31 replies to this topic

[epaloco]

While I was studyng with a friend I tryed to integrate this expression and I noticed that memory error,and crash of the calculator happens...

try this...integrate

(1-i)/((x+(1-x)i)^2 between 1 and i

ti89 gives 4/5 + 2/3 i
casio crash!!!!

another big problem wich is worst!is that it gives WRONG RESULTS!!!

the result of integrating the expression....


(1-(1/2)cosx)/(1-cosx+(1/4)) between 0 and 2Pi is Pi with the AFX

AND THE REAL RESULT WITH TI89 AND WITH COMPLEX ANALISIS THEOREMS APPLIED IS 2Pi.


SO PLEASE IF ANYONE KNOWS WHAT IS WRONG HERE PLEASE TELL ME I?M BEGINING TO DESESPERATE!!!!



Since this I?ve lost my trust in AFX!!!!I don?t know if my results are right or not!!!

WHATS HAPPENING!!!!

[BiTwhise]

For the seccond question
Ti has the right answer

The general integral will evaluate as:

x/2 + invTan(3 tan(x/2) )

as you can see, this is undefined at x = pi, or x = pi + 2k * pi

at x = pi, this will drop from undef (well, actually pi) to 0

quick evaluation of this graph shows that it's only valid for representing a fixed integral in the range pi < x < pi

since the AFX doesn't take this into consideration, but evaluates it normally (by substituting start and end points into the integral expression), it produces errors..

you see it yourself, if you were to substitute x with 2pi, the expression evaluates as pi (and for 0, it evals 0), so pi - 0 = pi

what you will need to do, is add pi (since it drops pi down) to the integral for every 2 pi, from and including x = pi


The AFX isn't too good at evaluating these things, so I would trust the TI more if I were you

I tried on the Classpad Emulator, and it seems to prodece the right answer, so they have improved the CAS a bit



As for the first one my Classpad emu gives the answer as:
4/5 + (2/5) i

(this answer is also obtained on the AFX, if you first cExpand the expression)

[epaloco]

thanks very much for your support bitwhise...!

I?ll take your advice..

And tell me where could I download the classpad 300 emulator?

byebye


epaloco

[BiTwhise]

The ClassPad Manager was available for download at www.classpad.de

For some reason they've taken the link away,
but the file is still hosted

So, here the direct link to the file: ClassPad Manager Setup

Note: It's a limited version of the Manager, in that it doesn't support all the features of the real counterpart. The final version, shipped with the calculator will.
The Manager will also be the communication tool between the computer and the calc (check out the manual)

[XYZ]

I am very disappointed with the AFX CAS...My ti-92 evaluates lin(-oo) to equal oo+pi.i whereas the afx2.0+ says it is just oo.....This is WRONG!
(At least that's what my calculus professor said, and I've verified the ti-92 answer)

[X-thunder28]

So you have to verify that you type correctly ( check brackets, for example), because I, I don't have any pb with CAS !

[BiTwhise]

So you have to verify that you type correctly ( check brackets, for example), because I, I don't have any pb with CAS !

It has nothing to do with mis-typed brackets

The Casio CAS is simply not as advanced as the TI one

[XYZ]

It just feels like such a beta-ish release to me. In fact I got so annoyed with some of the things the CAS did and didn't do (and indeed other AFX applications) that I've jotted down a whole page of complaints about it. I might send it to Casio, and perhaps they'll employ me as a design consultant to test future calcs

If there's a bug in a piece of pc software its not so bad, a new version can always been downloaded easily. But it's a different story with embedded software, if the thing doesn't know that ln(-oo) isn't actually defined for real numbers it should just say it's simply not defined rather than give a false answer.

[BiTwhise]

it seems the afx assumes 'oo +/- whatever = oo'
same for 'oo +/ whatever*i = oo'

makes for some strange answers, like your examples shows

[XYZ]

How it should be:
oo+/- real should=oo
oo+/- imag=oo +/- imag
oo-oo, oo/oo not defined
etc...

AFX
oo+i=oo
ln,log(-oo)=oo But as we know the log function isn't defined for -ve numbers so must have a complex solution if any.

AS another example, taking lin(i)=(Pi.i)/2 is fine (this is done in radian mode), but for ln(oo.i) it spits out oo again where it should be oo+(Pi.i)/2........

I would be very keen to hear what your lecturers/teachers have to say about this. Granted, we don't often need to take the log of -oo but when we do it should give a logical answer based on (for instance) Euler's exponential law (I forget exactly what it's called) which says that r.exp(i)=cis(theta)

[BiTwhise]

all these errors are due to that it assumes oo+i = oo

[XYZ]

The fatal mistake: assumtion.

