"> /// convert from string</span></div><div class="line"><a name="l00192"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#aebbb74586712f3f825c4fa4894fbf217"> 192</a></span> <span class="comment"></span> <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over_fixed_ring.html#aebbb74586712f3f825c4fa4894fbf217">PolynomialOverFixedRing</a>(<span class="keyword">const</span> <span class="keywordtype">char</span> *str) : <a class="code" href="class_polynomial_over.html">B</a>(str, ms_fixedRing) {}</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"></span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment"> /// convert from big-endian byte array</span></div><div class="line"><a name="l00195"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a38de0135bd58a61176cef61bc6397c47"> 195</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over_fixed_ring.html#a38de0135bd58a61176cef61bc6397c47">PolynomialOverFixedRing</a>(<span class="keyword">const</span> byte *encodedPoly, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> byteCount) : <a class="code" href="class_polynomial_over.html">B</a>(encodedPoly, byteCount) {}</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"></span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> /// convert from Basic Encoding Rules encoded byte array</span></div><div class="line"><a name="l00198"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#aeea00158952013a08cd97d1a416fa5a4"> 198</a></span> <span class="comment"></span> <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over_fixed_ring.html#aeea00158952013a08cd97d1a416fa5a4">PolynomialOverFixedRing</a>(<span class="keyword">const</span> byte *BEREncodedPoly) : <a class="code" href="class_polynomial_over.html">B</a>(BEREncodedPoly) {}</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"></span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> /// convert from BER encoded byte array stored in a BufferedTransformation object</span></div><div class="line"><a name="l00201"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#ac24e06202bb7b81088948d6aa2c9d54f"> 201</a></span> <span class="comment"></span> <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over_fixed_ring.html#ac24e06202bb7b81088948d6aa2c9d54f">PolynomialOverFixedRing</a>(<a class="code" href="class_buffered_transformation.html">BufferedTransformation</a> &bt) : <a class="code" href="class_polynomial_over.html">B</a>(bt) {}</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment"></span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment"> /// create a random PolynomialOverFixedRing</span></div><div class="line"><a name="l00204"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a49d91088bbec643b9e5b8db7c8c1e89b"> 204</a></span> <span class="comment"></span> <a class="code" href="class_polynomial_over_fixed_ring.html#a49d91088bbec643b9e5b8db7c8c1e89b">PolynomialOverFixedRing</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a> &parameter) : <a class="code" href="class_polynomial_over.html">B</a>(rng, parameter, ms_fixedRing) {}</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keyword">static</span> <span class="keyword">const</span> ThisType &Zero();</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keyword">static</span> <span class="keyword">const</span> ThisType &One();<span class="comment"></span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> /// \name ACCESSORS</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment"></span><span class="comment"> /// the zero polynomial will return a degree of -1</span></div><div class="line"><a name="l00213"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#adc7375389ed8759970361a61cce61ea0"> 213</a></span> <span class="comment"></span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_over_fixed_ring.html#adc7375389ed8759970361a61cce61ea0">Degree</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <a class="code" href="class_polynomial_over.html#a528a5722512381f2d7cb3b705bcbe8bb">B::Degree</a>(ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> /// degree + 1</span></div><div class="line"><a name="l00215"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a5e659b8a429b441a1ae1d6e544ebf189"> 215</a></span> <span class="comment"></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_over_fixed_ring.html#a5e659b8a429b441a1ae1d6e544ebf189">CoefficientCount</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> B::CoefficientCount(ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> /// return coefficient for x^i</span></div><div class="line"><a name="l00217"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a70982605b8e8c3cc07c08438d5fbdefa"> 217</a></span> <span class="comment"></span> CoefficientType <a class="code" href="class_polynomial_over_fixed_ring.html#a70982605b8e8c3cc07c08438d5fbdefa">GetCoefficient</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)<span class="keyword"> const </span>{<span class="keywordflow">return</span> <a class="code" href="class_polynomial_over.html#a6feeb70252350258e2439f8a864d563f">B::GetCoefficient</a>(i, ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> /// return coefficient for x^i</span></div><div class="line"><a name="l00219"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a5ff7d2a9165c23fba47f6cb2898f5e4b"> 219</a></span> <span class="comment"></span> CoefficientType <a class="code" href="class_polynomial_over_fixed_ring.html#a5ff7d2a9165c23fba47f6cb2898f5e4b">operator[]</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)<span class="keyword"> const </span>{<span class="keywordflow">return</span> <a class="code" href="class_polynomial_over.html#a6feeb70252350258e2439f8a864d563f">B::GetCoefficient</a>(i, ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment"> /// \name MANIPULATORS</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment"></span><span class="comment"> ///</span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment"></span> ThisType& operator=(<span class="keyword">const</span> ThisType& t) {B::operator=(t); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}<span class="comment"></span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment"> ///</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment"></span> ThisType& operator+=(<span class="keyword">const</span> ThisType& t) {Accumulate(t, ms_fixedRing); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}<span class="comment"></span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment"> ///</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"></span> ThisType& operator-=(<span class="keyword">const</span> ThisType& t) {Reduce(t, ms_fixedRing); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}<span class="comment"></span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> ///</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"></span> ThisType& operator*=(<span class="keyword">const</span> ThisType& t) {<span class="keywordflow">return</span> *<span class="keyword">this</span> = *<span class="keyword">this</span>*t;}<span class="comment"></span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment"> ///</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment"></span> ThisType& operator/=(<span class="keyword">const</span> ThisType& t) {<span class="keywordflow">return</span> *<span class="keyword">this</span> = *<span class="keyword">this</span>/t;}<span class="comment"></span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"> ///</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"></span> ThisType& operator%=(<span