HP 32SII - Manual (Page 187)

Simple Programming 12–25
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
Polynomial Expressions and Horner's Method
Some expressions, such as polynomials, use the same variable several times
for their solution. For example, the expression
Ax 4 + Bx 3 + Cx 2 + Dx + E
uses the variable x four different times. A program to calculate such an
expression using RPN operations could repeatedly recall a stored copy of x
from a variable. A shorter RPN programming method, however, would be to
use a stack which has been filled with the constant (see "Filling the Stack with
a Constant" in chapter 2).
Rorer's Method is a useful means of rearranging polynomial expressions to
cut calculation steps and calculation time. It is especially expedient with
SOLVE and
∫ FN, two relatively complex operations that use subroutines.
This method involves rewriting a polynomial expression in a nested fashion to
eliminate exponents greater than 1:
Ax 4 + 13x 3 + Cx 2 +D x + E
(Ax 3 + Bx 2 + Cx + D ) x + E
((Ax 2 + Bx + C ) x + D )x + E
(((Ax + B )x + C ) x + D )x + E
Example:
Write a program using RPN operations for 5x 4 + 2x 3 as (((5x + 2)x)x)x, then
evaluate it for x = 7.
Keys: Display: Description:
z d z
U Œ Œ

 ! 
z “ P
  
z ˆ X
š
  "! %
 ! 
Fills the stack with x.