WEIGHT _ _ _ _ _ _ _ _ _ _ _ _ command

The weight command is used to attach weights to kernels for asymptotic constraints.

syntax:

weight<kernel> =<number>

<kernel> must be a REDUCE kernel, <number> must be a positive integer, not 0.

examples:

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

Weights and wtlevel are used for asymptotic constraints, where higher-order terms are considered insignificant.

Weights are originally equivalent to 0 until set by a weight command. To remove a weight from a kernel, use the clear 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.

The weight level of the system is set by wtlevel, initially at 2. Since no kernels have weights, no effect from wtlevel can be seen. Once you assign weights to kernels, you must set wtlevel 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.