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<div>:: <span class="kw">deftheorem </span>   defines <a href="algnum_1.html#R1" title="ALGNUM_1:pred.1">is_integral_over</a> <a onclick="hs(this)" href="javascript:()">ALGNUM_1:def 2 : <br/></a><span> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">B</font> holds <br/> ( <font color="Olive" title="b3">x</font> <a href="algnum_1.html#R1" title="ALGNUM_1:pred.1">is_integral_over</a> <font color="Olive" title="b1">A</font> iff  ex <font color="Olive" title="b4">f</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">A</font> st <br/>(  <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">A</font> &amp;  <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">x</font>) <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="Olive" title="b2">B</font> ) );<br/></span></div>
