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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E66">defM</font></span>   defines <a href="field_14.html#K6" title="FIELD_14:func.6">multiplicity</a> <a onclick="hs(this)" href="javascript:()">FIELD_14:def 6 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="field_4.html#NM2" title="FIELD_4:NM.2">comRingExtension</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">p</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive">b<sub>5</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_14.html#K6" title="FIELD_14:func.6">multiplicity</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">a</font>) iff  ex <font color="Olive" title="b6">q</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b2">S</font> st <br/>( <font color="Olive" title="b6">q</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">p</font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="uproots.html#K6" title="UPROOTS:func.6">multiplicity</a> (<font color="Olive" title="b6">q</font>,<font color="Olive" title="b4">a</font>) ) );<br/></span></div>
