# Calculator comparison

75 views

### Ross

Feb 17, 2010, 5:40:45 PM2/17/10
to tinspire
I am curious to know who created and posted the document comparing the
ti 89 and the hp 49. If at all possible, I would really like to see
how the TI Nspire CAS and the HP calcs perform in a competition like
that, as I hear that for really complex things, the CAS is
significantly faster than the TI 89. I believe one example was a
problem that took almost 20 minutes on the TI 89 while it took 47
seconds on the CAS.

### T Tran

Feb 17, 2010, 7:52:40 PM2/17/10
to tinspire
It's me who posted it.
Actually, the Nspire CAS derived from the CAS of the Ti-89 family,
thus, you would expect predictable behavior between the two.
However, Nspire CAS has been improved over time.

For example, in arithmetic calculation, we see that

HP 50g (OS 2.09 2006) still takes the lead.
It can compute 99999^999 and display every single digit without
scientific notation.

2nd position.
It can compute 99999^198 without scientific notation.

Ti-89 Titanium comes last with 500^228
I have a classpad 300+ and Ti-Nspire CAS. I found myself using the
Nspire more than the classpad for quick calculation.

### Nelson Sousa

Feb 18, 2010, 5:39:55 AM2/18/10
that's not a very significant test.

I prefer to have them factor 2^67-1 to check integer arithmetic speed
and the taylor series of ln(sin(x)) around point 1 up to 5th order,
10th order, ... the expression grows immensely when the order
increases and you test both the symbolic manipulation routines and the
memory management of the operating system (by the way, I have no idea
how does the HPs behave with these two, I'm curious).

Having a calculator compute 99999^999 is only a matter of
specification: how many integer digits does it support. Not really
speed, algorithm sophistication or pure power. And on top of that,
having 999 digits instead of 610 of the TI-89 or 990 of the Nspire CAS
doesn't strike me as such an advantage.

Cheers,
Nelson

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### Joe

Feb 18, 2010, 7:22:32 AM2/18/10
to tinspire
Well said Nelson. Because of product differences, it is always
possible to design some obscure test that one product can do better
than another, but the results of an obscure test are not a rational
basis for deciding what product to buy and use.

> >http://lafacroft.com/archive/nspire.php- Hide quoted text -
>
> - Show quoted text -

### Andy Kemp

Feb 18, 2010, 7:27:29 AM2/18/10
Indeed on many occasions the best tool may not even be the quickest, or most powerful as the User Interface has a huge impact upon the usefulness...  An obvious example of this is the iPhone - less powerful than many smartphones I have owned, but still the best tool for most of the jobs I want to achieve becuase the UI makes things simple to do...

### supergems

Feb 19, 2010, 12:20:29 PM2/19/10
to tinspire
But the CAS of the HP 50g is more flexible ;-) .

supergems

### Luke Setzer

Feb 19, 2010, 1:37:09 PM2/19/10
to tinspire
The TI-Nspire CAS software for PC and Mac with files fully
interchangeable in native format to the calculator makes it an
immediate and easy winner -- no question -- no contest.

### Ross

Feb 19, 2010, 3:49:37 PM2/19/10
to tinspire
If you are going to talk about computer software, Luke, then I'm
pretty sure that Mathematica would win :)

### Andy Kemp

Feb 19, 2010, 3:53:31 PM2/19/10
Ross, you missed Luke's point he said having the software which was
compatible with the handheld.

Mathematica is great but doesn't run on a handheld.

Sent from my iPhone

### Ross

Feb 19, 2010, 8:56:01 PM2/19/10
to tinspire
I was trying to say that in a joking manner, because I did know that
he was talking about handheld compatible, but I also know that
Mathematica is the kind of the CAS world.

On 19 Feb, 15:53, Andy Kemp <a...@1kemp.co.uk> wrote:
> Ross, you missed Luke's point he said having the software which was
> compatible with the handheld.
>
> Mathematica is great but doesn't run on a handheld.
>
> Sent from my iPhone
>

### Luke Setzer

Feb 19, 2010, 9:16:03 PM2/19/10
to tinspire
What's nice about the dual platform is that mastery of one leads to
mastery of the other. Doing my homework on the PC software means
already knowing how to solve the problems quickly during the tests. I
can also keep homework problems on my calculator since most of my
professors are basically "out to lunch" when it comes to calculators.
Of course, time constraints make that clunky so I have to know what I
am doing anyway, but it is a reassuring feeling.

### John Hanna

Feb 19, 2010, 9:59:53 PM2/19/10
Someone posted a message about having a problem with >Frac and complex
numbers on the new TI-84 OS.

There is a known issue in 2.53MP that >Frac does not work with complex
numbers as on 2.43.

The workaround is to use imag(a+bi)>Frac and real(a+bi)>Frac.

