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<title>Crypto++: RingOfPolynomialsOver< T > Class Template Reference</title>
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<div id="projectname">Crypto++
 <span id="projectnumber">7.0</span>
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<div id="projectbrief">Free C++ class library of cryptographic schemes</div>
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<div class="title">RingOfPolynomialsOver< T > Class Template Reference</div> </div>
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<p>Ring of polynomials over another ring.
<a href="class_ring_of_polynomials_over.html#details">More...</a></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for RingOfPolynomialsOver< T >:</div>
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<img src="class_ring_of_polynomials_over.png" usemap="#RingOfPolynomialsOver_3C_20T_20_3E_map" alt=""/>
<map id="RingOfPolynomialsOver_3C_20T_20_3E_map" name="RingOfPolynomialsOver_3C_20T_20_3E_map">
<area href="class_abstract_euclidean_domain.html" alt="AbstractEuclideanDomain< PolynomialOver< T > >" shape="rect" coords="0,112,302,136"/>
<area href="class_abstract_ring.html" alt="AbstractRing< PolynomialOver< T > >" shape="rect" coords="0,56,302,80"/>
<area href="class_abstract_group.html" alt="AbstractGroup< PolynomialOver< T > >" shape="rect" coords="0,0,302,24"/>
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Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over_1_1_interpolation_failed.html">InterpolationFailed</a></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
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typedef T </td><td class="memItemRight" valign="bottom"><b>CoefficientRing</b></td></tr>
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<tr class="memitem:a5a9d435f7f8d004e1da6d46f16717704"><td class="memItemLeft" align="right" valign="top"><a id="a5a9d435f7f8d004e1da6d46f16717704"></a>
typedef <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< T > </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:a5a9d435f7f8d004e1da6d46f16717704"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad481c398f3ffa1af06ffa30d71c68659"><td class="memItemLeft" align="right" valign="top"><a id="ad481c398f3ffa1af06ffa30d71c68659"></a>
typedef Element::CoefficientType </td><td class="memItemRight" valign="bottom"><b>CoefficientType</b></td></tr>
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typedef <a class="el" href="class_polynomial_over_1_1_randomization_parameter.html">Element::RandomizationParameter</a> </td><td class="memItemRight" valign="bottom"><b>RandomizationParameter</b></td></tr>
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<tr class="inherit_header pub_types_class_abstract_euclidean_domain"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_abstract_euclidean_domain')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain< PolynomialOver< T > ></a></td></tr>
<tr class="memitem:a02903b4c46289ca070e2e7668e532bdc inherit pub_types_class_abstract_euclidean_domain"><td class="memItemLeft" align="right" valign="top"><a id="a02903b4c46289ca070e2e7668e532bdc"></a>
typedef <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< T > </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:a02903b4c46289ca070e2e7668e532bdc inherit pub_types_class_abstract_euclidean_domain"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_types_class_abstract_ring"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_abstract_ring')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_abstract_ring.html">AbstractRing< PolynomialOver< T > ></a></td></tr>
<tr class="memitem:acd93e8ce4e2897173310c68fcb60f3e9 inherit pub_types_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"><a id="acd93e8ce4e2897173310c68fcb60f3e9"></a>
typedef <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< T > </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:acd93e8ce4e2897173310c68fcb60f3e9 inherit pub_types_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_types_class_abstract_group"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_abstract_group')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_abstract_group.html">AbstractGroup< PolynomialOver< T > ></a></td></tr>
<tr class="memitem:a4a2b3308fb5c13f70fcc5746be52ba7b inherit pub_types_class_abstract_group"><td class="memItemLeft" align="right" valign="top"><a id="a4a2b3308fb5c13f70fcc5746be52ba7b"></a>
typedef <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< T > </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:a4a2b3308fb5c13f70fcc5746be52ba7b inherit pub_types_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ab8698eb9f89d728c0986eea4d4810728"><td class="memItemLeft" align="right" valign="top"><a id="ab8698eb9f89d728c0986eea4d4810728"></a>
 </td><td class="memItemRight" valign="bottom"><b>RingOfPolynomialsOver</b> (const CoefficientRing &ring)</td></tr>
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<tr class="memitem:ae91186ec32cf80f2ae1b180e21563edf"><td class="memItemLeft" align="right" valign="top"><a id="ae91186ec32cf80f2ae1b180e21563edf"></a>
<a class="el" href="class_polynomial_over.html">Element</a> </td><td class="memItemRight" valign="bottom"><b>RandomElement</b> (<a class="el" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, const <a class="el" href="class_polynomial_over_1_1_randomization_parameter.html">RandomizationParameter</a> &parameter)</td></tr>
<tr class="separator:ae91186ec32cf80f2ae1b180e21563edf"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9874b8b2aaee21b9c4f75a9372151489"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a9874b8b2aaee21b9c4f75a9372151489">Equal</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a9874b8b2aaee21b9c4f75a9372151489"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="#a9874b8b2aaee21b9c4f75a9372151489">More...</a><br /></td></tr>
