Yuku free message boards

Some calculator trivia: I believe the TI-89 has a CPU that's in the same family as the Genesis's CPU (Motorola 68000), but the TI-89's is a 32-bit version.

And I heard the HP 33s has a CPU similar to the NES's, the 6502 (but I heard the NES's was a custom version of that chip).

Okay, I tried entering just "123456789" with the two thumb method (generally, I'd hit 1, 4, and 7 with my left thumb, and the rest with my right) as fast as possible on a TI 36 and my Casios, and every time (so I can discount the possibility that I, rather than the calculator, missed a button) the TI 36 missed a number of the keystrokes, while the Casios always got every one (and in the right order, too, of course).

But in a way this could just prove my point, since a) everyone knows that (at least at the low price range) Casios are better than TIs and b) there still exist today calculator keyboards that can keep up with whatever demands you can make of them.


Another thing about these keyboard complaints is that they seem so inconsistent that I'd guess people would never be happy with whatever comes out now. Example: I guess the HP 49G had a keyboard similar to what you'd find on non-HP calculators. It got tons of complaints of being "too mushy". So then the 49G+ had much firmer keys. And everyone complained that they're too firm.

Okay, yeah, I know that there can be middle ground (and the 49G+'s keys are really firm. Someone compared pressing them to popping packing bubbles). But, firstly, I think that trying to pound the 49G+'s keys as fast as I pounded other calculators' keys would be really stupid (who would use a calculator like that for fast number crunching, when like 98% of a graphing calculators functions are accessible only from menus?) Complaints about the keyboard breaking would be more serious complaints than the keys' tactile response, but I wouldn't be surprised if the people that have broken keys have been pounding them.

Secondly, I think even for cases in the middle ground, people would complain. The BA II Plus Professional has firmer-than-average keys, while still being nowhere near as still as a 49G+'s. Yet if you go to a place like Amazon.com, you'll still find complaints that the keys are impossible to press.

Yay! I finished writing my first RPL program. It's yet another program that solves the cubic equation. The input is a,b,c,d, where the equation is ax^3+bx^2+cx+d=0. Here's the program:

%%HP: T(3)A(R)F(.);

\<< \-> A B C D

  \<< D A / B C * 3 A SQ * / - 2 B 3 ^ * 27 A 3 ^ * / + A B C D

  \>> \-> N A B C D

  \<< 3 A * C * B SQ - 3 A SQ * / A B C D N

  \>> \-> M A B C D N

  \<< M EVAL 0 SAME M EVAL 0. SAME OR

    IF

    THEN N 1 3 / ^ DUP DUP '-1/2+i*\v/3/2' * SWAP '-1/2-i*\v/3/2' * ROT B 3 A * / - 



ROT B 3 A * / - ROT B 3 A * / - ROT

    ELSE N SQ 4 M 3 ^ * 27 / + \v/ N - 2 / 1 3 / ^ DUP DUP '-1/2+i*\v/3/2' * SWAP '-



1/2-i*\v/3/2' * ROT DUP 3 * M SWAP / - B 3 A * / - ROT DUP 3 * M SWAP / - B 3 A * / - 



ROT DUP 3 * M SWAP / - B 3 A * / -

    END

  \>>

\>>

The downside of programming in RPL is obvious: If you don't know the language, it looks incomprehensible.

There are quite a few things I like better about this program than the program for the TI89. First, you could take that text there, right from the message board post, and upload it with ASCII transfer mode directly to a 49G+. I don't think there's any way of doing that with the TI89.

Also, that program both works with symbolic or numeric entries, and it leaves the result (the three roots to the equation) on the stack. You can do one or the other with the TI89, but not, as far as I know, both.

Going back to the original problem that started this thread, solving Z = log Z, or Z = e^Z, I just figured out a better way of solving it with this calculator. You only need to enter one short line:


ln Abs Ans + i arg Ans

Then hit equals to make it converge.