class="keyword">const</span> ThisType& t) {<span class="keywordflow">return</span> *<span class="keyword">this</span> = *<span class="keyword">this</span>%t;}</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"></span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> ///</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment"></span> ThisType& operator<<=(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) {ShiftLeft(n, ms_fixedRing); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}<span class="comment"></span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment"> ///</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment"></span> ThisType& operator>>=(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) {ShiftRight(n, ms_fixedRing); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"></span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment"> /// set the coefficient for x^i to value</span></div><div class="line"><a name="l00243"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#a7c797943b4cb9e864328d6d02dcb2444"> 243</a></span> <span class="comment"></span> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_over_fixed_ring.html#a7c797943b4cb9e864328d6d02dcb2444">SetCoefficient</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keyword">const</span> CoefficientType &value) {<a class="code" href="class_polynomial_over.html#aac4ab97afda49a151fc9dbd8eaf9aa16">B::SetCoefficient</a>(i, value, ms_fixedRing);}</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment"></span></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment"> ///</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment"></span> <span class="keywordtype">void</span> Randomize(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> RandomizationParameter &parameter) {B::Randomize(rng, parameter, ms_fixedRing);}</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="comment"></span></div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment"> ///</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment"></span> <span class="keywordtype">void</span> Negate() {B::Negate(ms_fixedRing);}</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordtype">void</span> swap(ThisType &t) {B::swap(t);}<span class="comment"></span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> /// \name UNARY OPERATORS</span></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment"></span><span class="comment"> ///</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment"></span> <span class="keywordtype">bool</span> operator!()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <a class="code" href="class_polynomial_over_fixed_ring.html#a5e659b8a429b441a1ae1d6e544ebf189">CoefficientCount</a>()==0;}<span class="comment"></span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="comment"> ///</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment"></span> ThisType operator+()<span class="keyword"> const </span>{<span class="keywordflow">return</span> *<span class="keyword">this</span>;}<span class="comment"></span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment"> ///</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment"></span> ThisType operator-()<span class="keyword"> const </span>{<span class="keywordflow">return</span> ThisType(Inverse(ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment"> /// \name BINARY OPERATORS</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment"></span><span class="comment"> ///</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment"></span> <span class="keyword">friend</span> ThisType operator>>(ThisType a, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) {<span class="keywordflow">return</span> ThisType(a>>=n);}<span class="comment"></span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment"> ///</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"></span> <span class="keyword">friend</span> ThisType operator<<(ThisType a, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) {<span class="keywordflow">return</span> ThisType(a<<=n);}<span class="comment"></span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> /// \name OTHER ARITHMETIC FUNCTIONS</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment"></span><span class="comment"> ///</span></div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment"></span> ThisType MultiplicativeInverse()<span class="keyword"> const </span>{<span class="keywordflow">return</span> ThisType(B::MultiplicativeInverse(ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment"> ///</span></div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment"></span> <span class="keywordtype">bool</span> IsUnit()<span class="keyword"> const </span>{<span class="keywordflow">return</span> B::IsUnit(ms_fixedRing);}</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment"></span></div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment"> ///</span></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment"></span> ThisType Doubled()<span class="keyword"> const </span>{<span class="keywordflow">return</span> ThisType(B::Doubled(ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment"> ///</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment"></span> ThisType Squared()<span class="keyword"> const </span>{<span class="keywordflow">return</span> ThisType(B::Squared(ms_fixedRing));}</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  CoefficientType EvaluateAt(<span class="keyword">const</span> CoefficientType &x)<span class="keyword"> const </span>{<span class="keywordflow">return</span> B::EvaluateAt(x, ms_fixedRing);}</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment"></span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment"> /// calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))</span></div><div class="line"><a name="l00287"></a><span class="lineno"><a class="line" href="class_polynomial_over_fixed_ring.html#ace18f8c67eb033dd6534b7ed6e7281b2"> 287</a></span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_over_fixed_ring.html#ace18f8c67eb033dd6534b7ed6e7281b2">Divide</a>(<a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a> &r, <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a> &q, <span class="keyword">const</span> <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a> &d)</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  {<a class="code" href="class_polynomial_over.html#aaa1a0b9d2470af2a01ae1c01d743b042">B::Divide</a>(r, q, a, d, ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment"></span><span class="comment"></span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment"> /// \name INPUT/OUTPUT</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment"></span><span class="comment"> //@{</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment"></span><span class="comment"> ///</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment"></span> <span class="keyword">friend</span> std::istream& operator>>(std::istream& in, ThisType &a)</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  {<span class="keywordflow">return</span> a.Input(in, ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment"> ///</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment"></span> <span class="keyword">friend</span> std::ostream& operator<<(std::ostream& out, <span class="keyword">const</span> ThisType &a)</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  {<span class="keywordflow">return</span> a.Output(out, ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"> //@}</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"></span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="keyword">private</span>:</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keyword">struct </span>NewOnePolynomial</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  {</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  ThisType * operator()()<span class="keyword"> const</span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keywordflow">return</span> <span class="keyword">new</span> ThisType(ms_fixedRing.MultiplicativeIdentity());</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  }</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  };</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keyword">static</span> <span class="keyword">const</span> Ring ms_fixedRing;</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> };</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment"></span></div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment">/// Ring of polynomials over another ring</span></div><div class="line"><a name="l00314"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html"> 314</a></span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">class </span><a class="code" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a><PolynomialOver<T> ></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> {</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keyword">typedef</span> T CoefficientRing;</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keyword">typedef</span> <a class="code" href="class_polynomial_over.html">PolynomialOver<T></a> <a class="code" href="class_polynomial_over.html">Element</a>;</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Element::CoefficientType CoefficientType;</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">Element::RandomizationParameter</a> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a>;</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> </div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>(<span class="keyword">const</span> CoefficientRing &ring) : m_ring(ring) {}</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> </div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <a class="code" href="class_polynomial_over.html">Element</a> RandomElement(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> <a class="code" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a> &parameter)</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  {<span class="keywordflow">return</span> <a class="code" href="class_polynomial_over.html">Element</a>(rng, parameter, m_ring);}</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span> </div><div class="line"><a name="l00327"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a9874b8b2aaee21b9c4f75a9372151489"> 327</a></span>  <span class="keywordtype">bool</span> <a class="code" href="class_ring_of_polynomials_over.html#a9874b8b2aaee21b9c4f75a9372151489">Equal</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> a.Equals(b, m_ring);}</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span> </div><div class="line"><a name="l00330"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a458ef6812fccb23fa063d9a15d27a67b"> 330</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a458ef6812fccb23fa063d9a15d27a67b">Identity</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = m_ring.Identity();}</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span> </div><div class="line"><a name="l00333"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a3ff8fa662fa5f4f6b850e9dc16958822"> 333</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a3ff8fa662fa5f4f6b850e9dc16958822">Add</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Plus(b, m_ring);}</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div><div class="line"><a name="l00336"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a6f6d9905144ff7e38b0f68401207d652"> 336</a></span>  <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a6f6d9905144ff7e38b0f68401207d652">Accumulate</a>(<a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="keyword"> </span>{a.Accumulate(b, m_ring); <span class="keywordflow">return</span> a;}</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div><div class="line"><a name="l00339"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#aa807d70d825213c7296b639dac60123b"> 339</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#aa807d70d825213c7296b639dac60123b">Inverse</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Inverse(m_ring);}</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div><div class="line"><a name="l00342"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#acf0bf71815e9b6d1a9caac9654a5c227"> 342</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#acf0bf71815e9b6d1a9caac9654a5c227">Subtract</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Minus(b, m_ring);}</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div><div class="line"><a name="l00345"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a3b71ffe9c999063225fa9baae5bbccda"> 345</a></span>  <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a3b71ffe9c999063225fa9baae5bbccda">Reduce</a>(<a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> a.Reduce(b, m_ring);}</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div><div class="line"><a name="l00348"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a8671a526a886b19474e5f47889bc404f"> 348</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a8671a526a886b19474e5f47889bc404f">Double</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Doubled(m_ring);}</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span> </div><div class="line"><a name="l00351"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#ab9713800e8ff192ab7f4c232b44cf31c"> 351</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#ab9713800e8ff192ab7f4c232b44cf31c">MultiplicativeIdentity</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = m_ring.MultiplicativeIdentity();}</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span> </div><div class="line"><a name="l00354"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a37731e8b8eecc4dac0b782443387dc95"> 354</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a37731e8b8eecc4dac0b782443387dc95">Multiply</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Times(b, m_ring);}</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div><div class="line"><a name="l00357"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a81b2df6ff2a50c000a9cc7dccd37ba5e"> 357</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a81b2df6ff2a50c000a9cc7dccd37ba5e">Square</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Squared(m_ring);}</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span> </div><div class="line"><a name="l00360"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a902a6f8e12158a1b2a8f18565463e5ce"> 360</a></span>  <span class="keywordtype">bool</span> <a class="code" href="class_ring_of_polynomials_over.html#a902a6f8e12158a1b2a8f18565463e5ce">IsUnit</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> a.IsUnit(m_ring);}</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span> </div><div class="line"><a name="l00363"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a75a3ae02cf9e1690dbc87be7e97f0248"> 