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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</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">S</font> being   <a href="field_4.html#NM2" title="FIELD_4:NM.2">comRingExtension</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">R</font> holds   <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b2">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">a</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">a</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="field_4.html#NM2" title="FIELD_4:NM.2">comRingExtension</a> of <font color="Maroon" title="c1">R</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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">R</font> holds   <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b3">q</font></span>)</span>,<font color="Olive" title="b1">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">a</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">a</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</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">p</font>, <font color="Olive" title="b2">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">R</font> holds   <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c3">a</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c3">a</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">R</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="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c5">q</font></span>)</span>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">a</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">a</font>)</span>)</span></span><br/>







<a NAME="E1:45"/>
<font color="Maroon" title="c1">R</font> is    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#D1" target="_self" onmouseover="rs('field_4/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:45"/>
 <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c5">q</font></span>)</span>,<font color="Maroon" title="c3">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">a</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">a</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="algnum_1.html#T20" onmouseover="rs('algnum_1/T20')" onmouseout="rh()">ALGNUM_1:20</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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