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<span class="kw">set </span><font color="Maroon" title="c4">p</font> =  <a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>);<br/>
<font color="Maroon" title="c2">k</font> = 
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#T27" onmouseover="rs('hurwitz/T27')" onmouseout="rh()">HURWITZ:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#D2" onmouseover="rs('hurwitz/D2')" onmouseout="rh()">HURWITZ:def 2</a></span>
;<br/>
<a NAME="E2:29_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span>
 
;<br/>
<a NAME="E3:29_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T34" onmouseover="rs('nat_d/T34')" onmouseout="rh()">NAT_D:34</a></span>;<br/>
<a NAME="E4:29_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#T25" onmouseover="rs('hurwitz/T25')" onmouseout="rh()">HURWITZ:25</a></span>;<br/>
<a NAME="E5:29_1_1"/><span class="kw">then </span>
 <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ratfunc1.html#D6" onmouseover="rs('ratfunc1/D6')" onmouseout="rh()">RATFUNC1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:29_1_1"/>
 <a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">a</font>) is  <a href="ring_4.html#NV4" title="RING_4:NV.4">monic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ratfunc1.html#D7" onmouseover="rs('ratfunc1/D7')" onmouseout="rh()">RATFUNC1:def 7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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