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+--- Thread: (11C/15C) Extended power function (/thread-16606.html)
(11C/15C) Extended power function - Nihotte(lma) - 04-05-2021 10:53 AM
(11C/15C) Extended power function
Hi,
A long time ago, I had to solve some equations like
f(t) = 2 + XROOT(3, (1 - 5t)) = 0
where XROOT(3, -8)=-2
But the HP15C (or the HP11C) could not handle -8^(1/3) without returning ERROR 0, out of the complex mode
So, I composed a function to compute Y^X with Y and X as decimal or natural numbers
It gave the following program for the HP15C
(The program also runs on the HP11C by using CF 0, SF 0 or F?0 instead of CF 8, SF 8 and F?8)
Code:
f LBL E
ENTER
g INT
x=y (5)
GTO .9
g CLx
g LSTx
f FRAC
1/x
g RND
g CF 8
2
÷
f FRAC
g x=0
GTO .9
g SF 8
R↓
x↔y
x>0 (1)
g CF 8
g ABS
g LN
x
e^x
g F? 8
CHS
g CF 8
g RTN
f LBL .9
R↓
y^x
g RTN
f LBA A
5
CHS
x
1
+
3
1/x
GSB E // calls extended Y^X
2
+
g RTNWith this usage :
-8
ENTER
3 1/x
GSB E
returns -2
Further, A is the function to solve
So, 0 ENTER 0
f SOLVE A returns 1.8 after running near a minute
Keep you safe !
RE: (11C/15C) Extended power function - Nihotte(lma) - 04-23-2021 03:50 PM
(04-05-2021 10:53 AM)Nihotte(lma) Wrote: (11C/15C) Extended power function
I have found out a copy of the decision tree which clarifies the process of the function. Here is a restitution, below:
Y^x
-----
Code:
x is a natural number (set of N)
--> general case
x is a rational number (set of Q)
1/x is even number (as 1/ 1/2)
Y >= 0
--> general case
Y < 0
F?8 enabled
--> Solution is a complex number (set of C)
F?8 is disabled
--> ERROR 0
1/x is odd number (as 1/ 1/3)
--> -e^(x*ln(|Y|)) where ln is natural logarithm and |Y| is abs function on YBy extension, you can unterstand that you should generalize the use of the F?0 flag between HP11C and HP15C and just authorize g SF 8 before running the search, in the case you want to avoid the ERROR 0 and open the resulting to the complex solution (x is even and Y is negative).
So, just read CF 0, SF 0 and F?0 in the initial code !
Keep you safe !
Laurent