One advantage is probably obvious: It takes many fewer keypresses to enter this. (The disadvantage is that the solution converges slower this way, but I still think it's easier to repeatedly hit Enter than different buttons, where mistakes are more likely to be made)

Other advantages:

The other solution needs to be very close to the correct answer to converge. Something like 5 + 5i as an initial value will diverge. This solution is very independent of initial value. You can enter something ridiculous, like 5e20 (1 + i) (or even a real number very close to zero) as the initial value and it'll still converge.

Also, it can find other solutions to the equation quite easily, by exploiting the exponential function's period of 2pi i.

For example, change the line to

ln Abs Ans + i arg Ans + 2 pi i

and you get the solution

2.06227773 + i 7.588631178

By the way, the 49G+ does seem to be a bit more powerful with evaluating integrals than the TI89.

For instance, that integral site randomly spat up

1/(x(a^2-x^2)^(3/2))

and the 49G+ could do it and the TI89 couldn't.

I've summarized their performances before (if only in my head) by saying three out of four times, the TI89 is easier to use; but three out of four times, the 49G+ is more powerful.

The exception here is that the TI89 has an easier time with

1/(x^5-1)

which it simply does. The 49G+ can't do it in exact mode without coaxing (a human should instantly notice the denominator can be factored as (x minus the various fifth roots of one), and then partial fractions can be applied. I think if you feed the 49G+ a suitably factored form, it might be able to get the answer.

Alternatively, it can do everything itself in approximate (and complex) mode, but the roots of one will be numerical.

For some reason 1/(x^7-1) is hell on the TI89. I tried it in an emulator, which can run faster than a real TI89, and it still just runs and runs... (it may eventually solve it, it might not)

In approximate mode, the 49G+ does it instantly... I've tried up to x^11, which is also done instantly. Oddly, in approximate mode, the TI89 doesn't even seem to try these integrals, not even the x^5 one.

I've been musing about the 49G+, and how I said that 3/4 of the time, the TI89 is easier to use.

I'm starting to doubt that. Is the TI89 easier to learn to use? Oh, yeah, without a doubt. Learning RPL is much more difficult than TI Basic (and it might even be more difficult after you learn it, but it can also do things TI Basic can't. The main thing I think RPL is lacking is a built in simple way of commenting. I guess you could just put comment strings into the program, and then delete them as soon as they get put on the stack, but that's inelegant). When I first messed around with the 49G+, I kept getting stuck without being able to figure out how to back up. That's because the 49G+ doesn't have an ESC[ape] button (it turns out that pressing the On button usually functions the same way). And the 49G+ has some weird commands. RISCH for indefinite integration? (Though you can use INT or INTVX) And you have to use one of the text commands, rather than the integral symbol, to do indefinite integration while in equation writer mode?

But there are a lot of things that make the 49G+ easier to use.

Foremost is the Equation Writer. When I first read about it, it seemed like a ridiculous Mickey Mouse feature. Indeed, using it to enter "1 + 2" would be foolish. But for complicated formulas, and in particular for complicated formulas with parts that have similarities (say, a huge expression repeated, but with + rather than -), it's a godsend. It's also easier to look at formulas (say, results the calculator spits out) with it than with the TI89. You can scroll it faster, and you can scroll it more vertically (if an expression takes up too much space vertically on the TI89, you won't be able to read it off with the "pretty print" feature; you'll have to paste it onto the formula bar and scroll through it).

And the normal formula entry area has some advantages, too. It isn't confined to one line, which means it looks much uglier than the neat TI89. But that makes it a lot easier to move through, since you can move through lines to advance quickly. I am kind of annoyed at the TI89's lack of a jump feature in the entry line (you can only jump straight to one end or the other; you can't jump ahead, say, twenty or forty characters). Also, the 49G+ automatically pairs parenthesis, so remembering to close them is a lot less tricky. When you get a warning on the TI89 that one isn't closed, you'll have to carefully search to find out which isn't paired.