363</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a75a3ae02cf9e1690dbc87be7e97f0248">MultiplicativeInverse</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.MultiplicativeInverse(m_ring);}</div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span> </div><div class="line"><a name="l00366"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a689e7df1b7183b782d8c78dba07760b7"> 366</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a689e7df1b7183b782d8c78dba07760b7">Divide</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.DividedBy(b, m_ring);}</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> </div><div class="line"><a name="l00369"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a8178e2835b054e1a2b57fa54568a552e"> 369</a></span>  <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a>& <a class="code" href="class_ring_of_polynomials_over.html#a8178e2835b054e1a2b57fa54568a552e">Mod</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> this->result = a.Modulo(b, m_ring);}</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span> </div><div class="line"><a name="l00372"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over.html#a333d8b90b9f7e5ca48056384136af1ca"> 372</a></span>  <span class="keywordtype">void</span> <a class="code" href="class_ring_of_polynomials_over.html#a333d8b90b9f7e5ca48056384136af1ca">DivisionAlgorithm</a>(<a class="code" href="class_polynomial_over.html">Element</a> &r, <a class="code" href="class_polynomial_over.html">Element</a> &q, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">Element</a> &d)<span class="keyword"> const</span></div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="keyword"> </span>{<a class="code" href="class_polynomial_over.html#aaa1a0b9d2470af2a01ae1c01d743b042">Element::Divide</a>(r, q, a, d, m_ring);}</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div><div class="line"><a name="l00375"></a><span class="lineno"><a class="line" href="class_ring_of_polynomials_over_1_1_interpolation_failed.html"> 375</a></span>  <span class="keyword">class </span><a class="code" href="class_ring_of_polynomials_over_1_1_interpolation_failed.html">InterpolationFailed</a> : <span class="keyword">public</span> <a class="code" href="class_exception.html">Exception</a></div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  {</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <a class="code" href="class_ring_of_polynomials_over_1_1_interpolation_failed.html">InterpolationFailed</a>() : <a class="code" href="class_exception.html#a30847048a4b7c9a7aae5e6178964dcfb">Exception</a>(<a class="code" href="class_exception.html#a8e53909d979479380e0274807c074c0aa27d9ee7704100a88e4ae4adcc4072015">OTHER_ERROR</a>, <span class="stringliteral">"RingOfPolynomialsOver<T>: interpolation failed"</span>) {}</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  };</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span> </div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <a class="code" href="class_polynomial_over.html">Element</a> Interpolate(<span class="keyword">const</span> CoefficientType x[], <span class="keyword">const</span> CoefficientType y[], <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) <span class="keyword">const</span>;</div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span> </div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="comment">// a faster version of Interpolate(x, y, n).EvaluateAt(position)</span></div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  CoefficientType InterpolateAt(<span class="keyword">const</span> CoefficientType &position, <span class="keyword">const</span> CoefficientType x[], <span class="keyword">const</span> CoefficientType y[], <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) <span class="keyword">const</span>;</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="comment">/*</span></div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="comment"> void PrepareBulkInterpolation(CoefficientType *w, const CoefficientType x[], unsigned int n) const;</span></div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="comment"> void PrepareBulkInterpolationAt(CoefficientType *v, const CoefficientType &position, const CoefficientType x[], const CoefficientType w[], unsigned int n) const;</span></div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="comment"> CoefficientType BulkInterpolateAt(const CoefficientType y[], const CoefficientType v[], unsigned int n) const;</span></div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="comment">*/</span></div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="keyword">protected</span>:</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="keywordtype">void</span> CalculateAlpha(std::vector<CoefficientType> &alpha, <span class="keyword">const</span> CoefficientType x[], <span class="keyword">const</span> CoefficientType y[], <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) <span class="keyword">const</span>;</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span> </div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  CoefficientRing m_ring;</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span> };</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span> </div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="keyword">template</span> <<span class="keyword">class</span> Ring, <span class="keyword">class</span> Element></div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="keywordtype">void</span> PrepareBulkPolynomialInterpolation(<span class="keyword">const</span> Ring &ring, Element *w, <span class="keyword">const</span> Element x[], <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n);</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="keyword">template</span> <<span class="keyword">class</span> Ring, <span class="keyword">class</span> Element></div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="keywordtype">void</span> PrepareBulkPolynomialInterpolationAt(<span class="keyword">const</span> Ring &ring, Element *v, <span class="keyword">const</span> Element &position, <span class="keyword">const</span> Element x[], <span class="keyword">const</span> Element w[], <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n);</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="keyword">template</span> <<span class="keyword">class</span> Ring, <span class="keyword">class</span> Element></div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span> Element BulkPolynomialInterpolateAt(<span class="keyword">const</span> Ring &ring, <span class="keyword">const</span> Element y[], <span class="keyword">const</span> Element v[], <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n);</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment"></span></div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment">///</span></div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="asn_8h.html#ab065716a8772762f9e717705901aa924">operator==</a>(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  {<span class="keywordflow">return</span> a.Equals(b, a.ms_fixedRing);}<span class="comment"></span></div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment">///</span></div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="asn_8h.html#acb32287cdfa32ecdb0a048aceb283f7d">operator!=</a>(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  {<span class="keywordflow">return</span> !