<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E70">mpol3</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: FIELD_6:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">E</font> being   <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">a</font> being  <font color="Olive">b<sub>1</sub></font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">E</font><br/>  for <font color="Olive" title="b4">p</font> being    <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 <br/> ( <font color="Olive" title="b4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="field_6.html#NK9" title="FIELD_6:NK.9">MinPoly</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">F</font>) iff ( <font color="Olive" title="b4">p</font> is  <a href="ring_4.html#NV4" title="RING_4:NV.4">monic</a>  &amp; <font color="Olive" title="b4">p</font> is  <a href="ring_2.html#V5" title="RING_2:attr.5">irreducible</a>  &amp;  <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b3">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">E</font> ) )</div></div>
