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<a href="#pub-methods">Public Member Functions</a> |
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<div class="title">Local2_32 Struct Reference<div class="ingroups"><a class="el" href="group__field.html">field</a></div></div> </div>
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<!-- doxytag: class="LinBox::Local2_32" --><!-- doxytag: inherits="LinBox::UnparametricField" -->
<p>Fast arithmetic mod 2^32, including gcd.
<a href="struct_lin_box_1_1_local2__32.html#details">More...</a></p>
<p><code>#include <local2_32.h></code></p>
<p>Inherits UnparametricField< K >.</p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">Common Object Interface for a LinBox Field.</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p>These methods and member types are required of all <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a> fields.</p>
<p>See <a class="el" href="class_lin_box_1_1_field_archetype.html">FieldArchetype</a> for detailed specifications. </p>
</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a372e01cec3ec4baa9ea342f9bc017d92"></a><!-- doxytag: member="LinBox::Local2_32::RandIter" ref="a372e01cec3ec4baa9ea342f9bc017d92" args="" -->
typedef <a class="el" href="class_lin_box_1_1_unparametric_rand_iter.html">UnparametricRandIter</a>< K > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a372e01cec3ec4baa9ea342f9bc017d92">RandIter</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Type of random field element generators. <br/></td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NTL::zz_p & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#addde9c4097f901609a5c725aa5eae459">inv</a> (NTL::zz_p &x, const NTL::zz_p &y) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NTL::zz_p & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ae2b7e56bffcb22ca6562bbeece999a7a">invin</a> (NTL::zz_p &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::ostream & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ac24cd0b2f1c2e8fd42ac413c926d4b19">write</a> (std::ostream &os) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#af849df6a115b541eae21a52eef563429">isZero</a> (const NTL::zz_p &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a7abb239cedd7a0dc8078c42da343ca7f">isOne</a> (const NTL::zz_p &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a24a8f9919df452027d2b035898127389">characteristic</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a378127401cdc57f10baa71e34c85e1c9">cardinality</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const</td></tr>
<tr><td colspan="2"><div class="groupHeader">Field Object Basics.</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9b2e67d87131ae67539834cd9cd3fa7a"></a><!-- doxytag: member="LinBox::Local2_32::inv" ref="a9b2e67d87131ae67539834cd9cd3fa7a" args="(Element &x, const Element &y) const " -->
Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a9b2e67d87131ae67539834cd9cd3fa7a">inv</a> (Element &x, const Element &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="acf833d5877bb610fef71aac14074d5ce"></a><!-- doxytag: member="LinBox::Local2_32::invin" ref="acf833d5877bb610fef71aac14074d5ce" args="(Element &x) const " -->
Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#acf833d5877bb610fef71aac14074d5ce">invin</a> (Element &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="acd22def76f55c19076bb6c86104beaf0"></a><!-- doxytag: member="LinBox::Local2_32::write" ref="acd22def76f55c19076bb6c86104beaf0" args="(std::ostream &os) const " -->
std::ostream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#acd22def76f55c19076bb6c86104beaf0">write</a> (std::ostream &os) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae9deecd1fa2dde00884d057829c9fcbb"></a><!-- doxytag: member="LinBox::Local2_32::write" ref="ae9deecd1fa2dde00884d057829c9fcbb" args="(std::ostream &os, const Element &p) const " -->
std::ostream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ae9deecd1fa2dde00884d057829c9fcbb">write</a> (std::ostream &os, const Element &p) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a0865272ef30f366f2a7a06323ee7cc22"></a><!-- doxytag: member="LinBox::Local2_32::isZero" ref="a0865272ef30f366f2a7a06323ee7cc22" args="(const Element &x) const " -->
bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a0865272ef30f366f2a7a06323ee7cc22">isZero</a> (const Element &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab37695d9e0fb5b0064c85e8449ed596b"></a><!-- doxytag: member="LinBox::Local2_32::isOne" ref="ab37695d9e0fb5b0064c85e8449ed596b" args="(const Element &x) const " -->
bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ab37695d9e0fb5b0064c85e8449ed596b">isOne</a> (const Element &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ace99140b87ee63f431d90fb021f93d1e"></a><!-- doxytag: member="LinBox::Local2_32::characteristic" ref="ace99140b87ee63f431d90fb021f93d1e" args="(long unsigned int &p) const " -->
long unsigned int </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ace99140b87ee63f431d90fb021f93d1e">characteristic</a> (long unsigned int &p) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a897da8ed179587ee29dbf724931e90cd"></a><!-- doxytag: member="LinBox::Local2_32::characteristic" ref="a897da8ed179587ee29dbf724931e90cd" args="() const " -->
long unsigned int </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a897da8ed179587ee29dbf724931e90cd">characteristic</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aea4d4c3f059080408c3a6344cf9fff10"></a><!-- doxytag: member="LinBox::Local2_32::characteristic" ref="aea4d4c3f059080408c3a6344cf9fff10" args="(integer &c) const " -->
<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#aea4d4c3f059080408c3a6344cf9fff10">characteristic</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="af10b022b118ae703a360fd5e78758575"></a><!-- doxytag: member="LinBox::Local2_32::cardinality" ref="af10b022b118ae703a360fd5e78758575" args="() const " -->
long unsigned int </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#af10b022b118ae703a360fd5e78758575">cardinality</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ade46ce0a344fcc718625a2296a8104ab"></a><!-- doxytag: member="LinBox::Local2_32::cardinality" ref="ade46ce0a344fcc718625a2296a8104ab" args="(integer &c) const " -->
