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<title>Crypto++: AbstractEuclideanDomain< 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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<a href="#pub-types">Public Types</a> |
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<div class="title">AbstractEuclideanDomain< T > Class Template Reference<span class="mlabels"><span class="mlabel">abstract</span></span></div> </div>
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<p>Abstract Euclidean domain.
<a href="class_abstract_euclidean_domain.html#details">More...</a></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for AbstractEuclideanDomain< T >:</div>
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<map id="AbstractEuclideanDomain_3C_20T_20_3E_map" name="AbstractEuclideanDomain_3C_20T_20_3E_map">
<area href="class_abstract_ring.html" title="Abstract ring." alt="AbstractRing< T >" shape="rect" coords="0,56,188,80"/>
<area href="class_abstract_group.html" title="Abstract group." alt="AbstractGroup< T >" shape="rect" coords="0,0,188,24"/>
<area href="class_euclidean_domain_of.html" title="Euclidean domain." alt="EuclideanDomainOf< T >" shape="rect" coords="0,168,188,192"/>
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<table class="memberdecls">
<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>Element</b></td></tr>
<tr class="separator:a02903b4c46289ca070e2e7668e532bdc"><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< 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 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< 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 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>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:aa4c2e05ad97912b00f9f0845b4b4adca"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_euclidean_domain.html#aa4c2e05ad97912b00f9f0845b4b4adca">DivisionAlgorithm</a> (Element &r, Element &q, const Element &a, const Element &d) const =0</td></tr>
<tr class="memdesc:aa4c2e05ad97912b00f9f0845b4b4adca"><td class="mdescLeft"> </td><td class="mdescRight">Performs the division algorithm on two elements in the ring. <a href="#aa4c2e05ad97912b00f9f0845b4b4adca">More...</a><br /></td></tr>
<tr class="separator:aa4c2e05ad97912b00f9f0845b4b4adca"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae7b90c25ce6359bb25c40e1b7a283261"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_euclidean_domain.html#ae7b90c25ce6359bb25c40e1b7a283261">Mod</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:ae7b90c25ce6359bb25c40e1b7a283261"><td class="mdescLeft"> </td><td class="mdescRight">Performs a modular reduction in the ring. <a href="#ae7b90c25ce6359bb25c40e1b7a283261">More...</a><br /></td></tr>
<tr class="separator:ae7b90c25ce6359bb25c40e1b7a283261"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a2044146d4eb49414e1f4f880a9858161"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_euclidean_domain.html#a2044146d4eb49414e1f4f880a9858161">Gcd</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a2044146d4eb49414e1f4f880a9858161"><td class="mdescLeft"> </td><td class="mdescRight">Calculates the greatest common denominator in the ring. <a href="#a2044146d4eb49414e1f4f880a9858161">More...</a><br /></td></tr>
<tr class="separator:a2044146d4eb49414e1f4f880a9858161"><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< 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:acc7079c244d980c670c329e483c4f107 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#acc7079c244d980c670c329e483c4f107">IsUnit</a> (const Element &a) const =0</td></tr>
<tr class="memdesc:acc7079c244d980c670c329e483c4f107 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="class_abstract_ring.html#acc7079c244d980c670c329e483c4f107">More...</a><br /></td></tr>
<tr class="separator:acc7079c244d980c670c329e483c4f107 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a390832165268e39e2a1f3263e5b44627 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a390832165268e39e2a1f3263e5b44627">MultiplicativeIdentity</a> () const =0</td></tr>
<tr class="memdesc:a390832165268e39e2a1f3263e5b44627 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="class_abstract_ring.html#a390832165268e39e2a1f3263e5b44627">More...</a><br /></td></tr>
<tr class="separator:a390832165268e39e2a1f3263e5b44627 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4ba8818fc72fa298cd52fd483bdd6ad4 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">Multiply</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:a4ba8818fc72fa298cd52fd483bdd6ad4 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">More...</a><br /></td></tr>
<tr class="separator:a4ba8818fc72fa298cd52fd483bdd6ad4 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aba109f4e7932d77a8251c1ec20627571 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">MultiplicativeInverse</a> (const Element &a) const =0</td></tr>
<tr class="memdesc:aba109f4e7932d77a8251c1ec20627571 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">More...</a><br /></td></tr>
<tr class="separator:aba109f4e7932d77a8251c1ec20627571 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a54b38c3a067b893e0c87495bee7adcef inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a54b38c3a067b893e0c87495bee7adcef">Square</a> (const Element &a) const</td></tr>
<tr class="memdesc:a54b38c3a067b893e0c87495bee7adcef inherit pub_methods_class_abstract_ring"><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="class_abstract_ring.html#a54b38c3a067b893e0c87495bee7adcef">More...</a><br /></td></tr>
<tr class="separator:a54b38c3a067b893e0c87495bee7adcef inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa7ce20a30d89a8257088930d1d06d0b7 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#aa7ce20a30d89a8257088930d1d06d0b7">Divide</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:aa7ce20a30d89a8257088930d1d06d0b7 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Divides elements in the group. <a href="class_abstract_ring.html#aa7ce20a30d89a8257088930d1d06d0b7">More...</a><br /></td></tr>
<tr class="separator:aa7ce20a30d89a8257088930d1d06d0b7 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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a0f011366054a4edb80be92f968083538">Exponentiate</a> (const Element &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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">CascadeExponentiate</a> (const Element &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const Element &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> (Element *results, const Element &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>< 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< T ></a></td></tr>
<tr class="memitem:a0d72cb663566b7c056f846a561547bec 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#a0d72cb663566b7c056f846a561547bec">Equal</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:a0d72cb663566b7c056f846a561547bec inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="class_abstract_group.html#a0d72cb663566b7c056f846a561547bec">More...</a><br /></td></tr>
<tr class="separator:a0d72cb663566b7c056f846a561547bec inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a929ba4e6a7d7d80344946efad0456d5b inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a929ba4e6a7d7d80344946efad0456d5b">Identity</a> () const =0</td></tr>