<tr class="separator:a9874b8b2aaee21b9c4f75a9372151489"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a458ef6812fccb23fa063d9a15d27a67b"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a458ef6812fccb23fa063d9a15d27a67b">Identity</a> () const</td></tr>
<tr class="memdesc:a458ef6812fccb23fa063d9a15d27a67b"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="#a458ef6812fccb23fa063d9a15d27a67b">More...</a><br /></td></tr>
<tr class="separator:a458ef6812fccb23fa063d9a15d27a67b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a3ff8fa662fa5f4f6b850e9dc16958822"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a3ff8fa662fa5f4f6b850e9dc16958822">Add</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a3ff8fa662fa5f4f6b850e9dc16958822"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="#a3ff8fa662fa5f4f6b850e9dc16958822">More...</a><br /></td></tr>
<tr class="separator:a3ff8fa662fa5f4f6b850e9dc16958822"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6f6d9905144ff7e38b0f68401207d652"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a6f6d9905144ff7e38b0f68401207d652">Accumulate</a> (<a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a6f6d9905144ff7e38b0f68401207d652"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="#a6f6d9905144ff7e38b0f68401207d652">More...</a><br /></td></tr>
<tr class="separator:a6f6d9905144ff7e38b0f68401207d652"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa807d70d825213c7296b639dac60123b"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#aa807d70d825213c7296b639dac60123b">Inverse</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a) const</td></tr>
<tr class="memdesc:aa807d70d825213c7296b639dac60123b"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="#aa807d70d825213c7296b639dac60123b">More...</a><br /></td></tr>
<tr class="separator:aa807d70d825213c7296b639dac60123b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acf0bf71815e9b6d1a9caac9654a5c227"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#acf0bf71815e9b6d1a9caac9654a5c227">Subtract</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:acf0bf71815e9b6d1a9caac9654a5c227"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="#acf0bf71815e9b6d1a9caac9654a5c227">More...</a><br /></td></tr>
<tr class="separator:acf0bf71815e9b6d1a9caac9654a5c227"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a3b71ffe9c999063225fa9baae5bbccda"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a3b71ffe9c999063225fa9baae5bbccda">Reduce</a> (<a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a3b71ffe9c999063225fa9baae5bbccda"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="#a3b71ffe9c999063225fa9baae5bbccda">More...</a><br /></td></tr>
<tr class="separator:a3b71ffe9c999063225fa9baae5bbccda"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8671a526a886b19474e5f47889bc404f"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a8671a526a886b19474e5f47889bc404f">Double</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a8671a526a886b19474e5f47889bc404f"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="#a8671a526a886b19474e5f47889bc404f">More...</a><br /></td></tr>
<tr class="separator:a8671a526a886b19474e5f47889bc404f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab9713800e8ff192ab7f4c232b44cf31c"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#ab9713800e8ff192ab7f4c232b44cf31c">MultiplicativeIdentity</a> () const</td></tr>
<tr class="memdesc:ab9713800e8ff192ab7f4c232b44cf31c"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="#ab9713800e8ff192ab7f4c232b44cf31c">More...</a><br /></td></tr>
<tr class="separator:ab9713800e8ff192ab7f4c232b44cf31c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a37731e8b8eecc4dac0b782443387dc95"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a37731e8b8eecc4dac0b782443387dc95">Multiply</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a37731e8b8eecc4dac0b782443387dc95"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="#a37731e8b8eecc4dac0b782443387dc95">More...</a><br /></td></tr>
<tr class="separator:a37731e8b8eecc4dac0b782443387dc95"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a81b2df6ff2a50c000a9cc7dccd37ba5e"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a81b2df6ff2a50c000a9cc7dccd37ba5e">Square</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a81b2df6ff2a50c000a9cc7dccd37ba5e"><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="class_square.html" title="Square block cipher. ">Square</a> an element in the group. <a href="#a81b2df6ff2a50c000a9cc7dccd37ba5e">More...</a><br /></td></tr>
<tr class="separator:a81b2df6ff2a50c000a9cc7dccd37ba5e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a902a6f8e12158a1b2a8f18565463e5ce"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a902a6f8e12158a1b2a8f18565463e5ce">IsUnit</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a902a6f8e12158a1b2a8f18565463e5ce"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="#a902a6f8e12158a1b2a8f18565463e5ce">More...</a><br /></td></tr>
<tr class="separator:a902a6f8e12158a1b2a8f18565463e5ce"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a75a3ae02cf9e1690dbc87be7e97f0248"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a75a3ae02cf9e1690dbc87be7e97f0248">MultiplicativeInverse</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a75a3ae02cf9e1690dbc87be7e97f0248"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="#a75a3ae02cf9e1690dbc87be7e97f0248">More...</a><br /></td></tr>