<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ade46ce0a344fcc718625a2296a8104ab">cardinality</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := cardinality of this field (-1 if infinite). <br/></td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a20cbd96d8b293aee5f2d234d611a014f"></a><!-- doxytag: member="LinBox::Local2_32::init" ref="a20cbd96d8b293aee5f2d234d611a014f" args="(Element &x, const Src &s) const " -->
template<typename Src > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">Element & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a20cbd96d8b293aee5f2d234d611a014f">init</a> (Element &x, const Src &s) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a054db1ecf60ae64391b553dfc6316205"></a><!-- doxytag: member="LinBox::Local2_32::read" ref="a054db1ecf60ae64391b553dfc6316205" args="(std::istream &is, Element &x) const " -->
std::istream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a054db1ecf60ae64391b553dfc6316205">read</a> (std::istream &is, Element &x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="afed7ab1451380411e8e013b34a8adeee"></a><!-- doxytag: member="LinBox::Local2_32::read" ref="afed7ab1451380411e8e013b34a8adeee" args="(std::istream &is) const " -->
std::istream & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#afed7ab1451380411e8e013b34a8adeee">read</a> (std::istream &is) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="ae3fb94223b3036ae9d9006cdf2b1773c"></a><!-- doxytag: member="LinBox::Local2_32::convert" ref="ae3fb94223b3036ae9d9006cdf2b1773c" args="(T &x, const Element &y) const " -->
template<typename T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ae3fb94223b3036ae9d9006cdf2b1773c">convert</a> (T &x, const Element &y) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">c := characteristic of this field (zero or prime). <br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">class RR.</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p>Rational number field.</p>
<p>This field is provided as a convenience in a few places. Use with caution because expression swell.</p>
<p>This specialization allows the <a class="el" href="group___unparametric_field.html">UnparametricField</a> template class to be used to wrap NTL's RR class as a <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a> field. </p>
</div></td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NTL::RR & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a4ab4e35f0e78ae716f9ba42cfe167351">inv</a> (NTL::RR &x, const NTL::RR &y) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NTL::RR & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a2297bddb2e9a22746c7e7ad1bec6e1d7">invin</a> (NTL::RR &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::ostream & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ac24cd0b2f1c2e8fd42ac413c926d4b19">write</a> (std::ostream &os) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a8e263fbf628f54675445ff48c2cdd1a8">isZero</a> (const NTL::RR &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#afcae003136710c3b0a6590ccb55b6226">isOne</a> (const NTL::RR &x) const</td></tr>
<tr><td colspan="2"><div class="groupHeader"></div></td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NTL::ZZ_p & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ae6fa705855d6601dc68421c3c0022bca">inv</a> (NTL::ZZ_p &x, const NTL::ZZ_p &y) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NTL::ZZ_p & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a56d79f5a490c9bbdfe66a12a864d7dc3">invin</a> (NTL::ZZ_p &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::ostream & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ac24cd0b2f1c2e8fd42ac413c926d4b19">write</a> (std::ostream &os) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#abec083fa3d65819f5c40a4faaba5a3f7">isZero</a> (const NTL::ZZ_p &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a0427cd8bbe74d98c7bbf2a359b35b93c">isOne</a> (const NTL::ZZ_p &x) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a24a8f9919df452027d2b035898127389">characteristic</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const</td></tr>
<tr><td class="memTemplParams" colspan="2">template<> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a378127401cdc57f10baa71e34c85e1c9">cardinality</a> (<a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> &c) const</td></tr>
<tr><td colspan="2"><div class="groupHeader">Implementation-Specific Methods.</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p>These methods are not required of all <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a> fields and are included only for the implementation of this field template. </p>
</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">const K & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#ac04298a7235c9229e6705eca35f1166e">operator()</a> (void) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constant access operator. <a href="#ac04298a7235c9229e6705eca35f1166e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">K & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#abb076830170962897c3e08c23bb350fd">operator()</a> (void)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Access operator. <a href="#abb076830170962897c3e08c23bb350fd"></a><br/></td></tr>
<tr><td colspan="2"><h2><a name="pro-static-methods"></a>
Static Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">static Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="struct_lin_box_1_1_local2__32.html#aa969c8cd6ea68444336f5a3c6e36c214">HGCD</a> (Element &g, Element &s, const Element &a, const Element &b)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Half GCD g = gcd (a, b). <a href="#aa969c8cd6ea68444336f5a3c6e36c214"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Fast arithmetic mod 2^32, including gcd. </p>
<p>Extend UnparametricField<uint32_t> which is a representation of Z_2^32. It is especially fast because it uses hardware arithmetic directly. This ring is a Local Principal Ideal Ring.</p>
