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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E75">LMM</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: E_TRANS2:41</font></span><br/></a><div class="add">(  <a href="power.html#K4" title="POWER:func.4">number_e</a>  is  <a href="algnum_1.html#V1" title="ALGNUM_1:attr.1">algebraic</a>  implies  ex <font color="Olive" title="b1">g</font> being   <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> st <br/>(  <a href="basel_2.html#K1" title="BASEL_2:func.1">@</a> <font color="Olive" title="b1">g</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="b1">g</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K9" title="STRUCT_0:func.9">In</a> (<a href="power.html#K4" title="POWER:func.4">number_e</a>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Olive" title="b1">g</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Olive" title="b1">g</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> ) )</div></div>
