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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E51">ppolydiv</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: FIELD_14:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">B1</font> being   non  <a href="termord.html#V1" title="TERMORD:attr.1">zero</a>  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">p</font> being    <a href="ring_5.html#M2" title="RING_5:mode.2">Ppoly</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">B1</font><br/>  for <font color="Olive" title="b4">q</font> being   non  <a href="ratfunc1.html#V1" title="RATFUNC1:attr.1">constant</a>   <a href="ring_4.html#NV4" title="RING_4:NV.4">monic</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">F</font> holds <br/> ( <font color="Olive" title="b4">q</font> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Olive" title="b3">p</font> iff  ex <font color="Olive" title="b5">B2</font> being   non  <a href="termord.html#V1" title="TERMORD:attr.1">zero</a>  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">F</font> st <br/>( <font color="Olive" title="b4">q</font> is    <a href="ring_5.html#M2" title="RING_5:mode.2">Ppoly</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b5">B2</font> &amp; <font color="Olive" title="b5">B2</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a> <font color="Olive" title="b2">B1</font> ) )</div></div>
