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<div><span class="kw">theorem </span><a NAME="T53"><span class="comment"><font color="firebrick">:: HURWITZ:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  st  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Olive" title="b1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp;  ex <font color="Olive" title="b2">rho</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> st <br/>(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Olive" title="b2">rho</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">rho</font>)</span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="hurwitz.html#K7" title="HURWITZ:func.7">*'</a></span>)</span>,<font color="Olive" title="b2">rho</font>)</span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> ) holds <br/> not <font color="Olive" title="b1">f</font> is  <a href="hurwitz.html#V1" title="HURWITZ:attr.1">Hurwitz</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#T50" target="_self" onmouseover="rs('hurwitz/T50')" onmouseout="rh()">Th49</a></span>;<br/></div></div>