I tried that integration as well (AFX2.0+) and got a totally bonkers answer.
integral((1-i)/(x+(1-x)i)^2,from 1 to i)

gives back the question (ie can't integrate) but changes the sign of the lone x in the denominator!! So it's answer is:

integral((1 - i) /(-x+(1-x)i)^2,from 1 to i)

If I do this:
integral((1 - i)/ (x+i(1-x))^2,from 1 to i)

answer is zero...

If I first expand (1-x)i:
integral((1 - i))/(x+i-xi)^2,from 1 to i)

the answer is 1/10-i/10

Nomatter if I expand the (1-x)i first or not, my ti-92 consistently gives 7/5+i/5+(1/5+3i/5).i which expands to 4/5+2i/5.....

As for integral((1-(1/2)cosx)/(1-cosx+(1/4))) from 0 to 2Pi my afx also gives pi in CAS, but numerical integration gives the correct answer, 2pi.

I am beginning to think there is a rather sleepy Homer Simpson inside there pressing random buttons!!

[BiTwhise]

I explained those results in my first reply..

You have to use cExpand to make the integral work

I also explained the seccond integral, from 0 to 2pi



The CAS is limited, but doesn't have all that many failures as you claim.
It's when you analyze the answers you see that the errors come from it's limitations, and not random assumptions


-- EDIT --
Just sent an email to Saltire about some of these issues

[Casto Productions]

Doesn't the site has a downloadable upgrade to the cas software? I thought they had a couple upgraded programs like algebra2 and things like that. Maybe they fixed a few of those problems and limitations with the software here http://www.casio.co....sources/add_in/.

[XYZ]

I don't agree that it is purely a limitation BitWise. My fx100w scientific calculator cannot raise e^i and gives an Ma ERROR. This is a limitation - it doesn't pretend to be able to do something when it can't, consequently giving a wrong answer.

By the distributive law, (1-x)i = i - ix and there is no reason why CAS should treat the two quantities any different (they are the same are they not?), whether it works with cExpand or not, the CAS IS flawed. I'm following up this argument because I think it is important - I've paid a lot of money for something that hasn't had all of its creases ironed out yet. This is akin to buying a new car whose headlights only work when it's raining/on the main road/parked in your garage. It's fine to use the calc for just playing games on, but I actually bought it to USE.

Good on you for contacting Saltire, I'm keen to hear their reply.

PS:
Casto Productions - I have a 2.0+ which is supposed to come with algebra2 and the revised CAS pre installed...

[BiTwhise]

integral((1-i)/(x+(1-x)i)^2,from 1 to i)

gives back the question (ie can't integrate) but changes the sign of the lone x in the denominator!! So it's answer is:

integral((1 - i) /(-x+(1-x)i)^2,from 1 to i)

I don't know how you managed this, but it does NOT change the sign of the lone x....

If I do this:
integral((1 - i)/ (x+i(1-x))^2,from 1 to i)

answer is zero...

again, I don't know how you got that answer.. manual substitution doesn't work unless you first cExpand your expression

If I first expand (1-x)i:
integral((1 - i))/(x+i-xi)^2,from 1 to i)

the answer is 1/10-i/10

Same with this

As for integral((1-(1/2)cosx)/(1-cosx+(1/4))) from 0 to 2Pi my afx also gives pi in CAS, but numerical integration gives the correct answer, 2pi.

I believe I explained this quite thorough in my previous reply..

My fx100w scientific calculator cannot raise e^i and gives an Ma ERROR. This is a limitation - it doesn't pretend to be able to do something when it can't, consequently giving a wrong answer.

The AFX can do e^i...
Anyways, there's a big difference in how numerical software evaluates expressions, and how algebraic software does it. If you still are reffering to your logarithmic errors you recieve when dealing with oo, those are all root in the same error..


We can all agree the CAS is limited, and has a few fatal assumptions. These errors are really not acceptable for a calculator, but once you know about them you can easilly avoid the bogus answers (cause it does not generate wrong answers at will)
If not for anything else, at leaste the Casio CAS makes you think

[XYZ]

Yes thanks for your in depth explanations
My point is this just isn't acceptable...
Believe it or not the sign sign did change for the integration! I'll tell you what software version I have soon. It may be a bug introduced to the 2.0+ CAS. My point about having to cExpand first was that CAS doesn't seem to have heard about order of operations. Actually I don't see how even that could affect it but I was as surprised as you about the answers I got!