<tr class="separator:a75a3ae02cf9e1690dbc87be7e97f0248"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a689e7df1b7183b782d8c78dba07760b7"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a689e7df1b7183b782d8c78dba07760b7">Divide</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a689e7df1b7183b782d8c78dba07760b7"><td class="mdescLeft"> </td><td class="mdescRight">Divides elements in the group. <a href="#a689e7df1b7183b782d8c78dba07760b7">More...</a><br /></td></tr>
<tr class="separator:a689e7df1b7183b782d8c78dba07760b7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8178e2835b054e1a2b57fa54568a552e"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a8178e2835b054e1a2b57fa54568a552e">Mod</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a8178e2835b054e1a2b57fa54568a552e"><td class="mdescLeft"> </td><td class="mdescRight">Performs a modular reduction in the ring. <a href="#a8178e2835b054e1a2b57fa54568a552e">More...</a><br /></td></tr>
<tr class="separator:a8178e2835b054e1a2b57fa54568a552e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a333d8b90b9f7e5ca48056384136af1ca"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_ring_of_polynomials_over.html#a333d8b90b9f7e5ca48056384136af1ca">DivisionAlgorithm</a> (<a class="el" href="class_polynomial_over.html">Element</a> &r, <a class="el" href="class_polynomial_over.html">Element</a> &q, const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &d) const</td></tr>
<tr class="memdesc:a333d8b90b9f7e5ca48056384136af1ca"><td class="mdescLeft"> </td><td class="mdescRight">Performs the division algorithm on two elements in the ring. <a href="#a333d8b90b9f7e5ca48056384136af1ca">More...</a><br /></td></tr>
<tr class="separator:a333d8b90b9f7e5ca48056384136af1ca"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7302177675f05f94654f0b0d772b09db"><td class="memItemLeft" align="right" valign="top"><a id="a7302177675f05f94654f0b0d772b09db"></a>
<a class="el" href="class_polynomial_over.html">Element</a> </td><td class="memItemRight" valign="bottom"><b>Interpolate</b> (const CoefficientType x[], const CoefficientType y[], unsigned int n) const</td></tr>
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<tr class="memitem:ad0bc9dc0c75782c7edad6c53432f8d7d"><td class="memItemLeft" align="right" valign="top"><a id="ad0bc9dc0c75782c7edad6c53432f8d7d"></a>
CoefficientType </td><td class="memItemRight" valign="bottom"><b>InterpolateAt</b> (const CoefficientType &position, const CoefficientType x[], const CoefficientType y[], unsigned int n) const</td></tr>
<tr class="separator:ad0bc9dc0c75782c7edad6c53432f8d7d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_abstract_euclidean_domain"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_abstract_euclidean_domain')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain< PolynomialOver< T > ></a></td></tr>
<tr class="memitem:a2044146d4eb49414e1f4f880a9858161 inherit pub_methods_class_abstract_euclidean_domain"><td class="memItemLeft" align="right" valign="top">virtual const <a class="el" href="class_polynomial_over.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_euclidean_domain.html#a2044146d4eb49414e1f4f880a9858161">Gcd</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_polynomial_over.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a2044146d4eb49414e1f4f880a9858161 inherit pub_methods_class_abstract_euclidean_domain"><td class="mdescLeft"> </td><td class="mdescRight">Calculates the greatest common denominator in the ring. <a href="class_abstract_euclidean_domain.html#a2044146d4eb49414e1f4f880a9858161">More...</a><br /></td></tr>
<tr class="separator:a2044146d4eb49414e1f4f880a9858161 inherit pub_methods_class_abstract_euclidean_domain"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_abstract_ring"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_abstract_ring')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_abstract_ring.html">AbstractRing< PolynomialOver< T > ></a></td></tr>
<tr class="memitem:ae55c525c1aa75bf898907bd6949e2b64 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"><a id="ae55c525c1aa75bf898907bd6949e2b64"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#ae55c525c1aa75bf898907bd6949e2b64">AbstractRing</a> ()</td></tr>
<tr class="memdesc:ae55c525c1aa75bf898907bd6949e2b64 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Construct an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <br /></td></tr>
<tr class="separator:ae55c525c1aa75bf898907bd6949e2b64 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acc8afd5ce95e32e45d3c30a710bf36dc inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#acc8afd5ce95e32e45d3c30a710bf36dc">AbstractRing</a> (const <a class="el" href="class_abstract_ring.html">AbstractRing</a> &source)</td></tr>
<tr class="memdesc:acc8afd5ce95e32e45d3c30a710bf36dc inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Copy construct an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <a href="class_abstract_ring.html#acc8afd5ce95e32e45d3c30a710bf36dc">More...</a><br /></td></tr>
<tr class="separator:acc8afd5ce95e32e45d3c30a710bf36dc inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a26709c02c869d09d756653ae1129f8a9 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_abstract_ring.html">AbstractRing</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a26709c02c869d09d756653ae1129f8a9">operator=</a> (const <a class="el" href="class_abstract_ring.html">AbstractRing</a> &source)</td></tr>
<tr class="memdesc:a26709c02c869d09d756653ae1129f8a9 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Assign an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <a href="class_abstract_ring.html#a26709c02c869d09d756653ae1129f8a9">More...</a><br /></td></tr>
<tr class="separator:a26709c02c869d09d756653ae1129f8a9 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0f011366054a4edb80be92f968083538 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_polynomial_over.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a0f011366054a4edb80be92f968083538">Exponentiate</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_integer.html">Integer</a> &e) const</td></tr>
