
<A NAME=WEIGHT>

<TITLE>WEIGHT</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>WEIGHT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>command</B><P>
<P>
 
The <em>weight</em> command is used to attach weights to kernels for asymptotic 

constraints. 
 <P> <H3> 
syntax: </H3>
<P>
<P>
<em>weight</em>&lt;kernel&gt; <em>=</em>&lt;number&gt; 
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&lt;kernel&gt; must be a REDUCE 
<A HREF=r37_0002.html>kernel</A>, &lt;number&gt; must be a 
positive integer, not 0. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
a := (x+y)**4; 

        4      3        2  2        3    4
  A := X  + 4*X *Y + 6*X *Y  + 4*X*Y  + Y  


weight x=2,y=3; 

wtlevel 8; 

a; 

   4
  X  


wtlevel 10; 

a; 

   2     2             2
  X *(6*Y  + 4*X*Y  + X ) 


int(x**2,x); 

  ***** X invalid as KERNEL

</TT></PRE><P>Weights and 
<A HREF=r37_0229.html>wtlevel</A> are used for asymptotic constraints, where 
higher-order terms are considered insignificant. 
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<P>
Weights are originally equivalent to 0 until set by a <em>weight</em> 
command. To remove a weight from a kernel, use the 
<A HREF=r37_0189.html>clear</A> 
command. Weights once assigned cannot be changed without clearing the 
identifier. Once a weight is assigned to a kernel, it is no longer a 
kernel and cannot be used in any REDUCE commands or operators that require 
kernels, until the weight is cleared. Note that terms are ordered by 
greatest weight. 
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The weight level of the system is set by 
<A HREF=r37_0229.html>wtlevel</A>, initially at 
2. Since no kernels have weights, no effect from <em>wtlevel</em> can be 
seen. Once you assign weights to kernels, you must set <em>wtlevel</em> 
correctly for the desired operation. When weighted variables appear in a 
term, their weights are summed for the total weight of the term (powers of 
variables multiply their weights). When a term exceeds the weight level 
of the system, it is discarded from the result expression. 
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