They even put some thought into the alpha lock mode. With the exception of z and divide, it's possible to use all letters, numbers, and arithmetic functions at the same time while in alpha lock mode. This means less mode switching than on the TI89.

So, how can I justify my original statement? I don't know if I can; I'll have to think about it more. I do like how it's easier to keep the TI89's memory clean. If you know you tend to use single letter variables for temporary things, the "NewProblem" function can clean out junk quickly and easily. The 49G+ can get clogged with variables, since even functions for graphing get stored among the other variables. It's also sort of nice to have 4 variables available unshifted on the TI89. The 49G+ just has the main variable ("X") unshifted; it does, however, have the trigonometric functions unshifted (unlike the TI89) (which I still probably don't use as much as the other variables). But another thing about the 49G+'s keyboard is that so many keys (or shifted keys) just are for menus, and menus that are in fact just subsets of the general "CAT[alog]" menu. I guess it's nice to have some functions grouped together in one small menu (in particular the programming functions) but I tend to just use CAT more than some of the more specialized functions. Also, CAT isn't even a face button; it's a shifted function of SYMB[ol].

On the other hand, the 49G+ has a "user keyboard" where you can define any key (even shifted) any function. I'm apprehensive about using that, though, because it's theoretically possible to fuck up the calculator by getting rid of some important function (maybe like the ability to turn the calculator off and on) and also getting rid of the function that redefines the user keyboard (so you can't fix it). I think you might be able to still fix that with the reset button, but I'm not sure.


I guess all this is just to say that I'm exceedingly impressed by the 49G+. (I'm still very impressed by the TI89, too)

I downloaded the Casio Classpad emulator and tried screwing around with it a little bit.

I guess it's probably Casio's highest-end graphing calculator (I don't know if Casio has any current calculators nearly comparible to it, though supposedly the Algebra FX 2 had a Computer Algebra System. I'm not sure how good it was, though), intended to compete with (say) the TI89, plus it has the gimmick of having a touch screen.

So, in broad terms, it can do many of the things the TI89 can do: Symbolic manipulations, 3D graphing, geometry (actually, not packaged with the TI89, but now TI has it available for download for free), statistics, programing, USB connectivity, etc., etc.

I just tried a few problems to test the CAS. It was able to integrate (2x^2 + 1)*exp(x^2), which the TI89 actually couldn't do (though the 49G+ could). But it couldn't integrate sin(x^2) + 2*x^2*cos(x^2) (though no other calculator can, either).

Oddly, it also couldn't integrate 1/(x^5-1) (The TI89 can do that in exact mode, the 49G+ in approximate). A human should be able to just look at it and know what to do.

I tried taking the composite of the function

f(x) = a*b*x/c + a*(a+1)*b*(b+1)*x^2/(2*c*(c+1))

with itself. (The function is the hypergeometric function, minus the constant term). The TI89 and 49G+ can do this. (But they both have trouble if you add the hypergeometric's x^3 term; actually, they try and try for many minutes, and I eventually just cancelled the operation to save the batteries. Maybe I should try that on an emulator sometime).

Anyway, it immediately said it was out of memory. So I guess the Classpad had less memory for symbolic manipulations than the TI89 or 49G+. But so far, I haven't done any other symbolic manipulations that exceeded the limits of the machine.

Actually, the calculator doesn't let you just enter f(f(x)). It says that's a "circular reference". So, you'd have to take what f(x) equals, and paste it into f( ). Weird.

3D graphing seems pretty fast, but I'm not sure how much faster the emulator is supposed to be than the real thing. (Some other calculator emulators let you run them at real speed, or faster).

I haven't screwed around with too much else yet. It seems to have something similar to the 49G+'s equation writer, but sort of crossed with Microsoft's equation writer. I guess that'd be something that'd be good to compare, though it might be better to try to come up with a real problem to use it with.

One thing that occured to me is that I could try the ClassPad with some homework assignments from last semester that I used my other calculators to solve before.