<tr class="memdesc:a0f011366054a4edb80be92f968083538 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Raises a base to an exponent in the group. <a href="class_abstract_ring.html#a0f011366054a4edb80be92f968083538">More...</a><br /></td></tr>
<tr class="separator:a0f011366054a4edb80be92f968083538 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:adb4d33ac59a8f8bff1752b75809136e6 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_polynomial_over.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">CascadeExponentiate</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const <a class="el" href="class_polynomial_over.html">Element</a> &y, const <a class="el" href="class_integer.html">Integer</a> &e2) const</td></tr>
<tr class="memdesc:adb4d33ac59a8f8bff1752b75809136e6 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">More...</a><br /></td></tr>
<tr class="separator:adb4d33ac59a8f8bff1752b75809136e6 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a63530b69e7bfa78e5ee7b072cc798f0a inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">SimultaneousExponentiate</a> (<a class="el" href="class_polynomial_over.html">Element</a> *results, const <a class="el" href="class_polynomial_over.html">Element</a> &base, const <a class="el" href="class_integer.html">Integer</a> *exponents, unsigned int exponentsCount) const</td></tr>
<tr class="memdesc:a63530b69e7bfa78e5ee7b072cc798f0a inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Exponentiates a base to multiple exponents in the Ring. <a href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">More...</a><br /></td></tr>
<tr class="separator:a63530b69e7bfa78e5ee7b072cc798f0a inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae19ef788f5ce5192e5867666ef38717f inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const <a class="el" href="class_abstract_group.html">AbstractGroup</a>< <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< T > > & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#ae19ef788f5ce5192e5867666ef38717f">MultiplicativeGroup</a> () const</td></tr>
<tr class="memdesc:ae19ef788f5ce5192e5867666ef38717f inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative group. <a href="class_abstract_ring.html#ae19ef788f5ce5192e5867666ef38717f">More...</a><br /></td></tr>
<tr class="separator:ae19ef788f5ce5192e5867666ef38717f inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_abstract_group"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_abstract_group')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_abstract_group.html">AbstractGroup< PolynomialOver< T > ></a></td></tr>
<tr class="memitem:a257836994abefe25b80293f4c6b10f60 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a257836994abefe25b80293f4c6b10f60">InversionIsFast</a> () const</td></tr>
<tr class="memdesc:a257836994abefe25b80293f4c6b10f60 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Determine if inversion is fast. <a href="class_abstract_group.html#a257836994abefe25b80293f4c6b10f60">More...</a><br /></td></tr>
<tr class="separator:a257836994abefe25b80293f4c6b10f60 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac01536b91c4fa3d0e0f929917143595b inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_polynomial_over.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ac01536b91c4fa3d0e0f929917143595b">ScalarMultiply</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &a, const <a class="el" href="class_integer.html">Integer</a> &e) const</td></tr>
<tr class="memdesc:ac01536b91c4fa3d0e0f929917143595b inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Performs a scalar multiplication. <a href="class_abstract_group.html#ac01536b91c4fa3d0e0f929917143595b">More...</a><br /></td></tr>
<tr class="separator:ac01536b91c4fa3d0e0f929917143595b inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a89bd24f1a83e62ac8cc5ad014cb5883e inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_polynomial_over.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a89bd24f1a83e62ac8cc5ad014cb5883e">CascadeScalarMultiply</a> (const <a class="el" href="class_polynomial_over.html">Element</a> &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const <a class="el" href="class_polynomial_over.html">Element</a> &y, const <a class="el" href="class_integer.html">Integer</a> &e2) const</td></tr>
<tr class="memdesc:a89bd24f1a83e62ac8cc5ad014cb5883e inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_abstract_group.html#a89bd24f1a83e62ac8cc5ad014cb5883e">More...</a><br /></td></tr>
<tr class="separator:a89bd24f1a83e62ac8cc5ad014cb5883e inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9c73ab688612e76786f43e311376eb8d inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a9c73ab688612e76786f43e311376eb8d">SimultaneousMultiply</a> (<a class="el" href="class_polynomial_over.html">Element</a> *results, const <a class="el" href="class_polynomial_over.html">Element</a> &base, const <a class="el" href="class_integer.html">Integer</a> *exponents, unsigned int exponentsCount) const</td></tr>
<tr class="memdesc:a9c73ab688612e76786f43e311376eb8d inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies a base to multiple exponents in a group. <a href="class_abstract_group.html#a9c73ab688612e76786f43e311376eb8d">More...</a><br /></td></tr>
<tr class="separator:a9c73ab688612e76786f43e311376eb8d inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<class T><br />
class RingOfPolynomialsOver< T ></h3>
<p>Ring of polynomials over another ring. </p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00314">314</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="a9874b8b2aaee21b9c4f75a9372151489"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9874b8b2aaee21b9c4f75a9372151489">◆ </a></span>Equal()</h2>
