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HP Forum Archive 18

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HP-50g CAS question
Message #1 Posted by Bill Triplett on 19 Nov 2008, 10:18 a.m.

If you start with all alphanumeric variables empty, I noticed that other CAS based calculators can be made to display their internal equations for trig functions. Does anyone know how to make the HP-50g do the same thing?

I asked this question a while back, and one response was to use the "trig" function. I read the manual, and I tried the trig function in every permutation I could think of. Obviously someone much smarter than me will need to explain the individual keystrokes, and any necessary mode settings.

Anyway, as an example, using a Casio ClassPad, on the main screen you can type cExpand(sin(a+ib)) where "i" is the square root of negative one. The ClassPad responds with cosh(b)sin(a)+i*sinh(b)cos(a).

The TI-89 is simpler. You don't need to use any special wrapper function like cExpand(). You just type sin(a+ib) and hit enter. The response is sin(a)cosh(b)+cos(a)sinh(b)i.

The same thing is true for the gray TI-nSpire. The nSpire seems to have the easiest interface for such work, because it has a dedicated "i" button, along with a dedicated "a" button and "b" button. You just type the expression, and hit enter without pressing any special shift, alt, alpha, or control keys.

I dearly hate the way the nSpire has been lobotomized to prevent programming anything with graphics, and I believe TI could easily make more money by correcting this marketing mistake, at least in the CAS version of the machine. Ugh. I should probably restrain myself ranting about that on a tangent.

I like the display clarity of the HP-50g better. Yes, even with fewer pixels. The display is easier to read, and the machine's interface it is easier to use for many common operations that make up the mainstay of daily work. I would just like to understand the 50g machine's CAS system better.

Bill

      
Re: HP-50g CAS question
Message #2 Posted by V-PN on 19 Nov 2008, 12:38 p.m.,
in response to message #1 by Bill Triplett

[TRIG] [NXT] [TEXPAN] and go back using [TCOLL]

            
Re: HP-50g CAS question
Message #3 Posted by Bill Triplett on 19 Nov 2008, 1:37 p.m.,
in response to message #2 by V-PN

That was helpful. Thanks. I had my HP-50g set to use vertically scrolling menus, so I had to access the texpand() function by using slightly different keystrokes. Using texpand shows that the HP-50g uses this internal equation:

sin(a+ib) = cos(ib)sin(a)+ sin(ib)cos(a)

This statement is true, technically, but we are still forced to do a bit of algebra so that we can get an expression for the real part that would be distinct from the imaginary part of the answer.

I am even more interested in knowing what equation the HP-50g would use internally for this expression:

ln(a+ib)

This is not a trig function, so we cannot use texpand.

The other three CAS based machines all respond with

ln(a^2+b^2)/2

for the real part of the answer, and

(signum(b)*pi/2 - arctan(a/b)) * i

for the imaginary part.

Perhaps for the HP-50g there is some function other than texpand that we can use in order to make the machine provide a symbolic result in this case with the ln() function?

I am not interested in functions beyond this one, just mostly curious to see whether the HP-50g also uses a hard coded pi constant as a part of its internal equation for complex logarithms.

Bill

                  
Re: HP-50g CAS question
Message #4 Posted by George Bailey (Bedford Falls) on 19 Nov 2008, 2:24 p.m.,
in response to message #3 by Bill Triplett

Try [LS][EXP&LN][TSIMP]

                        
Re: HP-50g CAS question
Message #5 Posted by Bill Triplett on 19 Nov 2008, 3:07 p.m.,
in response to message #4 by George Bailey (Bedford Falls)

The tsimp function produced a real mystery, or rather, an imaginary mystery.

The result was ln(a^2+b^2)/2 for the real part, so far so good.

I had (atan(b/a)+ 0 * pi/2)i for the imaginary result.

I wonder why the machine would just insert a zero into the expression for the imaginary part like that, instead of displaying some variation of a signum function.

Oh well. At least now we have a clue. It looks as if the machine probably uses the same internal equations as the other three CAS systems, but it does not seem quite as easy to display the general forms of the equations.

I would be curious to see whether some arcane incantation with mode settings might cause the machine to display the result without the zero inserted. I have complex mode turned on. The zero appears in the imaginary part of the result in approx mode, and when not in approx mode.

Thanks,

Bill


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