<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="field_14.html#R1" title="FIELD_14:pred.1">is_square-free_over</a> <a onclick="hs(this)" href="javascript:()">FIELD_14:def 2 : <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">p</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">R</font> holds <br/> ( <font color="Olive" title="b3">p</font> <a href="field_14.html#R1" title="FIELD_14:pred.1">is_square-free_over</a> <font color="Olive" title="b2">S</font> iff  for <font color="Olive" title="b4">q1</font> being   non  <a href="ratfunc1.html#V1" title="RATFUNC1:attr.1">constant</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b5">q2</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b2">S</font>  holds <br/>(  not <font color="Olive" title="b5">q2</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">p</font> or  not <font color="Olive" title="b4">q1</font> <a href="polynom5.html#K3" title="POLYNOM5:func.3">`^</a> 2 <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Olive" title="b5">q2</font> ) );<br/></span></div>