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<td class="memname">bool <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Equal </td>
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<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
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<p>Compare two elements for equality. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>true if the elements are equal, false otherwise</dd></dl>
<p><a class="el" href="class_ring_of_polynomials_over.html#a9874b8b2aaee21b9c4f75a9372151489" title="Compare two elements for equality. ">Equal()</a> tests the elements for equality using <code>a==b</code> </p>
<p>Implements <a class="el" href="class_abstract_group.html#a0d72cb663566b7c056f846a561547bec">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00327">327</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<a id="a458ef6812fccb23fa063d9a15d27a67b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a458ef6812fccb23fa063d9a15d27a67b">◆ </a></span>Identity()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Identity </td>
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<p>Provides the Identity element. </p>
<dl class="section return"><dt>Returns</dt><dd>the Identity element </dd></dl>
<p>Implements <a class="el" href="class_abstract_group.html#a929ba4e6a7d7d80344946efad0456d5b">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00330">330</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<a id="a3ff8fa662fa5f4f6b850e9dc16958822"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3ff8fa662fa5f4f6b850e9dc16958822">◆ </a></span>Add()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Add </td>
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<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
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<p>Adds elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the sum of <code>a</code> and <code>b</code> </dd></dl>
<p>Implements <a class="el" href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00333">333</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6f6d9905144ff7e38b0f68401207d652">◆ </a></span>Accumulate()</h2>
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<td class="memname"><a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Accumulate </td>
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<td class="paramtype"><a class="el" href="class_polynomial_over.html">Element</a> & </td>
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<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
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<p>TODO. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>TODO </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00336">336</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa807d70d825213c7296b639dac60123b">◆ </a></span>Inverse()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Inverse </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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<p>Inverts the element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the inverse of the element </dd></dl>
<p>Implements <a class="el" href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00339">339</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#acf0bf71815e9b6d1a9caac9654a5c227">◆ </a></span>Subtract()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Subtract </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
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<td>)</td>
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<p>Subtracts elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the difference of <code>a</code> and <code>b</code>. The element <code>a</code> must provide a Subtract member function. </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00342">342</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3b71ffe9c999063225fa9baae5bbccda">◆ </a></span>Reduce()</h2>
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<td class="memname"><a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Reduce </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
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<p>Reduces an element in the congruence class. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>element to reduce </td></tr>
<tr><td class="paramname">b</td><td>the congruence class </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the reduced element </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00345">345</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a8671a526a886b19474e5f47889bc404f">◆ </a></span>Double()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Double </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
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<p>Doubles an element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the element doubled </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#afaceaf9c9c24606efc38d30fd8aff5ee">AbstractGroup< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00348">348</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab9713800e8ff192ab7f4c232b44cf31c">◆ </a></span>MultiplicativeIdentity()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::MultiplicativeIdentity </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
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<p>Retrieves the multiplicative identity. </p>
<dl class="section return"><dt>Returns</dt><dd>the multiplicative identity </dd></dl>
