HP 15c - Manual (Page 79)

Section 6: Programming Basics 79
For example, ´b´A becomes ´bA, ´m´%
becomes ´m%, and O´# becomes O#.
The removal of the ´ is not ambiguous because the ´-shifted function
is the only logical one in these cases. The keycodes for such instructions do
not include the extraneous ´ even if you do key it in.
User Mode
User mode is a convenience to save keystrokes when addressing (calling
up) programs for execution. Pressing ´U will exchange the primary
functions and ´-shifted functions of the A through E keys only. In
User mode (USER annunciator displayed):
´ shift
Primary
A B C D E
¤ ' @ y ∕
| shift
x
2
LN LOG
 
Press | U again to deactivate User mode.
Polynomial Expressions and Horner's Method
Some expressions, such as polynomials, use the same variable several times
for their solution. For example, the expression
f(x) = Ax
4
+ Bx
3
+ Cx
2
+ Dx + E
uses the variable x four different times. A program to solve such an
equation could repeatedly recall a stored copy of x from a storage register.
A shorter programming method, however, would be to use a stack which
has been filled with the constant (refer to Loading the Stack with a
Constant, page 41).
Horner's Method is a useful means of rearranging polynomial expressions to
cut calculation steps and calculation time. It is especially expedient in
_ and f, two rather long-running functions that use subroutines.
This method involves rewriting a polynomial expression in a nested fashion
to eliminate exponents greater than 1:
Ax
4
+ Bx
3
+ Cx
2
+ Dx + 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