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<a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#712f72d653c33bc1256c729af9b21a11">MultiplicativeInverse</a> () const</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="923b70ee6d67cb50944a68340869fe01"></a><!-- doxytag: member="PolynomialOverFixedRing::IsUnit" ref="923b70ee6d67cb50944a68340869fe01" args="() const" -->bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#923b70ee6d67cb50944a68340869fe01">IsUnit</a> () const</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="605810fa5e4fa44788450f1c07075e9e"></a><!-- doxytag: member="PolynomialOverFixedRing::Doubled" ref="605810fa5e4fa44788450f1c07075e9e" args="() const" --><a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#605810fa5e4fa44788450f1c07075e9e">Doubled</a> () const</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="08c83de30a7c99d11d1c34eb76203d11"></a><!-- doxytag: member="PolynomialOverFixedRing::Squared" ref="08c83de30a7c99d11d1c34eb76203d11" args="() const" --><a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#08c83de30a7c99d11d1c34eb76203d11">Squared</a> () const</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="825685f191673bee3640711de56c681e"></a><!-- doxytag: member="PolynomialOverFixedRing::EvaluateAt" ref="825685f191673bee3640711de56c681e" args="(const CoefficientType &x) const " --><a class="el" href="class_polynomial_over_fixed_ring.html#0db1534646ae791c106da6244896e46f">CoefficientType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#825685f191673bee3640711de56c681e">EvaluateAt</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#0db1534646ae791c106da6244896e46f">CoefficientType</a> &x) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ce18f8c67eb033dd6534b7ed6e7281b2"></a><!-- doxytag: member="PolynomialOverFixedRing::Divide" ref="ce18f8c67eb033dd6534b7ed6e7281b2" args="(ThisType &r, ThisType &q, const ThisType &a, const ThisType &d)" -->static void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#ce18f8c67eb033dd6534b7ed6e7281b2">Divide</a> (<a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> &r, <a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> &q, const <a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> &a, const <a class="el" href="class_polynomial_over_fixed_ring.html">ThisType</a> &d)</td></tr><tr><td class="mdescLeft"> </td><td class="mdescRight">calculate r and q such that (a == d*q + r) && (0 <= r < abs(d)) <br></td></tr><tr><td colspan="2"><br><h2>BASIC ARITHMETIC ON POLYNOMIALS</h2></td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="62705fe9c3f930b8144e0aed003b676f"></a><!-- doxytag: member="PolynomialOverFixedRing::Equals" ref="62705fe9c3f930b8144e0aed003b676f" args="(const PolynomialOver< Ring > &t, const Ring &ring) const " -->bool </td><td class="memItemRight" valign="bottom"><b>Equals</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="de0983f77089c32d1f7ce07738ea4619"></a><!-- doxytag: member="PolynomialOverFixedRing::IsZero" ref="de0983f77089c32d1f7ce07738ea4619" args="(const Ring &ring) const " -->bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#de0983f77089c32d1f7ce07738ea4619">IsZero</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="fdbe0d8682ffa6b8f4934a8009fd3eb4"></a><!-- doxytag: member="PolynomialOverFixedRing::Plus" ref="fdbe0d8682ffa6b8f4934a8009fd3eb4" args="(const PolynomialOver< Ring > &t, const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><b>Plus</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ec317a68d34b85ec98373df7107e3875"></a><!-- doxytag: member="PolynomialOverFixedRing::Minus" ref="ec317a68d34b85ec98373df7107e3875" args="(const PolynomialOver< Ring > &t, const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><b>Minus</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="037a72b82d5acfcacbb94a73784b0d85"></a><!-- doxytag: member="PolynomialOverFixedRing::Inverse" ref="037a72b82d5acfcacbb94a73784b0d85" args="(const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#037a72b82d5acfcacbb94a73784b0d85">Inverse</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="da8afaf56db17f3ba16108dea67c5a08"></a><!-- doxytag: member="PolynomialOverFixedRing::Times" ref="da8afaf56db17f3ba16108dea67c5a08" args="(const PolynomialOver< Ring > &t, const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><b>Times</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="109132ca5627e17eda303344b038d97b"></a><!-- doxytag: member="PolynomialOverFixedRing::DividedBy" ref="109132ca5627e17eda303344b038d97b" args="(const PolynomialOver< Ring > &t, const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><b>DividedBy</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="29352d55c3ec296e5f256c6e260cd627"></a><!-- doxytag: member="PolynomialOverFixedRing::Modulo" ref="29352d55c3ec296e5f256c6e260cd627" args="(const PolynomialOver< Ring > &t, const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><b>Modulo</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1a24658cd38205e6a3edc607aaceedda"></a><!-- doxytag: member="PolynomialOverFixedRing::MultiplicativeInverse" ref="1a24658cd38205e6a3edc607aaceedda" args="(const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#1a24658cd38205e6a3edc607aaceedda">MultiplicativeInverse</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bd97055ea77f4c511d84cbde55fee6a0"></a><!-- doxytag: member="PolynomialOverFixedRing::IsUnit" ref="bd97055ea77f4c511d84cbde55fee6a0" args="(const Ring &ring) const " -->bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#bd97055ea77f4c511d84cbde55fee6a0">IsUnit</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a203a1d078cd60e48578053e2c5ea17a"></a><!