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

<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> 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="b2">b</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"><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="b2">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="Olive" title="b1">a</font> <a href="algstr_0.html#K12" title="ALGSTR_0:func.12">/</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</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> 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"><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="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="Olive" title="b1">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">b</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"><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="c3">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="c3">b</font></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">p</font> = <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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">B</font> =  <a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span>;<br/>
<a NAME="E1:36"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
 <a href="polynom5.html#K7" title="POLYNOM5:func.7">Roots</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="c3">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> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<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="c3">b</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#T10" target="_self" onmouseover="rs('polyvie1/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">E</font> =  <a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">Roots</a> <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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> as    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of  <a href="polynom5.html#K7" title="POLYNOM5:func.7">Roots</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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#T2" target="_self" onmouseover="rs('polyvie1/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">F</font> = <span class="p1">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">g</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">L</font><span class="kw"> such that </span><br/><a NAME="E4:36"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p4"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:36"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
<font color="Maroon" title="c8">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#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font>
 <span class="kw">and </span><br/><a NAME="E6:36"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Maroon" title="c8">g</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">j</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D12" onmouseover="rs('rlvect_1/D12')" onmouseout="rh()">RLVECT_1:def 12</a></span>;<br/>
<a NAME="E7:36"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
<font color="Maroon" title="c6">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<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="c3">b</font></span>)</span></span>)</span></span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="finseq_1.html#T94" onmouseover="rs('finseq_1/T94')" onmouseout="rh()">FINSEQ_1:94</a></span>;<br/>
<a NAME="E8:36"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E9:36"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="finseq_1.html#T39" onmouseover="rs('finseq_1/T39')" onmouseout="rh()">FINSEQ_1:39</a></span>;<br/>
<a NAME="E10:36"/><span class="lab"><font color="Green" title="E30">A8</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="finseq_3.html#T25" onmouseover="rs('finseq_3/T25')" onmouseout="rh()">FINSEQ_3:25</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A9</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
 <a href="uproots.html#K6" title="UPROOTS:func.6">multiplicity</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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span>,<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="c3">b</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="uproots.html#D9" onmouseover="rs('uproots/D9')" onmouseout="rh()">UPROOTS:def 9</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyvie1.html#T11" target="_self" onmouseover="rs('polyvie1/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E32">A10</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p4"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>
<br/>.= 
<font color="Maroon" title="c6">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">v</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E14:36"/><span class="lab"><font color="Green" title="E33">A11</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p3"><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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span></span>)</span> <a href="polyvie1.html#K1" title="POLYVIE1:func.1">(++)</a> <font color="Maroon" title="c6">E</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">thus </span> <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="c3">b</font></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> = 
<font color="Maroon" title="c8">g</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="polyvie1.html#D1" target="_self" onmouseover="rs('polyvie1/D1')" onmouseout="rh()">Def1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">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></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E14:36"><span class="lab"><font color="Green" title="E33">A11</font></span></a></span>
<br/>.= 
 <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="c3">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E12:36"><span class="lab"><font color="Green" title="E32">A10</font></span></a>, <a class="ref" href="finseq_4.html#T16" onmouseover="rs('finseq_4/T16')" onmouseout="rh()">FINSEQ_4:16</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>
