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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E18">defeval</font></span>   defines <a href="field_11.html#K4" title="FIELD_11:func.4">Ext_eval</a> <a onclick="hs(this)" href="javascript:()">FIELD_11:def 4 : <br/></a><span> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b4">p</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Olive" title="b3">n</font>,<font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b5">x</font> being   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <font color="Olive" title="b3">n</font>,<font color="Olive" title="b2">S</font><br/>  for <font color="Olive">b<sub>6</sub></font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">S</font> holds <br/> ( <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_11.html#K4" title="FIELD_11:func.4">Ext_eval</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">x</font>) iff  ex <font color="Olive" title="b7">y</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b2">S</font> st <br/>( <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <font color="Olive" title="b7">y</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Olive" title="b4">p</font></span>)</span>)</span>)</span> &amp; (  for <font color="Olive" title="b8">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b8">i</font> &amp; <font color="Olive" title="b8">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">y</font> holds <br/><font color="Olive" title="b7">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K9" title="STRUCT_0:func.9">In</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">p</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p4">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p5">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">n</font></span>)</span>,<span class="p5">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Olive" title="b4">p</font></span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">i</font></span>)</span>,<font color="Olive" title="b2">S</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">eval</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p4">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Olive" title="b3">n</font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Olive" title="b4">p</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b8">i</font></span>)</span>,<font color="Olive" title="b5">x</font>)</span>)</span> ) ) );<br/></span></div>
