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<title>Crypto++: EuclideanDomainOf< 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">EuclideanDomainOf< T > Class Template Reference</div> </div>
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<p>Euclidean domain.
<a href="class_euclidean_domain_of.html#details">More...</a></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for EuclideanDomainOf< T >:</div>
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<map id="EuclideanDomainOf_3C_20T_20_3E_map" name="EuclideanDomainOf_3C_20T_20_3E_map">
<area href="class_abstract_euclidean_domain.html" title="Abstract Euclidean domain. " alt="AbstractEuclideanDomain< T >" shape="rect" coords="0,112,188,136"/>
<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"/>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:aa7ae3206185edccff8c2e7d56eb9d47b"><td class="memItemLeft" align="right" valign="top"><a id="aa7ae3206185edccff8c2e7d56eb9d47b"></a>
typedef T </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:aa7ae3206185edccff8c2e7d56eb9d47b"><td class="memSeparator" colspan="2"> </td></tr>
<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< 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 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< 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:a59813252a0e0a490ea5a0420af5e9cc2"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a59813252a0e0a490ea5a0420af5e9cc2">Equal</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a59813252a0e0a490ea5a0420af5e9cc2"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="#a59813252a0e0a490ea5a0420af5e9cc2">More...</a><br /></td></tr>
<tr class="separator:a59813252a0e0a490ea5a0420af5e9cc2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6d35c27f3e48c24c4cb6f93275f5ed01"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a6d35c27f3e48c24c4cb6f93275f5ed01">Identity</a> () const</td></tr>
<tr class="memdesc:a6d35c27f3e48c24c4cb6f93275f5ed01"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="#a6d35c27f3e48c24c4cb6f93275f5ed01">More...</a><br /></td></tr>
<tr class="separator:a6d35c27f3e48c24c4cb6f93275f5ed01"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7112d4646dfb57a7437f0b04e605e653"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a7112d4646dfb57a7437f0b04e605e653">Add</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a7112d4646dfb57a7437f0b04e605e653"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="#a7112d4646dfb57a7437f0b04e605e653">More...</a><br /></td></tr>
<tr class="separator:a7112d4646dfb57a7437f0b04e605e653"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a59f13cb1ceab7359f62dcaa2ca6ad9a5"><td class="memItemLeft" align="right" valign="top">Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a59f13cb1ceab7359f62dcaa2ca6ad9a5">Accumulate</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a59f13cb1ceab7359f62dcaa2ca6ad9a5"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="#a59f13cb1ceab7359f62dcaa2ca6ad9a5">More...</a><br /></td></tr>
<tr class="separator:a59f13cb1ceab7359f62dcaa2ca6ad9a5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a277f3f0795e9a050c81d47a499971052"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a277f3f0795e9a050c81d47a499971052">Inverse</a> (const Element &a) const</td></tr>
<tr class="memdesc:a277f3f0795e9a050c81d47a499971052"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="#a277f3f0795e9a050c81d47a499971052">More...</a><br /></td></tr>
<tr class="separator:a277f3f0795e9a050c81d47a499971052"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac44bd3c9af42467bfdd822ef7046bc26"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#ac44bd3c9af42467bfdd822ef7046bc26">Subtract</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ac44bd3c9af42467bfdd822ef7046bc26"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="#ac44bd3c9af42467bfdd822ef7046bc26">More...</a><br /></td></tr>
<tr class="separator:ac44bd3c9af42467bfdd822ef7046bc26"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab7fa9e94f9583efdb69df0f8c6401e1e"><td class="memItemLeft" align="right" valign="top">Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#ab7fa9e94f9583efdb69df0f8c6401e1e">Reduce</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ab7fa9e94f9583efdb69df0f8c6401e1e"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="#ab7fa9e94f9583efdb69df0f8c6401e1e">More...</a><br /></td></tr>
<tr class="separator:ab7fa9e94f9583efdb69df0f8c6401e1e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af2ce6444adcefb7009b2e253db19af25"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#af2ce6444adcefb7009b2e253db19af25">Double</a> (const Element &a) const</td></tr>
<tr class="memdesc:af2ce6444adcefb7009b2e253db19af25"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="#af2ce6444adcefb7009b2e253db19af25">More...</a><br /></td></tr>
<tr class="separator:af2ce6444adcefb7009b2e253db19af25"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8112935a4dd4996e011fef24b4d2564a"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a8112935a4dd4996e011fef24b4d2564a">MultiplicativeIdentity</a> () const</td></tr>
<tr class="memdesc:a8112935a4dd4996e011fef24b4d2564a"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="#a8112935a4dd4996e011fef24b4d2564a">More...</a><br /></td></tr>
<tr class="separator:a8112935a4dd4996e011fef24b4d2564a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a570d89c94098cfd66ac5e5e2faa81d1b"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a570d89c94098cfd66ac5e5e2faa81d1b">Multiply</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a570d89c94098cfd66ac5e5e2faa81d1b"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="#a570d89c94098cfd66ac5e5e2faa81d1b">More...</a><br /></td></tr>