(a==b);}</div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment"></span></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment">///</span></div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator> (<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  {<span class="keywordflow">return</span> a.Degree() > b.Degree();}<span class="comment"></span></div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment">///</span></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#ab2c528cac1c470a5c25eb7afe6641b89">operator>=</a>(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  {<span class="keywordflow">return</span> a.Degree() >= b.Degree();}<span class="comment"></span></div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment">///</span></div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator< (const CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  {<span class="keywordflow">return</span> a.Degree() < b.Degree();}<span class="comment"></span></div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment">///</span></div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator<=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  {<span class="keywordflow">return</span> a.Degree() <= b.Degree();}</div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment"></span></div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span> <span class="comment">///</span></div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="keyword">inline</span> CryptoPP::PolynomialOverFixedRing<T, instance> <a class="code" href="asn_8h.html#a42ed33fff849360e31da99b7138dac49">operator+</a>(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  {<span class="keywordflow">return</span> CryptoPP::PolynomialOverFixedRing<T, instance>(a.Plus(b, a.ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="comment">///</span></div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="keyword">inline</span> CryptoPP::PolynomialOverFixedRing<T, instance> <a class="code" href="integer_8h.html#a608b1434db86edad946fd1c20737c05e">operator-</a>(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  {<span class="keywordflow">return</span> CryptoPP::PolynomialOverFixedRing<T, instance>(a.Minus(b, a.ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment">///</span></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="keyword">inline</span> CryptoPP::PolynomialOverFixedRing<T, instance> <a class="code" href="integer_8h.html#a83bd503d3921cad11bc71203754c2bef">operator*</a>(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  {<span class="keywordflow">return</span> CryptoPP::PolynomialOverFixedRing<T, instance>(a.Times(b, a.ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="comment">///</span></div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="keyword">inline</span> CryptoPP::PolynomialOverFixedRing<T, instance> operator/(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  {<span class="keywordflow">return</span> CryptoPP::PolynomialOverFixedRing<T, instance>(a.DividedBy(b, a.ms_fixedRing));}<span class="comment"></span></div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="comment">///</span></div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance></div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="keyword">inline</span> CryptoPP::PolynomialOverFixedRing<T, instance> operator%(<span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &a, <span class="keyword">const</span> CryptoPP::PolynomialOverFixedRing<T, instance> &b)</div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  {<span class="keywordflow">return</span> CryptoPP::PolynomialOverFixedRing<T, instance>(a.Modulo(b, a.ms_fixedRing));}</div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span> </div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span> NAMESPACE_END</div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span> </div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span> NAMESPACE_BEGIN(<a class="code" href="namespacestd.html">std</a>)</div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="keyword">template</span><<span class="keyword">class</span> T> <span class="keyword">inline</span> <span class="keywordtype">void</span> swap(CryptoPP::PolynomialOver<T> &a, CryptoPP::PolynomialOver<T> &b)</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span> {</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  a.swap(b);</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span> }</div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="keyword">template</span><<span class="keyword">class</span> T, <span class="keywordtype">int</span> i> <span class="keyword">inline</span> <span class="keywordtype">void</span> swap(CryptoPP::PolynomialOverFixedRing<T,i> &a, CryptoPP::PolynomialOverFixedRing<T,i> &b)</div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span> {</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  a.swap(b);</div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span> }</div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span> NAMESPACE_END</div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span> </div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span> <span class="preprocessor">#endif</span></div><div class="ttc" id="class_exception_html"><div class="ttname"><a href="class_exception.html">Exception</a></div><div class="ttdoc">Base class for all exceptions thrown by the library. </div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l00155">cryptlib.h:155</a></div></div>
<div class="ttc" id="gf2n_8h_html_ab2c528cac1c470a5c25eb7afe6641b89"><div class="ttname"><a href="gf2n_8h.html#ab2c528cac1c470a5c25eb7afe6641b89">operator>=</a></div><div class="ttdeci">bool operator>=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)</div><div class="ttdoc">compares degree </div><div class="ttdef"><b>Definition:</b> <a href="gf2n_8h_source.html#l00263">gf2n.h:263</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_af1e2af7d588db8db85d7f55df99c59eb"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#af1e2af7d588db8db85d7f55df99c59eb">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(Iterator first, Iterator last)</div><div class="ttdoc">construct polynomial with specified coefficients, starting from coefficient of x^0 ...</div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00188">polynomi.h:188</a></div></div>
<div class="ttc" id="class_polynomial_over_html_a528a5722512381f2d7cb3b705bcbe8bb"><div class="ttname"><a href="class_polynomial_over.html#a528a5722512381f2d7cb3b705bcbe8bb">PolynomialOver::Degree</a></div><div class="ttdeci">int Degree(const Ring &ring) const</div><div class="ttdoc">the zero polynomial will return a degree of -1 </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00091">polynomi.h:91</a></div></div>
<div class="ttc" id="integer_8h_html_a83bd503d3921cad11bc71203754c2bef"><div class="ttname"><a href="integer_8h.html#a83bd503d3921cad11bc71203754c2bef">operator*</a></div><div class="ttdeci">inline ::Integer operator*(const ::Integer &a, const ::Integer &b)</div><div class="ttdoc">Multiplication. </div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00750">integer.h:750</a></div></div>
<div class="ttc" id="class_polynomial_over_1_1_randomization_parameter_html"><div class="ttname"><a href="class_polynomial_over_1_1_randomization_parameter.html">PolynomialOver::RandomizationParameter</a></div><div class="ttdoc">specify the distribution for randomization functions </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00034">polynomi.h:34</a></div></div>