<p>Implements <a class="el" href="class_abstract_ring.html#a390832165268e39e2a1f3263e5b44627">AbstractRing< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00351">351</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a37731e8b8eecc4dac0b782443387dc95">◆ </a></span>Multiply()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Multiply </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td> const</td>
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<p>Multiplies elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the multiplicand </td></tr>
<tr><td class="paramname">b</td><td>the multiplier </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the product of a and b </dd></dl>
<p>Implements <a class="el" href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">AbstractRing< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00354">354</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a81b2df6ff2a50c000a9cc7dccd37ba5e">◆ </a></span>Square()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::<a class="el" href="class_square.html">Square</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
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<p><a class="el" href="class_square.html" title="Square block cipher. ">Square</a> an element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the element squared </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_ring.html#a54b38c3a067b893e0c87495bee7adcef">AbstractRing< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00357">357</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a902a6f8e12158a1b2a8f18565463e5ce">◆ </a></span>IsUnit()</h2>
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<td class="memname">bool <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::IsUnit </td>
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<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
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<p>Determines whether an element is a unit in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>true if the element is a unit after reduction, false otherwise. </dd></dl>
<p>Implements <a class="el" href="class_abstract_ring.html#acc7079c244d980c670c329e483c4f107">AbstractRing< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00360">360</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a75a3ae02cf9e1690dbc87be7e97f0248">◆ </a></span>MultiplicativeInverse()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::MultiplicativeInverse </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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<p>Calculate the multiplicative inverse of an element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<p>Implements <a class="el" href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">AbstractRing< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00363">363</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a689e7df1b7183b782d8c78dba07760b7">◆ </a></span>Divide()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Divide </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
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<p>Divides elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the dividend </td></tr>
<tr><td class="paramname">b</td><td>the divisor </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the quotient </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_ring.html#aa7ce20a30d89a8257088930d1d06d0b7">AbstractRing< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00366">366</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a8178e2835b054e1a2b57fa54568a552e">◆ </a></span>Mod()</h2>
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<td class="memname">const <a class="el" href="class_polynomial_over.html">Element</a>& <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::Mod </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
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<td>)</td>
<td></td><td> const</td>
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<p>Performs a modular reduction in the ring. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
<tr><td class="paramname">b</td><td>the modulus </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the result of <code>ab</code>. </dd></dl>
<p>Implements <a class="el" href="class_abstract_euclidean_domain.html#ae7b90c25ce6359bb25c40e1b7a283261">AbstractEuclideanDomain< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00369">369</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a333d8b90b9f7e5ca48056384136af1ca">◆ </a></span>DivisionAlgorithm()</h2>
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<td class="memname">void <a class="el" href="class_ring_of_polynomials_over.html">RingOfPolynomialsOver</a>< T >::DivisionAlgorithm </td>
<td>(</td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>q</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_polynomial_over.html">Element</a> & </td>
<td class="paramname"><em>d</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Performs the division algorithm on two elements in the ring. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">r</td><td>the remainder </td></tr>
<tr><td class="paramname">q</td><td>the quotient </td></tr>
<tr><td class="paramname">a</td><td>the dividend </td></tr>
<tr><td class="paramname">d</td><td>the divisor </td></tr>
</table>
</dd>
</dl>
<p>Implements <a class="el" href="class_abstract_euclidean_domain.html#aa4c2e05ad97912b00f9f0845b4b4adca">AbstractEuclideanDomain< PolynomialOver< T > ></a>.</p>
<p class="definition">Definition at line <a class="el" href="polynomi_8h_source.html#l00372">372</a> of file <a class="el" href="polynomi_8h_source.html">polynomi.h</a>.</p>
</div>
</div>
<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="polynomi_8h_source.html">polynomi.h</a></li>
<li><a class="el" href="polynomi_8cpp_source.html">polynomi.cpp</a></li>
</ul>
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