<p>These needed PIR functions are added: gcdin(), isUnit(), also inv() is modified to work correctly. The type Exponent is added: more effective rep of the powers of 2, which are important because gcds are powers of 2). This entails some new versions of divin(), mulin(), isUnit().</p>
<p>Those are the function needed for the LocalSmith algorithm. Further appropriate PIR functions may be added later. </p>
<dl><dt><b>Examples: </b></dt><dd>
<p><a class="el" href="examples_2smith_8_c-example.html#_a10">examples/smith.C</a>.</p>
</dd>
</dl></div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="aa969c8cd6ea68444336f5a3c6e36c214"></a><!-- doxytag: member="LinBox::Local2_32::HGCD" ref="aa969c8cd6ea68444336f5a3c6e36c214" args="(Element &g, Element &s, const Element &a, const Element &b)" -->
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<td class="memname">static Element& HGCD </td>
<td>(</td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>g</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>s</em>, </td>
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<td class="paramkey"></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><code> [inline, static, protected]</code></td>
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<p>Half GCD g = gcd (a, b). </p>
<p>exists t, such that: s * a + t * b = g. return g. </p>
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<td class="memname">NTL::zz_p & inv </td>
<td>(</td>
<td class="paramtype">NTL::zz_p & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const NTL::zz_p & </td>
<td class="paramname"><em>y</em> </td>
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<td></td>
<td>)</td>
<td></td><td> const<code> [inherited]</code></td>
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<p>x = 1 / y This function assumes both field elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field element. </td></tr>
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</dd>
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<a class="anchor" id="a4ab4e35f0e78ae716f9ba42cfe167351"></a><!-- doxytag: member="LinBox::Local2_32::inv" ref="a4ab4e35f0e78ae716f9ba42cfe167351" args="(NTL::RR &x, const NTL::RR &y) const" -->
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<td class="memname">NTL::RR & inv </td>
<td>(</td>
<td class="paramtype">NTL::RR & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const NTL::RR & </td>
<td class="paramname"><em>y</em> </td>
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<td></td><td> const<code> [inherited]</code></td>
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<p>x = 1 / y This function assumes both field elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field element. </td></tr>
</table>
</dd>
</dl>
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<a class="anchor" id="ae6fa705855d6601dc68421c3c0022bca"></a><!-- doxytag: member="LinBox::Local2_32::inv" ref="ae6fa705855d6601dc68421c3c0022bca" args="(NTL::ZZ_p &x, const NTL::ZZ_p &y) const" -->
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<td class="memname">NTL::ZZ_p & inv </td>
<td>(</td>
<td class="paramtype">NTL::ZZ_p & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const NTL::ZZ_p & </td>
<td class="paramname"><em>y</em> </td>
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<td>)</td>
<td></td><td> const<code> [inherited]</code></td>
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<p>x = 1 / y This function assumes both field elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element (reference returned). </td></tr>
<tr><td class="paramname">y</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
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<a class="anchor" id="ae2b7e56bffcb22ca6562bbeece999a7a"></a><!-- doxytag: member="LinBox::Local2_32::invin" ref="ae2b7e56bffcb22ca6562bbeece999a7a" args="(NTL::zz_p &x) const" -->
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<td>(</td>
<td class="paramtype">NTL::zz_p & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<p>x = 1 / x This function assumes both field elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element (reference returned). </td></tr>
</table>
</dd>
</dl>
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<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<p>x = 1 / x This function assumes both field elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element (reference returned). </td></tr>
</table>
</dd>
</dl>
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<td>(</td>
<td class="paramtype">NTL::ZZ_p & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<p>x = 1 / x This function assumes both field elements have already been constructed and initialized. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to x. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element (reference returned). </td></tr>
</table>
</dd>
</dl>
</div>
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<a class="anchor" id="ac24cd0b2f1c2e8fd42ac413c926d4b19"></a><!-- doxytag: member="LinBox::Local2_32::write" ref="ac24cd0b2f1c2e8fd42ac413c926d4b19" args="(std::ostream &os) const" -->
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<td> const<code> [inherited]</code></td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>output stream to which field is written. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">os</td><td>output stream to which field is written. </td></tr>
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</dd>
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<td class="paramname"><em>os</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>output stream to which field is written. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">os</td><td>output stream to which field is written. </td></tr>
</table>
</dd>
</dl>
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<td>(</td>
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<td class="paramname"><em>os</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<dl class="return"><dt><b>Returns:</b></dt><dd>output stream to which field is written. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">os</td><td>output stream to which field is written. </td></tr>
