Calculator test

[Thomas Klemm]

(12-08-2024 07:36 AM)C.Ret Wrote:  This observation exactly match how the HP-15C works, except there is no specific command apart setting flag 8 which is the complex-mode toggle or indicator.

The HP-15C does not have a complex data type, so the result can only be determined using flag 8. However, the HP-42S can also calculate with complex numbers in REALRES mode.
In addition, toggling flag 8 clears the imaginary part of the complex numbers in the stack.
The default is different, which is why Darren received an Error 0.

These are subtleties, but I agree they are similar.

[AnnoyedOne]

As a student EE we also used the z representation of complex numbers per p69 of the HP-15C AFH.

Quote:In these definitions, a complex number is denoted by z = x + iy

That said in EE 'j' is used instead of 'i' (which is reserved for current).

In theory that made some of the math "easier" but as I recall it still got pretty "hairy" at times Fortunately mostly used in RF (Radio Frequency) work which I ignored like the plague and promptly forgot. Mostly HPFM (Hocus Pocus <a rude word> Magic) IMHO.

Fortunately the end result was usually a real number that solved an actual (vs theoretical) problem.

FYI the HP-15C will calculate (along with the 4 basic arithmetic operations)

Quote:1/z
e^z
10^z
ln(z)
log(z)
sin(z)
arcsin(z)
cos(z)
arccos(z)
tan(z)
arctan(z)
sinh(z)
arcsinh(z)
cosh(z)
arccosh(z)
tanh(z)
arctanh(z)

I'm not sure how many other calculators can do that. IMO most are only designed for HS level math these days.

A1

[dm319]

(12-06-2024 10:27 PM)Commie Wrote:  As expected, my hp15ce and ti30x pro mp throws up error 0, which didn't surprise me.

This gives me 0+3.14i on the DM-15L. I don't have a HP-15ce which I thought behaved the same way.

I've been very curious about complex number handling recently, posted recently about i^x=2. I'm really surprised what isn't available on Casio and TI scientifics. I.e. sqrt(-1) on Casios just gives error, even on complex mode. TIs can raise to 2 or 3 and that's it. But the graphical ones seem to be far more proficient (i.e. my TI83+ handles complex numbers very well, but I'll have to check this one, brb).

[Commie]

(12-08-2024 01:20 PM)AnnoyedOne Wrote:  I'm not sure how many other calculators can do that.

A1

Yeah, what I can't get my head around was this computational power was available way back in 1982 in the HP15C. It must have been ground breaking at the time.

My ti84+ can also do all the complex functions aswell.

Cheers
Darren

[Thomas Klemm]

(12-08-2024 01:20 PM)AnnoyedOne Wrote:  FYI the HP-15C will calculate (along with the 4 basic arithmetic operations)
(…)

You missed a few:

• \(\sqrt{x}\)
• \(x^2\)
• \(y^x\)
• \(\text{ABS}\)
  

Unfortunately \(x!\) is not supported.
Only the real part of the number is used.

(12-08-2024 01:20 PM)AnnoyedOne Wrote:  I'm not sure how many other calculators can do that.

The HP-42S and the HP-48 come to my mind.
I'm not familiar with newer models or other brands.

[carey]

(12-08-2024 02:06 PM)Commie Wrote:  My ti84+ can also do all the complex functions aswell.

Hmm…from the TI-84 Plus manual for the sine function: “Returns the sine of a real number, expression, or list.” Same description for the other trig functions and their inverses.

[AnnoyedOne]

Not missed. Just unsure.

(12-08-2024 02:51 PM)Thomas Klemm Wrote:  \(\sqrt{z}\)

I don't think I've seen that one. The others yes.

A1

[Thomas Klemm]

(12-08-2024 03:34 PM)AnnoyedOne Wrote:  I don't think I've seen that one.

Its key is in the upper left corner (key code 11):


Example

3 ENTER 4 f I
\(\sqrt{x}\)

2.0000

f (i)
1.0000

[AnnoyedOne]

(12-08-2024 02:06 PM)Commie Wrote:  ...what I can't get my head around was this computational power was available way back in 1982...

Back then you used a mainframe or a minicomputer (assuming that you had access). No PC's etc.

The HP-15C was the solution to that problem.

A1

[Thomas Klemm]

(12-08-2024 04:04 PM)AnnoyedOne Wrote:  No PC's etc.

From IBM Personal Computer:

Quote:Released on August 12, 1981

[dm319]

(12-08-2024 02:51 PM)Thomas Klemm Wrote:  Unfortunately \(x!\) is not supported.

Yes, this is a shame, though I love that the gamma function is shoed into factorial. That you can do -0.5 and it will calculate x!.

I don't know why I tried, but of course the fx-992s, fx-115w - couldn't calculate ln(-1). The TI-83+ gave the correct answer instantly.

It surprises me the fx-6300G doesn't have complex. I thought this was a higher end calculator with programming and graphing, and assumed it would.

[Commie]

(12-08-2024 03:15 PM)carey Wrote:  Hmm…from the TI-84 Plus manual for the sine function: “Returns the sine of a real number, expression, or list.” Same description for the other trig functions and their inverses.

It seems you are correct, my ti84+ throws an error when trying to solve complex trig functions. I assumed it would work because ln(z) functions correctly.Thanks for highlighting this carey.

While I am here, I've just tested my hp35s, on complex trig. functions and yes it works.


Cheers
Darren

[Steve Simpkin]

(12-08-2024 02:06 PM)Commie Wrote:  ...
Yeah, what I can't get my head around was this computational power was available way back in 1982 in the HP15C. It must have been ground breaking at the time.
...
Cheers
Darren

By most measures, the feature set and mathematical capabilities of the HP-15C were strongly determined by one person, Professor William Kahan.

