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<div class="title">field/modular.h File Reference<div class="ingroups"><a class="el" href="group__field.html">field</a></div></div> </div>
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<p>A Modular field is a representations of <code>Z/mZ</code>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include <iostream></code><br/>
<code>#include <climits></code><br/>
<code>#include <cmath></code><br/>
<code>#include "<a class="el" href="integer_8h.html">linbox/integer.h</a>"</code><br/>
<code>#include "linbox/vector/vector-domain.h"</code><br/>
<code>#include "linbox/matrix/matrix-domain.h"</code><br/>
<code>#include "linbox/field/field-interface.h"</code><br/>
<code>#include "linbox/util/field-axpy.h"</code><br/>
<code>#include "linbox/vector/vector-traits.h"</code><br/>
<code>#include "linbox/linbox-config.h"</code><br/>
<code>#include <linbox/field/field-traits.h></code><br/>
<code>#include "linbox/field/modular.inl"</code><br/>
<code>#include "linbox/randiter/modular.h"</code><br/>
<code>#include "linbox/field/modular-int32.h"</code><br/>
<code>#include "<a class="el" href="modular-short_8h.html">linbox/field/modular-short.h</a>"</code><br/>
<code>#include "<a class="el" href="modular-byte_8h.html">linbox/field/modular-byte.h</a>"</code><br/>
<code>#include "<a class="el" href="modular-double_8h.html">linbox/field/modular-double.h</a>"</code><br/>
<code>#include "<a class="el" href="modular-float_8h.html">linbox/field/modular-float.h</a>"</code><br/>
</div><table class="memberdecls">
<tr><td colspan="2"><h2><a name="nested-classes"></a>
Data Structures</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_modular.html">Modular< _Element ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Prime fields of positive characteristic implemented directly in <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a>. <a href="class_lin_box_1_1_modular.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_modular_3_01uint8__t_01_4.html">Modular< uint8_t ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Allows compact storage when the modulus is less than 2^8. <a href="class_lin_box_1_1_modular_3_01uint8__t_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_modular_3_01uint16__t_01_4.html">Modular< uint16_t ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of class <a class="el" href="class_lin_box_1_1_modular.html" title="Prime fields of positive characteristic implemented directly in LinBox.">Modular</a> for uint16_t element type. <a href="class_lin_box_1_1_modular_3_01uint16__t_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html">Modular< uint32_t ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of class <a class="el" href="class_lin_box_1_1_modular.html" title="Prime fields of positive characteristic implemented directly in LinBox.">Modular</a> for uint32_t element type. <a href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01___element_01_4_01_4.html">FieldAXPY< Modular< _Element > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_field_a_x_p_y.html" title="FieldAXPY object.">FieldAXPY</a> for parameterized modular field. <a href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01___element_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01uint8__t_01_4_01_4.html">FieldAXPY< Modular< uint8_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_field_a_x_p_y.html" title="FieldAXPY object.">FieldAXPY</a> for uint8_t modular field. <a href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01uint8__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01uint16__t_01_4_01_4.html">FieldAXPY< Modular< uint16_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_field_a_x_p_y.html" title="FieldAXPY object.">FieldAXPY</a> for uint16_t modular field. <a href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01uint16__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01uint32__t_01_4_01_4.html">FieldAXPY< Modular< uint32_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_field_a_x_p_y.html" title="FieldAXPY object.">FieldAXPY</a> for unsigned short modular field. <a href="class_lin_box_1_1_field_a_x_p_y_3_01_modular_3_01uint32__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_dot_product_domain_3_01_modular_3_01uint8__t_01_4_01_4.html">DotProductDomain< Modular< uint8_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of DotProductDomain for unsigned short modular field. <a href="class_lin_box_1_1_dot_product_domain_3_01_modular_3_01uint8__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_dot_product_domain_3_01_modular_3_01uint16__t_01_4_01_4.html">DotProductDomain< Modular< uint16_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of DotProductDomain for unsigned short modular field. <a href="class_lin_box_1_1_dot_product_domain_3_01_modular_3_01uint16__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_dot_product_domain_3_01_modular_3_01uint32__t_01_4_01_4.html">DotProductDomain< Modular< uint32_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of DotProductDomain for uint32_t modular field. <a href="class_lin_box_1_1_dot_product_domain_3_01_modular_3_01uint32__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_v_product_domain_3_01_modular_3_01uint8__t_01_4_01_4.html">MVProductDomain< Modular< uint8_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_m_v_product_domain.html" title="Helper class to allow specializations of certain matrix-vector products.">MVProductDomain</a> for uint8_t modular field. <a href="class_lin_box_1_1_m_v_product_domain_3_01_modular_3_01uint8__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_v_product_domain_3_01_modular_3_01uint16__t_01_4_01_4.html">MVProductDomain< Modular< uint16_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_m_v_product_domain.html" title="Helper class to allow specializations of certain matrix-vector products.">MVProductDomain</a> for uint16_t modular field. <a href="class_lin_box_1_1_m_v_product_domain_3_01_modular_3_01uint16__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_v_product_domain_3_01_modular_3_01uint32__t_01_4_01_4.html">MVProductDomain< Modular< uint32_t > ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Specialization of <a class="el" href="class_lin_box_1_1_m_v_product_domain.html" title="Helper class to allow specializations of certain matrix-vector products.">MVProductDomain</a> for uint32_t modular field. <a href="class_lin_box_1_1_m_v_product_domain_3_01_modular_3_01uint32__t_01_4_01_4.html#details">More...</a><br/></td></tr>
<tr><td colspan="2"><h2><a name="namespaces"></a>
Namespaces</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="namespace_lin_box.html">LinBox</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Namespace in which all linbox code resides. </p>
<br/></td></tr>
</p>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>A Modular field is a representations of <code>Z/mZ</code>. </p>
<p>This file groups many implementations/specialisations of modular fields.</p>
<ul>
<li>Modular arithmetic is provided in the <code>ModularXXX<T></code> classes.</li>
<li>Specialisations for FieldAXPY, MVProductDomain, DotProductDomain.</li>
<li>Random Iterators</li>
</ul>
</div></div>
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