<tr class="memdesc:a929ba4e6a7d7d80344946efad0456d5b inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="class_abstract_group.html#a929ba4e6a7d7d80344946efad0456d5b">More...</a><br /></td></tr>
<tr class="separator:a929ba4e6a7d7d80344946efad0456d5b inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa813430d9e4244de24c487d090eb5797 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">Add</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:aa813430d9e4244de24c487d090eb5797 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">More...</a><br /></td></tr>
<tr class="separator:aa813430d9e4244de24c487d090eb5797 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab22563bc0dcb544399d7e22b3589e165 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">Inverse</a> (const Element &a) const =0</td></tr>
<tr class="memdesc:ab22563bc0dcb544399d7e22b3589e165 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">More...</a><br /></td></tr>
<tr class="separator:ab22563bc0dcb544399d7e22b3589e165 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </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:afaceaf9c9c24606efc38d30fd8aff5ee inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#afaceaf9c9c24606efc38d30fd8aff5ee">Double</a> (const Element &a) const</td></tr>
<tr class="memdesc:afaceaf9c9c24606efc38d30fd8aff5ee inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="class_abstract_group.html#afaceaf9c9c24606efc38d30fd8aff5ee">More...</a><br /></td></tr>
<tr class="separator:afaceaf9c9c24606efc38d30fd8aff5ee inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa19e1bef00198fb30eb01df3f7076717 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">Subtract</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:aa19e1bef00198fb30eb01df3f7076717 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">More...</a><br /></td></tr>
<tr class="separator:aa19e1bef00198fb30eb01df3f7076717 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab03cc0a23f23c6aa1c003e11f9abb8c5 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">Accumulate</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ab03cc0a23f23c6aa1c003e11f9abb8c5 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">More...</a><br /></td></tr>
<tr class="separator:ab03cc0a23f23c6aa1c003e11f9abb8c5 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a40f7de55eddc193e07a7c3b5acad781a inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">Reduce</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a40f7de55eddc193e07a7c3b5acad781a inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">More...</a><br /></td></tr>
<tr class="separator:a40f7de55eddc193e07a7c3b5acad781a 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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ac01536b91c4fa3d0e0f929917143595b">ScalarMultiply</a> (const Element &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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a89bd24f1a83e62ac8cc5ad014cb5883e">CascadeScalarMultiply</a> (const Element &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const Element &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> (Element *results, const Element &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>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<class T><br />
class AbstractEuclideanDomain< T ></h3>
<p>Abstract Euclidean domain. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>element class or type</td></tr>
</table>
</dd>
</dl>
<p><code>const Element&</code> returned by member functions are references to internal data members. Since each object may have only one such data member for holding results, the following code will produce incorrect results: </p><pre> abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre><p> But this should be fine: </p><pre> abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00276">276</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="aa4c2e05ad97912b00f9f0845b4b4adca"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa4c2e05ad97912b00f9f0845b4b4adca">◆ </a></span>DivisionAlgorithm()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class T> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">virtual void <a class="el" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a>< T >::DivisionAlgorithm </td>
<td>(</td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>q</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </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">pure 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>Implemented in <a class="el" href="class_ring_of_polynomials_over.html#a333d8b90b9f7e5ca48056384136af1ca">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#affb95c21c906572aecf829451f73395c">EuclideanDomainOf< T ></a>, and <a class="el" href="class_euclidean_domain_of.html#affb95c21c906572aecf829451f73395c">EuclideanDomainOf< PolynomialMod2 ></a>.</p>
</div>
</div>
<a id="ae7b90c25ce6359bb25c40e1b7a283261"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae7b90c25ce6359bb25c40e1b7a283261">◆ </a></span>Mod()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class T > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">const T & <a class="el" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a>< T >::Mod </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</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">pure virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<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>Implemented in <a class="el" href="class_ring_of_polynomials_over.html#a8178e2835b054e1a2b57fa54568a552e">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#af27cd160da0909dca14ffad646672695">EuclideanDomainOf< T ></a>, and <a class="el" href="class_euclidean_domain_of.html#af27cd160da0909dca14ffad646672695">EuclideanDomainOf< PolynomialMod2 ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00049">49</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
</div>
</div>
<a id="a2044146d4eb49414e1f4f880a9858161"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2044146d4eb49414e1f4f880a9858161">◆ </a></span>Gcd()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class T > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">const T & <a class="el" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a>< T >::Gcd </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</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">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Calculates the greatest common denominator in the ring. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the first element </td></tr>
<tr><td class="paramname">b</td><td>the second element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the the greatest common denominator of a and b. </dd></dl>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00056">56</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
</div>
</div>
<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="algebra_8h_source.html">algebra.h</a></li>
<li><a class="el" href="algebra_8cpp_source.html">algebra.cpp</a></li>
</ul>
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