<tr class="separator:a570d89c94098cfd66ac5e5e2faa81d1b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acb21bd68efa18945d012b6a879d661e8"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#acb21bd68efa18945d012b6a879d661e8">Square</a> (const Element &a) const</td></tr>
<tr class="memdesc:acb21bd68efa18945d012b6a879d661e8"><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="#acb21bd68efa18945d012b6a879d661e8">More...</a><br /></td></tr>
<tr class="separator:acb21bd68efa18945d012b6a879d661e8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad17003ea655d6638d40b1dcd17534186"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#ad17003ea655d6638d40b1dcd17534186">IsUnit</a> (const Element &a) const</td></tr>
<tr class="memdesc:ad17003ea655d6638d40b1dcd17534186"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="#ad17003ea655d6638d40b1dcd17534186">More...</a><br /></td></tr>
<tr class="separator:ad17003ea655d6638d40b1dcd17534186"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a317c5a5b15b53b0087fc2c1acc2738c0"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a317c5a5b15b53b0087fc2c1acc2738c0">MultiplicativeInverse</a> (const Element &a) const</td></tr>
<tr class="memdesc:a317c5a5b15b53b0087fc2c1acc2738c0"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="#a317c5a5b15b53b0087fc2c1acc2738c0">More...</a><br /></td></tr>
<tr class="separator:a317c5a5b15b53b0087fc2c1acc2738c0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a52cd96d2233db782eb7c74d3645be28d"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#a52cd96d2233db782eb7c74d3645be28d">Divide</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a52cd96d2233db782eb7c74d3645be28d"><td class="mdescLeft"> </td><td class="mdescRight">Divides elements in the group. <a href="#a52cd96d2233db782eb7c74d3645be28d">More...</a><br /></td></tr>
<tr class="separator:a52cd96d2233db782eb7c74d3645be28d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af27cd160da0909dca14ffad646672695"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#af27cd160da0909dca14ffad646672695">Mod</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:af27cd160da0909dca14ffad646672695"><td class="mdescLeft"> </td><td class="mdescRight">Performs a modular reduction in the ring. <a href="#af27cd160da0909dca14ffad646672695">More...</a><br /></td></tr>
<tr class="separator:af27cd160da0909dca14ffad646672695"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:affb95c21c906572aecf829451f73395c"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_euclidean_domain_of.html#affb95c21c906572aecf829451f73395c">DivisionAlgorithm</a> (Element &r, Element &q, const Element &a, const Element &d) const</td></tr>
<tr class="memdesc:affb95c21c906572aecf829451f73395c"><td class="mdescLeft"> </td><td class="mdescRight">Performs the division algorithm on two elements in the ring. <a href="#affb95c21c906572aecf829451f73395c">More...</a><br /></td></tr>
<tr class="separator:affb95c21c906572aecf829451f73395c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a79b45bf034bba50452c7af7479a16bb2"><td class="memItemLeft" align="right" valign="top"><a id="a79b45bf034bba50452c7af7479a16bb2"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator==</b> (const <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T > &rhs) const</td></tr>
<tr class="separator:a79b45bf034bba50452c7af7479a16bb2"><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< T ></a></td></tr>
<tr class="memitem:a2044146d4eb49414e1f4f880a9858161 inherit pub_methods_class_abstract_euclidean_domain"><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 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< 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 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: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 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 EuclideanDomainOf< T ></h3>
<p>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#l00315">315</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="a59813252a0e0a490ea5a0420af5e9cc2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a59813252a0e0a490ea5a0420af5e9cc2">◆ </a></span>Equal()</h2>
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<td class="memname">bool <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Equal </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<td></td><td> const</td>
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<p>Compare two elements for equality. </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>true if the elements are equal, false otherwise</dd></dl>
<p><a class="el" href="class_euclidean_domain_of.html#a59813252a0e0a490ea5a0420af5e9cc2" 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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00322">322</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6d35c27f3e48c24c4cb6f93275f5ed01">◆ </a></span>Identity()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Identity </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00325">325</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
</div>
</div>
<a id="a7112d4646dfb57a7437f0b04e605e653"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7112d4646dfb57a7437f0b04e605e653">◆ </a></span>Add()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Add </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<td></td>