</table>
</dd>
</dl>
</div>
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<a class="anchor" id="af849df6a115b541eae21a52eef563429"></a><!-- doxytag: member="LinBox::Local2_32::isZero" ref="af849df6a115b541eae21a52eef563429" args="(const NTL::zz_p &x) const" -->
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<td class="memname">bool isZero </td>
<td>(</td>
<td class="paramtype">const NTL::zz_p & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<p>Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsZero function is called. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals zero, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
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<td>(</td>
<td class="paramtype">const NTL::RR & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<p>Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsZero function is called. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals zero, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
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<td>(</td>
<td class="paramtype">const NTL::ZZ_p & </td>
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<td> const<code> [inherited]</code></td>
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<p>Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsZero function is called. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals zero, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
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<td>(</td>
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<p>Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsOne function is called. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals one, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
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<td>(</td>
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<p>Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsOne function is called. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals one, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
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<td>(</td>
<td class="paramtype">const NTL::ZZ_p & </td>
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<td> const<code> [inherited]</code></td>
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<p>Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsOne function is called. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>boolean true if equals one, false if not. </dd></dl>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>field element. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a24a8f9919df452027d2b035898127389"></a><!-- doxytag: member="LinBox::Local2_32::characteristic" ref="a24a8f9919df452027d2b035898127389" args="(integer &c) const" -->
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<td class="memname"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & characteristic </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
<td class="paramname"><em>c</em></td><td>)</td>
<td> const<code> [inherited]</code></td>
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<p>Return integer representing characteristic of the field. Returns the modulus of the field, which should be prime. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>integer representing characteristic of the field. </dd></dl>
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<td class="memname"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & characteristic </td>
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<td class="paramtype"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
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<p>Return integer representing characteristic of the field. Returns the modulus of the field, which should be prime. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>integer representing characteristic of the field. </dd></dl>
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<td class="memname"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & cardinality </td>
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<td> const<code> [inherited]</code></td>
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<p>Return integer representing cardinality of the field. Returns the modulus of the field, which should be prime. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>integer representing cardinality of the field </dd></dl>
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<td class="memname"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & cardinality </td>
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<td class="paramtype"><a class="el" href="group__integers.html#gad62eceb96963b157a2357aba991f6d6e">integer</a> & </td>
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<td> const<code> [inherited]</code></td>
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<p>Return integer representing cardinality of the field. Returns the modulus of the field, which should be prime. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>integer representing cardinality of the field </dd></dl>
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<td class="memname">const K& operator() </td>
<td>(</td>
<td class="paramtype">void </td>
<td class="paramname"></td><td>)</td>
<td> const<code> [inline, inherited]</code></td>
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<p>Constant access operator. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>constant reference to field object </dd></dl>
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<td class="memname">K& operator() </td>
<td>(</td>
<td class="paramtype">void </td>
<td class="paramname"></td><td>)</td>
<td><code> [inline, inherited]</code></td>
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<p>Access operator. </p>
<dl class="return"><dt><b>Returns:</b></dt><dd>reference to field object </dd></dl>
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<hr/>The documentation for this struct was generated from the following file:<ul>
<li>local2_32.h</li>
</ul>
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