<div class="ttc" id="class_polynomial_over_html_aac4ab97afda49a151fc9dbd8eaf9aa16"><div class="ttname"><a href="class_polynomial_over.html#aac4ab97afda49a151fc9dbd8eaf9aa16">PolynomialOver::SetCoefficient</a></div><div class="ttdeci">void SetCoefficient(unsigned int i, const CoefficientType &value, const Ring &ring)</div><div class="ttdoc">set the coefficient for x^i to value </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8cpp_source.html#l00182">polynomi.cpp:182</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a6f6d9905144ff7e38b0f68401207d652"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a6f6d9905144ff7e38b0f68401207d652">RingOfPolynomialsOver::Accumulate</a></div><div class="ttdeci">Element & Accumulate(Element &a, const Element &b) const</div><div class="ttdoc">TODO. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00336">polynomi.h:336</a></div></div>
<div class="ttc" id="class_polynomial_over_html_a7a4e4504a189d1594961879fc10cba43"><div class="ttname"><a href="class_polynomial_over.html#a7a4e4504a189d1594961879fc10cba43">PolynomialOver::PolynomialOver</a></div><div class="ttdeci">PolynomialOver(Iterator begin, Iterator end)</div><div class="ttdoc">construct polynomial with specified coefficients, starting from coefficient of x^0 ...</div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00068">polynomi.h:68</a></div></div>
<div class="ttc" id="misc_8h_html"><div class="ttname"><a href="misc_8h.html">misc.h</a></div><div class="ttdoc">Utility functions for the Crypto++ library. </div></div>
<div class="ttc" id="class_polynomial_over_html_a393c8f0c973d431d7e04d3d3682b333d"><div class="ttname"><a href="class_polynomial_over.html#a393c8f0c973d431d7e04d3d3682b333d">PolynomialOver::PolynomialOver</a></div><div class="ttdeci">PolynomialOver(const PolynomialOver< Ring > &t)</div><div class="ttdoc">copy constructor </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00060">polynomi.h:60</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a38de0135bd58a61176cef61bc6397c47"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a38de0135bd58a61176cef61bc6397c47">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(const byte *encodedPoly, unsigned int byteCount)</div><div class="ttdoc">convert from big-endian byte array </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00195">polynomi.h:195</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a8e10a57bab595f53a2055bcfb03fb66e"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a8e10a57bab595f53a2055bcfb03fb66e">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(unsigned int count=0)</div><div class="ttdoc">creates the zero polynomial </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00177">polynomi.h:177</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a9874b8b2aaee21b9c4f75a9372151489"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a9874b8b2aaee21b9c4f75a9372151489">RingOfPolynomialsOver::Equal</a></div><div class="ttdeci">bool Equal(const Element &a, const Element &b) const</div><div class="ttdoc">Compare two elements for equality. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00327">polynomi.h:327</a></div></div>
<div class="ttc" id="class_exception_html_a30847048a4b7c9a7aae5e6178964dcfb"><div class="ttname"><a href="class_exception.html#a30847048a4b7c9a7aae5e6178964dcfb">Exception::Exception</a></div><div class="ttdeci">Exception(ErrorType errorType, const std::string &s)</div><div class="ttdoc">Construct a new Exception. </div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l00180">cryptlib.h:180</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_aebbb74586712f3f825c4fa4894fbf217"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#aebbb74586712f3f825c4fa4894fbf217">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(const char *str)</div><div class="ttdoc">convert from string </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00192">polynomi.h:192</a></div></div>
<div class="ttc" id="namespace_name_html_a87f7b89127f1053f118c879e865ab212"><div class="ttname"><a href="namespace_name.html#a87f7b89127f1053f118c879e865ab212">Name::Identity</a></div><div class="ttdeci">const char * Identity()</div><div class="ttdoc">ConstByteArrayParameter. </div><div class="ttdef"><b>Definition:</b> <a href="argnames_8h_source.html#l00094">argnames.h:94</a></div></div>
<div class="ttc" id="cryptlib_8h_html"><div class="ttname"><a href="cryptlib_8h.html">cryptlib.h</a></div><div class="ttdoc">Abstract base classes that provide a uniform interface to this library. </div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_ad63e985a7c37535ea710b7779ecfb3aa"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#ad63e985a7c37535ea710b7779ecfb3aa">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(const ThisType &t)</div><div class="ttdoc">copy constructor </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00180">polynomi.h:180</a></div></div>
<div class="ttc" id="class_abstract_euclidean_domain_html"><div class="ttname"><a href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a></div><div class="ttdoc">Abstract Euclidean domain. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8h_source.html#l00276">algebra.h:276</a></div></div>
<div class="ttc" id="class_exception_html_a8e53909d979479380e0274807c074c0aa27d9ee7704100a88e4ae4adcc4072015"><div class="ttname"><a href="class_exception.html#a8e53909d979479380e0274807c074c0aa27d9ee7704100a88e4ae4adcc4072015">Exception::OTHER_ERROR</a></div><div class="ttdoc">Some other error occurred not belonging to other categories. </div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l00174">cryptlib.h:174</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a8178e2835b054e1a2b57fa54568a552e"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a8178e2835b054e1a2b57fa54568a552e">RingOfPolynomialsOver::Mod</a></div><div class="ttdeci">const Element & Mod(const Element &a, const Element &b) const</div><div class="ttdoc">Performs a modular reduction in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00369">polynomi.h:369</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_aeea00158952013a08cd97d1a416fa5a4"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#aeea00158952013a08cd97d1a416fa5a4">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(const byte *BEREncodedPoly)</div><div class="ttdoc">convert from Basic Encoding Rules encoded byte array </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00198">polynomi.h:198</a></div></div>
<div class="ttc" id="namespacestd_html"><div class="ttname"><a href="namespacestd.html">std</a></div><div class="ttdoc">STL namespace. </div></div>
<div class="ttc" id="class_random_number_generator_html"><div class="ttname"><a href="class_random_number_generator.html">RandomNumberGenerator</a></div><div class="ttdoc">Interface for random number generators. </div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l01330">cryptlib.h:1330</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_adbff44242557cef909c01a74d75d181e"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#adbff44242557cef909c01a74d75d181e">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(const CoefficientType &element)</div><div class="ttdoc">construct constant polynomial </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00185">polynomi.h:185</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_aa807d70d825213c7296b639dac60123b"><div class="ttname"><a href="class_ring_of_polynomials_over.html#aa807d70d825213c7296b639dac60123b">RingOfPolynomialsOver::Inverse</a></div><div class="ttdeci">const Element & Inverse(const Element &a) const</div><div class="ttdoc">Inverts the element in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00339">polynomi.h:339</a></div></div>