<td>)</td>
<td></td><td> const</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>
</table>
</dd>
</dl>
<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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00328">328</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<a id="a59f13cb1ceab7359f62dcaa2ca6ad9a5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a59f13cb1ceab7359f62dcaa2ca6ad9a5">◆ </a></span>Accumulate()</h2>
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<td class="memname">Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Accumulate </td>
<td>(</td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<td></td>
<td>)</td>
<td></td><td> const</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00331">331</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a277f3f0795e9a050c81d47a499971052">◆ </a></span>Inverse()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Inverse </td>
<td>(</td>
<td class="paramtype">const Element & </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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00334">334</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<a id="ac44bd3c9af42467bfdd822ef7046bc26"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac44bd3c9af42467bfdd822ef7046bc26">◆ </a></span>Subtract()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Subtract </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </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>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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00337">337</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<a id="ab7fa9e94f9583efdb69df0f8c6401e1e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab7fa9e94f9583efdb69df0f8c6401e1e">◆ </a></span>Reduce()</h2>
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<td class="memname">Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Reduce </td>
<td>(</td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>a</em>, </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>
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</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00340">340</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af2ce6444adcefb7009b2e253db19af25">◆ </a></span>Double()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Double </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00343">343</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a8112935a4dd4996e011fef24b4d2564a">◆ </a></span>MultiplicativeIdentity()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00346">346</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a570d89c94098cfd66ac5e5e2faa81d1b">◆ </a></span>Multiply()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Multiply </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>
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</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00349">349</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#acb21bd68efa18945d012b6a879d661e8">◆ </a></span>Square()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::<a class="el" href="class_square.html">Square</a> </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00352">352</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ad17003ea655d6638d40b1dcd17534186">◆ </a></span>IsUnit()</h2>
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<td class="memname">bool <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::IsUnit </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00355">355</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a317c5a5b15b53b0087fc2c1acc2738c0">◆ </a></span>MultiplicativeInverse()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::MultiplicativeInverse </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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</table>
</td>
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<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00358">358</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a52cd96d2233db782eb7c74d3645be28d">◆ </a></span>Divide()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< T >::Divide </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>
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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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00361">361</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af27cd160da0909dca14ffad646672695">◆ </a></span>Mod()</h2>
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<td class="memname">const Element& <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</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">inline</span><span class="mlabel">virtual</span></span> </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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00364">364</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#affb95c21c906572aecf829451f73395c">◆ </a></span>DivisionAlgorithm()</h2>
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<td class="memname">void <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</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>
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<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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00367">367</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="algebra_8h_source.html">algebra.h</a></li>
</ul>
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