[BiTwhise]

I got a reply from Saltire

Quoting some key parts:

Thanks for the input. Saltire developed the original CAS for Casio, but Casio has taken over development of the CAS for the past few years.

I've responded with my opinion to each issue below. I've also forwarded your email to the developers at Casio.

I'm happy at least they seem to care.. this is more of an answer than I ever got from Casio

About infinity and imaginary numbers

You are correct, and Casio is correct. infinity is not a number, but a limit. As the real part goes towards infinity, the angle between the real and imaginary parts tends towards 0, thus the limit goes to infinity.

limit(ln(-x),x=infinity) --> infinity

Because infinity is actually being treated like an extended number though, I believe you may be correct. infinity+i*pi can be considered to be the same as infinity MOST of the time, but not all of the time. Any time the pure imaginary component is used exclusively, I believe Casio will give the wrong answer.

limit(im(ln(-x)),x=infinity) --> i*pi

...but Casio returns...

limit(im(ln(-x)),x=infinity) --> 0


I do not think this is easy to correct through, because it is an underlying assumption used by the CAS. If it is changed, many integrations and limits may break.

If Casio does make this change it will take a large amount of re-testing and corrections to other parts of the CAS.

An expected explanation

The rest was all about how the other errors were fixed on the Classpad, but they didn't know if they could do the same on the AFX due to memory constraints..

i.e, the integral of (1-(1/2)cosx)/(1-cosx+(1/4)) , in the range 0 to 2pi:

This problem has been fixed on the Classpad. Due to memory constraints is may take time for this fix to work its way into the FX.

the fact that it doesn't manipulate or rearrange expressions automatically to solve them

This has been improved on the Classpad. It is possible that for now, this improvement might not be added to the FX due to memory constraints.

[Casto Productions]

About the classpad....
I read what was on the official casio site about the newest calc but I was wondering if anyone had any real dealing with an actual unit. It says something about 500k RAM and 4MB flash availible. But did Casio break the flash memory into chunks again instead of simply having the OS handle the memory allocation? And half the buttons of a normal calc aren't on the main body, so are most commands through the touch screen and drop down menus?

[Killer83Z]

Yeah, I think they made a big mistake making the keyboard go touchscreen. The classpad is more pda than calculator.

I'll get a TI-89...

[AlephMobius]

I dont like the classpad either. TI-89 is a good choice. I think im gonna get an HP-49g before long.

[Killer83Z]

I'm waiting for both to get cheaper on ebay.

[XYZ]

Why not get a 92? I've got one and the qwerty keyboard is a godsend. It is damn big so not so good for carrying around in your backpack though...
Large screen is good too.
The whole 92/89 OS is really intuitive, its great. I wouldn't mind trying out a 49g too. One day when prices eventually fall...

[AlephMobius]

TI-92s are big, clunky and ugly. TI-89s look a lot better. If you are gonna get a TI-92 just go for the Voyage 200. I have the HP-49g emulated, it is nice and much quicker than the HP-48gx.

[Casto Productions]

The TI-92's can be spotted by a teacher a mile away as well, much easier to sneak a TI-89 past on a test.

[AlephMobius]

I have heard of people who take 83 and 86 cases and put them on TI-89 internals so they can use them on the SAT.

[CrimsonCasio]

the fools, there is nothing on the SATs that could merrit the use of a CAS, its the ACTs that it could be usefull on... the ironic part is that the SATs allow the use of an AFX while the ACTs dont.

[XYZ]

Ha, if you are the sort of person who survives math by using a CAS and can't differentiate on your own you probably shouldn't have one
I use cas for checking whether my solution to things like f'''(x) is correct late at night when I'm dropping off to sleep and can't read my hand writing any more!

Peace

[BiTwhise]

Totally agree

-- EDIT --
@Crimson:

Ok, it's a two word post

But it's a reply to xyz, and a statement to show that my opinions is the same as that of his

I can agree it's not particularly contributing to the subject, but it is contributing to any coming debate obout the purpose of CAS and my stand point in such a debate

However, you have point, and I'll try to get my act together

[CrimsonCasio]

um, bitwise... your setting a bad example, were telling people not to post like that and here you go with a two word post...
I'll leave it to you to edit or delete.



On topic: you have to remember that even though a person may be able to do something without a CAS it is sometimes faster to do it with, that I can understand.

--EDIT--
good, we have to set a good example. Also, I really don't want to see Mohamed explode and kill you .

[Killer83Z]

Two word posts are great. I totally agree as well.

[CrimsonCasio]

I serriously doubt that you'll find any dissention amoung present company, unless someone just feels like starting an argument