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