<?xml version="1.0"?>
<div class="add">

<a NAME="E1:127_1_1"/>
 ex <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM4" title="STRUCT_0:NM.4">Function</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> st <br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>  st <font color="Olive" title="b3">b</font> <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> <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> holds <br/> ex <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> st <br/>( <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">q</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b5">r</font> &amp; ( <font color="Olive" title="b5">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> or <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">b</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="ring_2.html#E61"><span class="lab"><font color="Green" title="E47">thEucl2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:127_1_1"/>
 <a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">L</font> is  <a href="int_3.html#V1" title="INT_3:attr.1">Euclidian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_3.html#D8" onmouseover="rs('int_3/D8')" onmouseout="rh()">INT_3:def 8</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/>


</div>
