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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E64">Z5</font></span>: <a NAME="T65"><span class="comment"><font color="firebrick">:: FIELD_9:65</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   non 2 <a href="ring_3.html#V3" title="RING_3:attr.3">-characteristic</a>   <a href="field_3.html#V3" title="FIELD_3:attr.3">polynomial_disjoint</a>   non  <a href="field_9.html#V3" title="FIELD_9:attr.3">quadratic_complete</a>  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">p</font> being   <a href="field_9.html#V1" title="FIELD_9:attr.1">quadratic</a>   non  <a href="field_9.html#V4" title="FIELD_9:attr.4">DC-square</a>   <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span> holds  <font color="Olive" title="b2">p</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K5" title="FIELD_7:func.5">@</a> (<span class="p2">(<span class="default"><a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <font color="Olive" title="b2">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="field_6.html#K6" title="FIELD_6:func.6">FAdj</a> (<font color="Olive" title="b1">F</font>,<span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="field_9.html#K16" title="FIELD_9:func.16">sqrt</a> <span class="p5">(<span class="default"><a href="field_9.html#NK8" title="FIELD_9:NK.8">DC</a> <font color="Olive" title="b2">p</font></span>)</span></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>)</span>)</span>)</span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_9.html#K2" title="FIELD_9:func.2">X-</a> <span class="p3">(<span class="default"><a href="field_9.html#K18" title="FIELD_9:func.18">Root1</a> <font color="Olive" title="b2">p</font></span>)</span></span>)</span> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <span class="p2">(<span class="default"><a href="field_9.html#K2" title="FIELD_9:func.2">X-</a> <span class="p3">(<span class="default"><a href="field_9.html#K19" title="FIELD_9:func.19">Root2</a> <font color="Olive" title="b2">p</font></span>)</span></span>)</span></span>)</span></div></div>
