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 5
x
4
+ 2
x
3
as (((5
x
+ 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
.