<div class="ttc" id="algebra_8h_html"><div class="ttname"><a href="algebra_8h.html">algebra.h</a></div><div class="ttdoc">Classes for performing mathematics over different fields. </div></div>
<div class="ttc" id="class_buffered_transformation_html"><div class="ttname"><a href="class_buffered_transformation.html">BufferedTransformation</a></div><div class="ttdoc">Interface for buffered transformations. </div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l01545">cryptlib.h:1545</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a81b2df6ff2a50c000a9cc7dccd37ba5e"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a81b2df6ff2a50c000a9cc7dccd37ba5e">RingOfPolynomialsOver::Square</a></div><div class="ttdeci">const Element & Square(const Element &a) const</div><div class="ttdoc">Square an element in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00357">polynomi.h:357</a></div></div>
<div class="ttc" id="class_polynomial_over_html"><div class="ttname"><a href="class_polynomial_over.html">PolynomialOver</a></div><div class="ttdoc">represents single-variable polynomials over arbitrary rings </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00021">polynomi.h:21</a></div></div>
<div class="ttc" id="class_polynomial_over_html_aef039d41b917e8297e14c050568a37a2"><div class="ttname"><a href="class_polynomial_over.html#aef039d41b917e8297e14c050568a37a2">PolynomialOver::PolynomialOver</a></div><div class="ttdeci">PolynomialOver(const char *str, const Ring &ring)</div><div class="ttdoc">convert from string </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00072">polynomi.h:72</a></div></div>
<div class="ttc" id="asn_8h_html_ab065716a8772762f9e717705901aa924"><div class="ttname"><a href="asn_8h.html#ab065716a8772762f9e717705901aa924">operator==</a></div><div class="ttdeci">bool operator==(const OID &lhs, const OID &rhs)</div><div class="ttdoc">Compare two OIDs for equality. </div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a8671a526a886b19474e5f47889bc404f"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a8671a526a886b19474e5f47889bc404f">RingOfPolynomialsOver::Double</a></div><div class="ttdeci">const Element & Double(const Element &a) const</div><div class="ttdoc">Doubles an element in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00348">polynomi.h:348</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html"><div class="ttname"><a href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a></div><div class="ttdoc">Ring of polynomials over another ring. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00314">polynomi.h:314</a></div></div>
<div class="ttc" id="secblock_8h_html"><div class="ttname"><a href="secblock_8h.html">secblock.h</a></div><div class="ttdoc">Classes and functions for secure memory allocations. </div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a37731e8b8eecc4dac0b782443387dc95"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a37731e8b8eecc4dac0b782443387dc95">RingOfPolynomialsOver::Multiply</a></div><div class="ttdeci">const Element & Multiply(const Element &a, const Element &b) const</div><div class="ttdoc">Multiplies elements in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00354">polynomi.h:354</a></div></div>
<div class="ttc" id="asn_8h_html_acb32287cdfa32ecdb0a048aceb283f7d"><div class="ttname"><a href="asn_8h.html#acb32287cdfa32ecdb0a048aceb283f7d">operator!=</a></div><div class="ttdeci">bool operator!=(const OID &lhs, const OID &rhs)</div><div class="ttdoc">Compare two OIDs for inequality. </div></div>
<div class="ttc" id="integer_8h_html_a608b1434db86edad946fd1c20737c05e"><div class="ttname"><a href="integer_8h.html#a608b1434db86edad946fd1c20737c05e">operator-</a></div><div class="ttdeci">inline ::Integer operator-(const ::Integer &a, const ::Integer &b)</div><div class="ttdoc">Subtraction. </div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00747">integer.h:747</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a3ff8fa662fa5f4f6b850e9dc16958822"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a3ff8fa662fa5f4f6b850e9dc16958822">RingOfPolynomialsOver::Add</a></div><div class="ttdeci">const Element & Add(const Element &a, const Element &b) const</div><div class="ttdoc">Adds elements in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00333">polynomi.h:333</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a5e659b8a429b441a1ae1d6e544ebf189"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a5e659b8a429b441a1ae1d6e544ebf189">PolynomialOverFixedRing::CoefficientCount</a></div><div class="ttdeci">unsigned int CoefficientCount() const</div><div class="ttdoc">degree + 1 </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00215">polynomi.h:215</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a458ef6812fccb23fa063d9a15d27a67b"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a458ef6812fccb23fa063d9a15d27a67b">RingOfPolynomialsOver::Identity</a></div><div class="ttdeci">const Element & Identity() const</div><div class="ttdoc">Provides the Identity element. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00330">polynomi.h:330</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a689e7df1b7183b782d8c78dba07760b7"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a689e7df1b7183b782d8c78dba07760b7">RingOfPolynomialsOver::Divide</a></div><div class="ttdeci">const Element & Divide(const Element &a, const Element &b) const</div><div class="ttdoc">Divides elements in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00366">polynomi.h:366</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a75a3ae02cf9e1690dbc87be7e97f0248"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a75a3ae02cf9e1690dbc87be7e97f0248">RingOfPolynomialsOver::MultiplicativeInverse</a></div><div class="ttdeci">const Element & MultiplicativeInverse(const Element &a) const</div><div class="ttdoc">Calculate the multiplicative inverse of an element in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00363">polynomi.h:363</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a70982605b8e8c3cc07c08438d5fbdefa"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a70982605b8e8c3cc07c08438d5fbdefa">PolynomialOverFixedRing::GetCoefficient</a></div><div class="ttdeci">CoefficientType GetCoefficient(unsigned int i) const</div><div class="ttdoc">return coefficient for x^i </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00217">polynomi.h:217</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html">PolynomialOverFixedRing</a></div><div class="ttdoc">Polynomials over a fixed ring. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00163">polynomi.h:163</a></div></div>
<div class="ttc" id="asn_8h_html_a42ed33fff849360e31da99b7138dac49"><div class="ttname"><a href="asn_8h.html#a42ed33fff849360e31da99b7138dac49">operator+</a></div><div class="ttdeci">OID operator+(const OID &lhs, unsigned long rhs)</div><div class="ttdoc">Append a value to an OID. </div></div>
<div class="ttc" id="class_polynomial_over_html_a9a479be6ed6b88ac4f74a1c0ca72849c"><div class="ttname"><a href="class_polynomial_over.html#a9a479be6ed6b88ac4f74a1c0ca72849c">PolynomialOver::PolynomialOver</a></div><div class="ttdeci">PolynomialOver()</div><div class="ttdoc">creates the zero polynomial </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00053">polynomi.h:53</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a7c797943b4cb9e864328d6d02dcb2444"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a7c797943b4cb9e864328d6d02dcb2444">PolynomialOverFixedRing::SetCoefficient</a></div><div class="ttdeci">void SetCoefficient(unsigned int i, const CoefficientType &value)</div><div class="ttdoc">set the coefficient for x^i to value </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00243">polynomi.h:243</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_1_1_interpolation_failed_html"><div class="ttname"><a href="class_ring_of_polynomials_over_1_1_interpolation_failed.html">RingOfPolynomialsOver::InterpolationFailed</a></div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00375">polynomi.h:375</a></div></div>
