<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E59">Th43</font></span>: <a NAME="T43"><span class="comment"><font color="firebrick">:: POLYNOM8:43</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">L</font><br/>  for <font color="Olive" title="b4">m</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>   st <font color="Olive" title="b4">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Olive" title="b2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">m</font> &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Olive" title="b3">q</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">m</font> holds <br/> for <font color="Olive" title="b5">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b5">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b4">m</font> holds <br/> <a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b3">q</font></span>)</span>,<font color="Olive" title="b5">x</font>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b4">m</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b4">m</font></span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b4">m</font></span>)</span>,<font color="Olive" title="b1">L</font>)</span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b3">q</font></span>)</span></div></div>
