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<?xml>GAPIBNP 5  for Polynomials>

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</pre></div>

<p><a id  1 , ,[2 ]  1  ,[,2 1 ]



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<p>These two functions generalise the <strong class="pkg">GBNP</strong> functions <code class="code">LtNP</code> and <code class="code">GtNP</code> which (confusingly) apply only to monomials. They compare a pair of polynomials with respect to the monomial ordering currently being used. In the <pGivenalistof , thislooks      class"L4


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<span class="GAPprompt">gap></span> <span class="GAPinput">L4 := [u,v,u2,v2];</span>
[ [ [ [ 1, 1, 2 ], [ 2, 1 ], [ 1 ] ], [ 3, 2, -1 ] ], 
  [ [ [ 1, 1, 2, 1 ], [ 1, 2, 2 ], [ 2, 1 ] ], [ 4, -2, 1 ] ], 
  [ [ [ 1, 1, 2 ], [ 2, 1 ], [ 1 ] ], [ 6, 4, -2 ] ], 
  [ [ [ 1, 1, 2, 1 ], [ 1, 2, 2 ], [ 2, 1 ] ], [ 4, -2, -9 ] ] ]
<span class="GAPprompt">gap></span> <span class="GAPinput">Sort( L4, GtNPoly );</span>
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[ [ [ [ 1, 1, 2, 1 ], [ 1, 2, 2 ], [ 2, 1 ] ], [ 4, -2, 1 ] ], 
  [ [ [ 1, 1, 2, 1 ], [ 1, 2, 2 ], [ 2, 1 ] ], [ 4, -2, -9 ] ], 
  [ [ [ 1, 1, 2 ], [ 2, 1 ], [ 1 ] ], [ 6, 4, -2 ] ], 
  [ [ [ 1, 1, 2 ], [ 2, 1 ], [ 1 ] ], [ 3, 2, -1 ] ] ]

</pre></div>

<p><a id="X79B2E02082C8799E" name="X79B2E02082C8799E"></a></p>

<h5>5.1-4 LowestLeadMonomialPosNP</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; LowestLeadMonomialPosNP</code>( <var class="Arg">polylist</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Given a list of polynomials, this function looks at all the leading monomials and returns the position of the smallest lead monomial with respect to the monomial ordering currently being used. In the example, since <code class="code">L4</code> is sorted, the fourth polynomial is the least.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">LowestLeadMonomialPosNP( L4 );</span>
4

</pre></div>


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