Cubic Formula: HP 71B

[Eddie W. Shore]

Calculator Blog

(Updated 7/1/12 - thanks everyone!)

Edited: 1 July 2012, 4:49 p.m. after one or more responses were posted

[Diego Diaz]

Hi Eddie,

Thanks for sharing this interesting approach.

Just for sake of precision, in your program listing, line 36 seems truncated and merged with line 38; and line 54 can be removed.

Hope this helps.

Best wishes.

Diego.

[Gerson W. Barbosa]

Also, there's a typo in line 30. It should be

30 P = 2*B^3 - 9*A*B*C + 27*A^2*D. 

If line 36 is changed to

36 IF A1 < 0 THEN 48

it will work for his first and last examples. Assuming line 36 is correct, there's still one typo left because of the byte count (547 bytes instead of 549). There is another typo in X1 in the second example (an extra zero between 4 and 6).
This will be a nice program to convert to RPN when Eddie fixes the typos.

Regards,

Gerson.

[Eddie W. Shore]

Quote:

---

Also, there's a typo in line 30. It should be

30 P = 2*B^3 - 9*A*B*C + 27*A^2*D. 

If line 36 is changed to

36 IF A1 < 0 THEN 48

it will work for his first and last examples. Assuming line 36 is correct, there's still one typo left because of the byte count (547 bytes instead of 549). There is another typo in X1 in the second example (an extra zero between 4 and 6).
This will be a nice program to convert to RPN when Eddie fixes the typos.

Regards,

Gerson.

---

Diego and Gerson: Thank you so much. I made the corrections. In addition to deleting line 54, I also deleted line 100. I also had to make corrections on one of the examples.

The program is now 533 bytes.

The link on the original post is updated. I appreciate that you pointed my errors to me. :)

[Gerson W. Barbosa]

Eddie,

Would you please double-check the lines 48, 50 and 52? It still doesn't work when A1<0 (your second and fourth examples). Two bytes are still missing. X1 in the second example should be -3.46050487001, not -3.406050487001.

Thank you,

Gerson.

[Eddie W. Shore]

For Example 2
A = 1,

B = 4,

C = 1,

D = -3

I get:

P = 11

Q = 13

A1 = -2166.75

For Example 4

A = 1

B = -2

C = -5

D = 6

I get:

P = 56

Q = 19

A1 = -6075

Does this help?

Edited: 2 July 2012, 8:54 a.m.

[Eddie W. Shore]

Quote:

---

Eddie,

Would you please double-check the lines 48, 50 and 52? It still doesn't work when A1<0 (your second and fourth examples). Two bytes are still missing. X1 in the second example should be -3.46050487001, not -3.406050487001.

Thank you,

Gerson.

---

Line 52 should be

52 X1 = -B/(3*A) - 2/(3*A) * (P1^(1/3)*COS(P2/3))

On a separate note, I edited line 68 to:

68 IF K>=0 THEN 70 ELSE 90

This corrects the display for repeated roots (Example 5)

I edited the blog too.

Edited: 2 July 2012, 9:40 a.m.

[Gerson W. Barbosa]

Hello Eddie,

Thanks for the program! The algorithm will be perfect for calculators that don't have native complex numbers. Thanks also for your prompt fixing of the typos. All examples work fine now:

>RUN

CUBIC

A,B,C,D 3,3,-3,6

X1=-1.99999999999

REAL= .499999999995

IMAG= .866025403772

>RUN

CUBIC

A,B,C,D 1,4,1,-3

X1=-3.46050487001

X2= .699628148275

X3=-1.23912327826

>RUN

CUBIC

A,B,C,D -2,0,-1,5

X1= 1.23477282504

REAL=-.61738641252

IMAG=-1.28198983892

>RUN

CUBIC

A,B,C,D 1,-2,-5,6

X1=-1.99999999999

X2= 3

X3= .999999999985

>RUN

CUBIC

A,B,C,D 1,-3,3,-1

X1= 1

X2= 1

X3= 1

Have you considered using Jean-François Garnier's
Emu71 emulator? You can avoid typing errors by editing your program on the emulator and copying the program lines from the DOS windows and pasting them to your text editor (I think this should be possible also on Christoph Giesselink's HP71B Emulator).
Since there is no line between lines 68 and 70, you can save a few bytes by rewriting line 68 as

68 IF K<0 THEN 90

Best regards,

Gerson.

[Eddie W. Shore]

I like emulators, but for me, there is nothing like operating on the real thing.