algebraic simplification on the 50G



#2

Hi folks,

Please consider the following expression:
cuberoot(a^2 * b) * cuberoot(a^4 * b)
which algebraically simplifies to:
a^2 * b^(2/3) (a squared times b to the two thirds)

simplifying this expression with my 50G I get:
(exp^(ln(b)/3))^2 * (exp^(ln(a)/3))^6

(this is obtained using the SIMPL function in the editing environment). Using the EVAL function leaves the original expression untouched


is there no way to obtain the simpler algebraic results, rather than the results containing the natural log terms on the 50G?

Have tried all the pertainent flag settings to no avail, and I can't seem to find detailed info on each system flag in the UG.

Perhaps I should be using a different function?


Any help appreciated. Hal


#3

Best I can do is as follows:

- enter the expression: cuberoot(a^2 * b) * cuberoot(a^4 * b)

- then go to the ALG menu: [right-shift] 4

- then LIN, LNCOLLECT, EXPAND (or F5, F4, F2)

That should get you to:

cuberoot(b^2*a*6)

Can't get the further simplification to a^2 * cuberoot(b)

**********

However, if you enter the same expression initially as:

cuberoot (a^2) * cuberoot (b) * cuberoot (a^4) * cuberoot (b)

then it simplifies to the desired form with two EVALs

Edited: 26 Aug 2008, 6:06 p.m.

#4

Hi Hal!

One possible way to get not exactly what you want but perhaps close enough for you.

First of all switch to complex mode, or each variable will be put in absolute value marks (||). You could still remain real mode if you add the assumptions a>0 and b>0 before you go further, but it is cumbersome to remember all assumptions, and that could cause problems at some later time when you work again with a, b, and so on.

Now, with your expression in stack level 1 issue the command SIMPLIFY, which should return: (EXP(LN(b)/3))^2*(EXP(LN(a)/3))^6.

Now issue the command EXP2POW which should have the grace to return: (XROOT(3,b))^2*(XROOT(3,a))^6 .

Finally EXPAND this to get: a^2*(XROOT(3,b))^2

Hope it was good enough.

Cheers!

Nick

P.S.: At last something else in this forum than the eternal boring holy cows of the "applications" of a... paleolithic 4 stack level "number cruncher"! Thanks a lot for that Hal!


#5

Gee, thanks Nick. Well, once the comet arrives, the ecosystem will be unfettered by many of the 4 stack genus. Then the small furrry critters can come out to take over the world. ;)

P.S. last time I checked, it *was* a museum site. Isn't that where we find paleolithic specimens?

Except for me, of course. I was recently thawed out.

-MikeO


Edited: 26 Aug 2008, 7:18 p.m.


#6

Mike, what can I tell you..

As I already said to George, the 48 is already in the museum, next comes the 49s and the 50s and the "enhanced" versions of the 48s in all their pretty variations. And after these machines we wait some years more and the museum says then, "the successor was the HP35S with its LBLs, and XEQs and whatever". That's not even turning yesterday to today. That's turning yesterday to today *after* there has been tomorrow, isn't it?

Not much better in other forums too about the real flagship. They discuss most of the time about how to use this or that font, or how to enhance the built-in filer, and similar nonsense. Questions about the CAS? Anything about how to use the CAS in some really advanced way for solving a mathematical problem? Any kind of news about using the already powerful command set for constructing another even more powerful set of CAS commands? Nooo, forget that! We want LBLs and XEQs or fonts and filers. And so, this is all what we will remain with. While the world passes us by at the speed of light!

We had the possibility for getting the next CAS-calculator and what did we do? We threw it away by insisting on a resurection of the dead. So, when the museum is going to expose the HP35S *after* the 49s and the 50s we will still dream of that "golden past" and its strange and nowadays completely dead LBLs and the like? Unfortunately past is past and dead is dead, ey?

But OK, if somebody demands to sit down and re-re-re-cook the same old algorithm in yet another new flavor of the same old cold soup, it really doesn't matter at all to anybody. The world doesn't sit and wait for "HP-classics" or any other myth.

Cheers!

Nick


#7

Hi Nick,
Well, all (or nearly all) kidding aside, I completely agree with you on many of your points.

I do think the HP35s serves a useful purpose for those who need quick, pre-defined, calculation functions. The programming model is archaic, but, in modern terms, it's merely a macro keystroke language (KSL). Memory and CPU is now cheap enough to allow both approaches, RPL, and KSL, on a single platform. Why not? This approach is akin to having Shell interpreters and C++ on the same platform. Each language has its uses. Talk about the future being the past again!

