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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>





<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E59">A1</font></i>: 
( 0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font> &amp; <font color="Maroon" title="c3">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> <font color="Maroon" title="c2">m</font> )
 ;<br/>

<a NAME="E2:63"/><i><font color="Green" title="E60">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="polynom8.html#E1:63"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="polynom8.html#T30" target="_self" title="POLYNOM8:th.30">Th30</a></i>;<br/>
<a NAME="E3:63"/><i><font color="Green" title="E61">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a>  <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="txt" href="polynom8.html#E1:63"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="polynom8.html#T31" target="_self" title="POLYNOM8:th.31">Th31</a></i>;<br/>
<span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">m</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom8.html#E2:63"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="vectsp_1.html#T73" title="VECTSP_1:th.73">VECTSP_1:73</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c1">L</font></span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">m</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom8.html#E1:63"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="polynom8.html#E3:63"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="polynom8.html#T39" target="_self" title="POLYNOM8:th.39">Th39</a></i>
;<br/>
<b>hence </b><a NAME="E5:63"/>
<span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#NK8" title="POLYNOM8:NK.8">VM</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom8.html#E1:63"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="polynom8.html#T39" target="_self" title="POLYNOM8:th.39">Th39</a></i>;<br/>


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