-- doxytag: member="PolynomialOverFixedRing::Accumulate" ref="a203a1d078cd60e48578053e2c5ea17a" args="(const PolynomialOver< Ring > &t, const Ring &ring)" --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > & </td><td class="memItemRight" valign="bottom"><b>Accumulate</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring)</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5d9626d31d87e4f4d25f132ae6d64ee2"></a><!-- doxytag: member="PolynomialOverFixedRing::Reduce" ref="5d9626d31d87e4f4d25f132ae6d64ee2" args="(const PolynomialOver< Ring > &t, const Ring &ring)" --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > & </td><td class="memItemRight" valign="bottom"><b>Reduce</b> (const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &t, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring)</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dad14cc6a75b706ef0a6705134bb78d9"></a><!-- doxytag: member="PolynomialOverFixedRing::Doubled" ref="dad14cc6a75b706ef0a6705134bb78d9" args="(const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#dad14cc6a75b706ef0a6705134bb78d9">Doubled</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="adf21161e0af900a33e9ca669a1efd27"></a><!-- doxytag: member="PolynomialOverFixedRing::Squared" ref="adf21161e0af900a33e9ca669a1efd27" args="(const Ring &ring) const " --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#adf21161e0af900a33e9ca669a1efd27">Squared</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5e862bcafe11988e184db0893d086b3c"></a><!-- doxytag: member="PolynomialOverFixedRing::EvaluateAt" ref="5e862bcafe11988e184db0893d086b3c" args="(const CoefficientType &x, const Ring &ring) const " --><a class="el" href="class_polynomial_over_fixed_ring.html#0db1534646ae791c106da6244896e46f">CoefficientType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#5e862bcafe11988e184db0893d086b3c">EvaluateAt</a> (const <a class="el" href="class_polynomial_over_fixed_ring.html#0db1534646ae791c106da6244896e46f">CoefficientType</a> &x, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring) const </td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="961c5f23af4e1d59554cd8d56ae7c608"></a><!-- doxytag: member="PolynomialOverFixedRing::ShiftLeft" ref="961c5f23af4e1d59554cd8d56ae7c608" args="(unsigned int n, const Ring &ring)" --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#961c5f23af4e1d59554cd8d56ae7c608">ShiftLeft</a> (unsigned int n, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring)</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c24e2a39771e36b36ae3ab550e529d70"></a><!-- doxytag: member="PolynomialOverFixedRing::ShiftRight" ref="c24e2a39771e36b36ae3ab550e529d70" args="(unsigned int n, const Ring &ring)" --><a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#c24e2a39771e36b36ae3ab550e529d70">ShiftRight</a> (unsigned int n, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring)</td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e4e0b0beb7bfab492d6f7343630c2df9"></a><!-- doxytag: member="PolynomialOverFixedRing::Divide" ref="e4e0b0beb7bfab492d6f7343630c2df9" args="(PolynomialOver< Ring > &r, PolynomialOver< Ring > &q, const PolynomialOver< Ring > &a, const PolynomialOver< Ring > &d, const Ring &ring)" -->static void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over.html#e4e0b0beb7bfab492d6f7343630c2df9">Divide</a> (<a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &r, <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &q, const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &a, const <a class="el" href="class_polynomial_over.html">PolynomialOver</a>< <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> > &d, const <a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a> &ring)</td></tr><tr><td class="mdescLeft"> </td><td class="mdescRight">calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d) <br></td></tr><tr><td colspan="2"><br><h2>Public Types</h2></td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e2df1daefb676d6ff79290c7ca0e8ac5"></a><!-- doxytag: member="PolynomialOverFixedRing::Ring" ref="e2df1daefb676d6ff79290c7ca0e8ac5" args="" -->typedef T </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#e2df1daefb676d6ff79290c7ca0e8ac5">Ring</a></td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0db1534646ae791c106da6244896e46f"></a><!-- doxytag: member="PolynomialOverFixedRing::CoefficientType" ref="0db1534646ae791c106da6244896e46f" args="" -->typedef T::Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#0db1534646ae791c106da6244896e46f">CoefficientType</a></td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7c46ac2217af15c40b628022053e4979"></a><!-- doxytag: member="PolynomialOverFixedRing::DivideByZero" ref="7c46ac2217af15c40b628022053e4979" args="" -->typedef <a class="el" href="class_polynomial_over_1_1_divide_by_zero.html">B::DivideByZero</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#7c46ac2217af15c40b628022053e4979">DivideByZero</a></td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b606ab5ea3059ba7b6725973bfc3fa5d"></a><!-- doxytag: member="PolynomialOverFixedRing::RandomizationParameter" ref="b606ab5ea3059ba7b6725973bfc3fa5d" args="" -->typedef <a class="el" href="class_polynomial_over_1_1_randomization_parameter.html">B::RandomizationParameter</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#b606ab5ea3059ba7b6725973bfc3fa5d">RandomizationParameter</a></td></tr><tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr><tr><td colspan="2"><div class="groupHeader">ACCESSORS</div></td></tr><tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dc7375389ed8759970361a61cce61ea0"></a><!-- doxytag: member="PolynomialOverFixedRing::Degree" ref="dc7375389ed8759970361a61cce61ea0" args="() const" -->int </td><td class="memItemRight" valign="bottom"><a class="el" href="class_polynomial_over_fixed_ring.html#dc7375389ed8759970361a61cce61ea0">Degree</a> () const</td></tr>
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