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<div class="title">NTL_zz_p Struct Reference<div class="ingroups"><a class="el" href="group__field.html">field</a></div></div> </div>
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<!-- doxytag: class="LinBox::NTL_zz_p" --><!-- doxytag: inherits="LinBox::UnparametricField" -->
<p>long ints modulo a positive integer.
<a href="struct_lin_box_1_1_n_t_l__zz__p.html#details">More...</a></p>
<p><code>#include <ntl-lzz_p.h></code></p>
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<img id="dynsection-0-trigger" src="closed.png"/> Inheritance diagram for NTL_zz_p:</div>
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<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">typedef K </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_unparametric_field.html#a3f09bdc246930a5dde1ed03a2357b656">Element</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">The field's element type. <a href="#a3f09bdc246930a5dde1ed03a2357b656"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a372e01cec3ec4baa9ea342f9bc017d92"></a><!-- doxytag: member="LinBox::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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::NTL_zz_p::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>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>long ints modulo a positive integer. </p>
<p>While NTL allows any int to serve as the modulus, only prime moduli yield fields. The primality of the modulus will not be checked, so it is the programmer's responsibility to supply a prime modulus if a field is wanted. These specializations allow the <a class="el" href="group___unparametric_field.html">UnparametricField</a> template class to be used to wrap NTL's <code>zz_p</code> class as a <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a> field. Uses nice trick for mod p via floating point. </p>
</div><hr/><h2>Member Typedef Documentation</h2>
<a class="anchor" id="a3f09bdc246930a5dde1ed03a2357b656"></a><!-- doxytag: member="LinBox::NTL_zz_p::Element" ref="a3f09bdc246930a5dde1ed03a2357b656" args="" -->
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<p>The field's element type. </p>
<p>Type K must provide a default constructor, a copy constructor, a destructor, and an assignment operator. </p>
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<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="addde9c4097f901609a5c725aa5eae459"></a><!-- doxytag: member="LinBox::NTL_zz_p::inv" ref="addde9c4097f901609a5c725aa5eae459" args="(NTL::zz_p &x, const NTL::zz_p &y) const" -->
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<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>
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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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<td>(</td>
<td class="paramtype">NTL::RR & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramtype">const NTL::RR & </td>
<td class="paramname"><em>y</em> </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="ae6fa705855d6601dc68421c3c0022bca"></a><!-- doxytag: member="LinBox::NTL_zz_p::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>
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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="ae2b7e56bffcb22ca6562bbeece999a7a"></a><!-- doxytag: member="LinBox::NTL_zz_p::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>
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<td>(</td>
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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>
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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>
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</dd>
</dl>
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<a class="anchor" id="ac24cd0b2f1c2e8fd42ac413c926d4b19"></a><!-- doxytag: member="LinBox::NTL_zz_p::write" ref="ac24cd0b2f1c2e8fd42ac413c926d4b19" args="(std::ostream &os) const" -->
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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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<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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<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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<a class="anchor" id="af849df6a115b541eae21a52eef563429"></a><!-- doxytag: member="LinBox::NTL_zz_p::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>
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<a class="anchor" id="a8e263fbf628f54675445ff48c2cdd1a8"></a><!-- doxytag: member="LinBox::NTL_zz_p::isZero" ref="a8e263fbf628f54675445ff48c2cdd1a8" args="(const NTL::RR &x) const" -->
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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>
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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>
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<a class="anchor" id="a7abb239cedd7a0dc8078c42da343ca7f"></a><!-- doxytag: member="LinBox::NTL_zz_p::isOne" ref="a7abb239cedd7a0dc8078c42da343ca7f" args="(const NTL::zz_p &x) const" -->
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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>
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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>
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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>
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<a class="anchor" id="a24a8f9919df452027d2b035898127389"></a><!-- doxytag: member="LinBox::NTL_zz_p::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>
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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>
<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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<a class="anchor" id="a378127401cdc57f10baa71e34c85e1c9"></a><!-- doxytag: member="LinBox::NTL_zz_p::cardinality" ref="a378127401cdc57f10baa71e34c85e1c9" args="(integer &c) const" -->
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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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<a class="anchor" id="a378127401cdc57f10baa71e34c85e1c9"></a><!-- doxytag: member="LinBox::NTL_zz_p::cardinality" ref="a378127401cdc57f10baa71e34c85e1c9" args="(integer &c) const" -->
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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>
<td class="paramname"><em>c</em></td><td>)</td>
<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>ntl-lzz_p.h</li>
</ul>
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