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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <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">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><br/>  for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">d</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds   <a href="polyvie1.html#K2" title="POLYVIE1:func.2">SumRoots</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">d</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Olive" title="b3">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">c</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Olive" title="b4">d</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <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">  for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">d</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds   <a href="polyvie1.html#K2" title="POLYVIE1:func.2">SumRoots</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Olive" title="b2">d</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Olive" title="b1">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Olive" title="b2">d</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">d</font> be   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <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">  <a href="polyvie1.html#K2" title="POLYVIE1:func.2">SumRoots</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Maroon" title="c5">d</font></span>)</span></span>)</span></span><br/>





<a NAME="E1:38"/>
(  <a href="polyvie1.html#K2" title="POLYVIE1:func.2">SumRoots</a> <span class="p1"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Maroon" title="c4">b</font></span>)</span> &amp;  <a href="polyvie1.html#K2" title="POLYVIE1:func.2">SumRoots</a> <span class="p1"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Maroon" title="c5">d</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#T27" target="_self" onmouseover="rs('polyvie1/T27')" onmouseout="rh()">Th27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:38"/>
 <a href="polyvie1.html#K2" title="POLYVIE1:func.2">SumRoots</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <span class="p2"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Maroon" title="c5">d</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#T28" target="_self" onmouseover="rs('polyvie1/T28')" onmouseout="rh()">Th28</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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