As a consultant, Professor William Kahan assisted Hewlett Packard with the mathematical functions of a number of its calculators over the years. His work work on algorithms included improving the accuracy of functions, increasing the performance of complex functions and adding to the feature-set of many HP models including the Solver and Integration functions. As an interesting side note, Professor Kahan was instrumental in the development of the original HP-15C and its feature set. From the 2005 oral history listed below:

“Well, we could go on now with more of the Hewlett-Packard stuff because I had another ambition: the HP-15C. That was my ambition. I wanted to have a calculator that could be used by practically all engineering and most science students. And I wanted that calculator to be able to do all the math they were going to use up to their sophomore year except for divs, grads, and curls because on a calculator, you can’t really display regions and things like that. But you could certainly do everything else. You could do an awful lot of circuit calculation. You’d be able to do an awful lot of the calculation for the distortion of elastic structures in civil and mechanical engineering. You’d be able to solve some of the differential equations in kinematics for simple cases. You’d be able to do complex variables cases, so you could plot various flows. You know, I had a fair idea of the things that they have to learn, you see, up into their sophomore year. And I said, “I wanted a calculator that they could do all that stuff.” That would mean that professors like me could give them problems that were simultaneously more realistic and less tedious. And at that time, there weren’t personal computers in large numbers. Personal computers were a hobby.“

More about the work Professor Kahan did concerning the HP-15C and why HP did not sell as many of them as it could have is in the following 2005 oral history. His history with the HP-15C starts on page 151. The HP-15C Collectors Edition (and DM15L) is also running the original 1982 HP-15C firmware code with slight patches to accommodate more memory.
https://drive.google.com/file/d/1Jlg9EWQ...sp=sharing

[AnnoyedOne]

(12-08-2024 05:33 PM)dm319 Wrote:  ...the gamma function...

FYI the HP-15C AFH contains a program (p65) that calculates ln(gamma(z)) so calculating z! is possible.

A1

[dm319]

(12-08-2024 05:39 PM)AnnoyedOne Wrote:  FYI the HP-15C AFH contains a program (p65) that calculates ln(gamma(z)) so calculating z! is possible.

Yes, good spot! They must have run out of ROM or else they would have implemented it for the function I bet.

[Thomas Klemm]

(12-08-2024 05:34 PM)Commie Wrote:  While I am here, I've just tested my hp35s, on complex trig. functions and yes it works.

From the HP 35s User's Guide:

Quote:Operations with Complex Numbers

It has operations for complex arithmetic (+, -, ×, ÷), complex trigonometry (sin, cos, tan), and the mathematics functions \(-z\), \(1/z\), \(z_1^{z_2}\), \(\ln z\), and \(e^z\). (where \(z_1\) and \(z_2\) are complex numbers).

In addition to that \(\text{ABS}(z)\) and \(\text{ARG}(z)\) are supported.

No luck with \(\sqrt{z}\), \(10^z\), \(\log(z)\), \(\sin^{-1}(z)\), \(\cos^{-1}(z)\) or \(\tan^{-1}(z)\).

[naddy]

(12-08-2024 04:04 PM)AnnoyedOne Wrote:  

(12-08-2024 02:06 PM)Commie Wrote:  ...what I can't get my head around was this computational power was available way back in 1982...

Back then you used a mainframe or a minicomputer (assuming that you had access). No PC's etc.
The HP-15C was the solution to that problem.

Yep. When the HP-15C was designed, in 1980 or so, it would have been the only personal computing device for most of its users, in particular university students. I was too young then, but I think video terminals were still scarce and if undergrad engineering students wanted/had to use a computer, that meant submitting a stack of punch cards and waiting for a printout.

Obviously this had completely changed ten years later, when terminals and workstations had become widely available on campus, and you would expect most engineering students to have some sort of computer at home.

The 15C is a mean machine. It's principal limitations stem from the display technology available at the time. It was designed as an engineering tool, not as a toy for high school math class.

[John Keith]

(12-08-2024 02:51 PM)Thomas Klemm Wrote:  Unfortunately \(x!\) is not supported.
Only the real part of the number is used.

Even on the hp 49/50 ! does not support complex numbers, but GAMMA does.

[naddy]

(12-08-2024 07:36 AM)C.Ret Wrote:  Note, that trying the equation \(e^{\pi\cdot i}=^-1\) the opposite direction, show an interesting fact (or flow) about HP-15C precision in complex computations:
[g][ ∏ ][f][Re⇋Im][ ◀- ][ e^x ] exactly display real part -1.0000 but the imaginary part is not exactly what we expect; [f][(i)] or [f][Re⇋Im] display 4.1000  -10.

The fault lies with your expectation. The [π] key gives you 3.141592654. This is not π. You get the result for a calculation with 3.141592654, not the one you would get for π. This is in fact covered in the appendix of the Advanced Functions Handbook.

[AnnoyedOne]

(12-08-2024 06:37 PM)naddy Wrote:  ...in particular university students.

I had mainframe access in first year engineering but not after. Via punchcards and terminals. Limited to 40 minutes per week as I recall. Unless you went to the "computing center" after 9pm (which I did sometimes).

(12-08-2024 06:37 PM)naddy Wrote:  The 15C is a mean machine.

Agreed. Hence its popularity here.

(12-08-2024 06:37 PM)naddy Wrote:  It was designed as an engineering tool, not as a toy for high school math class.

Exactly. Designed by engineers for use by engineers that were trying to solve real-world problems vs homework/exams.

A1