<div class="ttc" id="class_polynomial_over_html_a33a595d1ea6d44eef7ac3636c195a869"><div class="ttname"><a href="class_polynomial_over.html#a33a595d1ea6d44eef7ac3636c195a869">PolynomialOver::PolynomialOver</a></div><div class="ttdeci">PolynomialOver(RandomNumberGenerator &rng, const RandomizationParameter &parameter, const Ring &ring)</div><div class="ttdoc">create a random PolynomialOver<T> </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00084">polynomi.h:84</a></div></div>
<div class="ttc" id="class_polynomial_over_html_af3f01459e456891391d9650e4b82b8b0"><div class="ttname"><a href="class_polynomial_over.html#af3f01459e456891391d9650e4b82b8b0">PolynomialOver::PolynomialOver</a></div><div class="ttdeci">PolynomialOver(const CoefficientType &element)</div><div class="ttdoc">construct constant polynomial </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00064">polynomi.h:64</a></div></div>
<div class="ttc" id="class_polynomial_over_html_aaa1a0b9d2470af2a01ae1c01d743b042"><div class="ttname"><a href="class_polynomial_over.html#aaa1a0b9d2470af2a01ae1c01d743b042">PolynomialOver::Divide</a></div><div class="ttdeci">static void Divide(PolynomialOver< Ring > &r, PolynomialOver< Ring > &q, const PolynomialOver< Ring > &a, const PolynomialOver< Ring > &d, const Ring &ring)</div><div class="ttdoc">calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d) </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8cpp_source.html#l00430">polynomi.cpp:430</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a902a6f8e12158a1b2a8f18565463e5ce"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a902a6f8e12158a1b2a8f18565463e5ce">RingOfPolynomialsOver::IsUnit</a></div><div class="ttdeci">bool IsUnit(const Element &a) const</div><div class="ttdoc">Determines whether an element is a unit in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00360">polynomi.h:360</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_ace18f8c67eb033dd6534b7ed6e7281b2"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#ace18f8c67eb033dd6534b7ed6e7281b2">PolynomialOverFixedRing::Divide</a></div><div class="ttdeci">static void Divide(ThisType &r, ThisType &q, const ThisType &a, const ThisType &d)</div><div class="ttdoc">calculate r and q such that (a == d*q + r) && (0 <= r < abs(d)) </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00287">polynomi.h:287</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a333d8b90b9f7e5ca48056384136af1ca"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a333d8b90b9f7e5ca48056384136af1ca">RingOfPolynomialsOver::DivisionAlgorithm</a></div><div class="ttdeci">void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const</div><div class="ttdoc">Performs the division algorithm on two elements in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00372">polynomi.h:372</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_ac24e06202bb7b81088948d6aa2c9d54f"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#ac24e06202bb7b81088948d6aa2c9d54f">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(BufferedTransformation &bt)</div><div class="ttdoc">convert from BER encoded byte array stored in a BufferedTransformation object </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00201">polynomi.h:201</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a5ff7d2a9165c23fba47f6cb2898f5e4b"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a5ff7d2a9165c23fba47f6cb2898f5e4b">PolynomialOverFixedRing::operator[]</a></div><div class="ttdeci">CoefficientType operator[](unsigned int i) const</div><div class="ttdoc">return coefficient for x^i </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00219">polynomi.h:219</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_adc7375389ed8759970361a61cce61ea0"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#adc7375389ed8759970361a61cce61ea0">PolynomialOverFixedRing::Degree</a></div><div class="ttdeci">int Degree() const</div><div class="ttdoc">the zero polynomial will return a degree of -1 </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00213">polynomi.h:213</a></div></div>
<div class="ttc" id="namespace_crypto_p_p_html"><div class="ttname"><a href="namespace_crypto_p_p.html">CryptoPP</a></div><div class="ttdoc">Crypto++ library namespace. </div></div>
<div class="ttc" id="class_polynomial_over_html_a6feeb70252350258e2439f8a864d563f"><div class="ttname"><a href="class_polynomial_over.html#a6feeb70252350258e2439f8a864d563f">PolynomialOver::GetCoefficient</a></div><div class="ttdeci">CoefficientType GetCoefficient(unsigned int i, const Ring &ring) const</div><div class="ttdoc">return coefficient for x^i </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8cpp_source.html#l00086">polynomi.cpp:86</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_ab9713800e8ff192ab7f4c232b44cf31c"><div class="ttname"><a href="class_ring_of_polynomials_over.html#ab9713800e8ff192ab7f4c232b44cf31c">RingOfPolynomialsOver::MultiplicativeIdentity</a></div><div class="ttdeci">const Element & MultiplicativeIdentity() const</div><div class="ttdoc">Retrieves the multiplicative identity. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00351">polynomi.h:351</a></div></div>
<div class="ttc" id="class_polynomial_over_1_1_divide_by_zero_html"><div class="ttname"><a href="class_polynomial_over_1_1_divide_by_zero.html">PolynomialOver::DivideByZero</a></div><div class="ttdoc">division by zero exception </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00027">polynomi.h:27</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_acf0bf71815e9b6d1a9caac9654a5c227"><div class="ttname"><a href="class_ring_of_polynomials_over.html#acf0bf71815e9b6d1a9caac9654a5c227">RingOfPolynomialsOver::Subtract</a></div><div class="ttdeci">const Element & Subtract(const Element &a, const Element &b) const</div><div class="ttdoc">Subtracts elements in the group. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00342">polynomi.h:342</a></div></div>
<div class="ttc" id="class_ring_of_polynomials_over_html_a3b71ffe9c999063225fa9baae5bbccda"><div class="ttname"><a href="class_ring_of_polynomials_over.html#a3b71ffe9c999063225fa9baae5bbccda">RingOfPolynomialsOver::Reduce</a></div><div class="ttdeci">Element & Reduce(Element &a, const Element &b) const</div><div class="ttdoc">Reduces an element in the congruence class. </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00345">polynomi.h:345</a></div></div>
<div class="ttc" id="class_polynomial_over_fixed_ring_html_a49d91088bbec643b9e5b8db7c8c1e89b"><div class="ttname"><a href="class_polynomial_over_fixed_ring.html#a49d91088bbec643b9e5b8db7c8c1e89b">PolynomialOverFixedRing::PolynomialOverFixedRing</a></div><div class="ttdeci">PolynomialOverFixedRing(RandomNumberGenerator &rng, const RandomizationParameter &parameter)</div><div class="ttdoc">create a random PolynomialOverFixedRing </div><div class="ttdef"><b>Definition:</b> <a href="polynomi_8h_source.html#l00204">polynomi.h:204</a></div></div>
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