Yes, I agree. Let's have more discussion of problem solving! I'll do my best to bring up some interesting questions as I work towards my graduate degree in applied mathematics.

Regards,
Mike OShea

#8

The sequence SIMPLIFY, EXP2POW, and EVAL did the trick for me.

Note that SIMPLIFY and EXP2POW are both in the CONVERT REWRITE menu (or left-shift 6, F4). EVAL of course is on the keyboard.

It worked for me in Real Mode, with "Simp Non-Rational" checked in the CAS mode.


#9

Yep! Thanks a lot for that, Norris!

The identical work of EXPAND and EVAl in this case saves some key-strokes and that's always good!

Cheers!

Nick

#10

The TI NSpire gives you this.


#11

Quote:
The TI NSpire gives you this.

Indeed, as does the TI 89 emulator.

Best regards, Hal
#12

Quote:
The TI NSpire gives you this.

The real TI89 Titanium does it right after entering the expression and pressing Enter - without any further need for any search in menus or such!

I'm also pleased to see some CAS problems posted here. An inspiring mix with paleolithic stuff would be best! ;-)


#13

George, how do you do that on the Titanium? I can't find a symbol for cube root, and raising the expression to the 1/3 power does not seem to work for me.

#14

OK, I must have been doing something wrong. I did get it to work using raising to the (1/3) power. Is there a cube root symbol on the Titanium?


#15

While we're finding keys on the TI-89 / (titainium), where, pray tell, are such staples as 10^x, log, and 1/x ?

regards, Hal


#16

Quote:
While we're finding keys on the TI-89 / (titainium), where, pray tell, are such staples as 10^x, log, and 1/x ?

regards, Hal

LOG(, 10^( and ^-1 (=1/x) are in the CATALOG.

For what you don't find there, you may use the STO function to store DIY functions. Like so

y^(1/x) STO xroot(x,y) (DEFINE will do something similar)

Then type the function in ALPHA mode or retrieve it with [2nd][Var-Link].

If you type xroot(3,8) you will get 2 as an answer.

(Paraphrased from the manual)


Edited: 27 Aug 2008, 2:04 p.m.

#17

George, auto-simplification is not necessarily a "universal advantage". I would also really really prefer the easy way of the Titanium many times, but there are also many other cases.

Many too many problems and ways to solve them are much better understandable, or say "visible", when such expressions are not "simplified" down to the most simple level. Which of course auto-generates (;-)) the question about what simplification actually is. It seems to depend on the problem one works with. Perhaps the best compromise is to leave the entered object unchanged and at the same time provide good commands (and also manuals! ;-)) for manipulating it easily and correctly in any possible mathematical way? A hard problem.

As about the paleolithic, well, the HP48 is already in the museum, isn't it? So, guess who's next! ;-) Perhaps we are only just a bit ahead of that time when we talk here about EXP2POW and SIMPLIFY, ey? But soon the 49 and the 50 are to follow. And then... after that... what? Perhaps... exposing the HP35S and the fantastic achievements of developing software for (solely) number crunching using LBL A, and XEQ, and RTN?? Will *this* be the exposed piece of top calc technology after the HP50? What else are we going to hear on this world?

Admitting that a museum has to come up with things as they have been in the past, which of course is extremely interesting for itself, I start having a very strange by-taste that the once pioneering community of HP-enthusiasts has converted to something like a diva on her 90th birthday who simply can't accept that she isn't 20 anymore. Yes, we might have been up to the limit once, but the limit didn't wait for us. It didn't even care! And why should it? Time has no contracts with HP or anybody else. Now it is the year 2007 where we live and not 1970. This steady "glorification" of "those wonderful HP-machines" is nothing else than trying to reverse time where it once has been when "I was ooohh so young and enthusiastic".

The question is if I can still be that in *my* days.

Cheers!

Nick


#18

Nick;

while I agree with most of what you said, I had a good laugh at this:

Quote:
Message #15 Posted by Nick on 28 Aug 2008, 10:27 a.m.,

Quote:
Now it is the year 2007 ...


#19

Gasp!!! At the end perhaps I also long for yesterday?? Or perhaps I didn't notice that time was passing by while I was preaching, ey? ;-)

Cheers!

Nick

#20

Gentlemen, as always, thanks very much. I'm honored to be in the company of such adroit minds.

Hal


#21

I tried the same (substituting cuberoot with ^(1/3)) on my Casio classpad and it didn't anything to the expression. Did I miss something?


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