John Hanna
jeh...@optonline.net
973.398.3815
T3 - Teachers Teaching with Technology

### supergems

Feb 20, 2010, 4:48:13 AM2/20/10
to tinspire
I would not be so sure! I rather think that the best solution is the
Casio ClassPad Manager and calculator ;-).

### Luke Setzer

Feb 20, 2010, 2:12:04 PM2/20/10
to tinspire
On Feb 20, 4:48 am, supergems <simone.cer...@gmail.com> wrote:

> I would not be so sure! I rather think that the best solution is the
> Casio ClassPad Manager and calculator ;-).

I just surfed their site and found it rather unfriendly compared to
the TI site.

### Joe

Feb 20, 2010, 2:17:04 PM2/20/10
to tinspire
:-)

### Luke Setzer

Feb 20, 2010, 2:17:08 PM2/20/10
to tinspire

It is also not allowed on the AP Calculus examination.

Bah, I say.

### Ross

Feb 20, 2010, 7:01:32 PM2/20/10
to tinspire
is the casio classpad a touch screen calc or something, because I know
those aren't allowed on any exams.

### T Tran

Feb 20, 2010, 9:01:24 PM2/20/10
to tinspire
Yes, the classpad is touch screen calculator.
I think Casio did that on purpose to prevent students from cheating.
We knew the case-swapping business in the old Ti-89 with Ti-83.

### Joe

Feb 21, 2010, 1:16:11 PM2/21/10
to tinspire
I think it is more likely that they wanted to use a more up to date
technology than the old 1990's style black and white screens. I
mention this because I avoided touch screen technology in favor of a
hard keyboard approach for quite a while. But now that I've used a
touch pad, I like it quite a bit. I can type words quite fast but I
never seem to get good at using the top row of keys with a standard
keyboard. Much to my surprize I found that I am faster with a touch
pad than a regular keyboard when using numbers and symbols.

> > > Bah, I say.- Hide quoted text -

### Nelson Sousa

Feb 21, 2010, 1:22:45 PM2/21/10
nevertheless, Classpad has a B&W screen and as far as I know it
doesn't even have grayscale. And with half the resolution of the
Nspire.
A bit last century if you ask me...

Plus, when I tried the Classpad the user interface was a bit hard to
use. Too cluttered and too many symbols for such a small screen. Touch
screen doesn't make up for that.

Nelson

### Joe

Feb 21, 2010, 7:37:10 PM2/21/10
to tinspire
If I can be allowed to reply, I don't recall any touch screens used on
comercial products in the last century, but perhaps that is just my
failing memory. Also, it is not fair to compare an old Casio design to
a new TI design, but honestly Nelson, don't you think the Classpad 3D
graphing is better than that provided by the nspire? And how about
the Laplace and Fourier transforms? Perhaps I shouldn't point out the
superiority of an older design, but what is the justification for
going from 3d graphing on the 89, to no 3d graphing on the nspire/
nspire cas? Is TI under the impression that they don't need a
superior product, that they can sell anything based on their name and
reputation alone?

I am aware that the site moderator/censor doesn't like controversial
posts like this, but it needs to be said none the less because it is
the truth regarding these and other features such as ease of
programability, and now I'll shut up for a while knowing that
ultimately the market place will pronounce a final judgement on such
things.

> >http://lafacroft.com/archive/nspire.php- Hide quoted text -

### supergems

Mar 24, 2010, 4:40:41 AM3/24/10
to tinspire
The FACTOR is time ;-)

"

Factors long integer. Brent-Pollard, with the assumption that trial
division has been done already. When a small factor is found SFactor
is
called to get full short factorization. Since the factorization can
potentially take a very long time, an execution test is used to abort
factoring very long integers (limit is 60s for each composite). The
factors are sorted at exit.
"

With EMU48 and my AMD PC:
'2^67-1' FACTOR --> '193707721*761838257287' in 25.3344 sec.
'2^256-1' FACTOR --> '3*5*17*257*641*65537*274177*6700417*
22894341011050090868949881974522315437050433829130497' in 118.5233
sec.
How long NSPIRE CAS software uses to factorize '2^256-1' ? On my PC
after an hour it was still running...!

The HP 49g/49g+/50g can handle infinite-precision integers! :D

Taylor series of 'LN(SIN(X))' around point 1 up to 20th order with
real HP 50G:

'LN(SIN(X))' 1 20 SERIES

after about half an hour -->

2: { :Limit: 'LN(SIN(1))' :Equiv: '
LN(SIN(1))' :Expans: '(
4951498053124095*COS(1)*SIN(1)^
20+167586815066767360*COS(1)^3*
SIN(1)^18+1889431986777882624*
COS(1)^5*SIN(1)^16+
10666592309335818240*COS(1)^7*
SIN(1)^14+35384430172443770880*
COS(1)^9*SIN(1)^12+
74371001944316313600*COS(1)^11*
SIN(1)^10+102243157431032217600*
COS(1)^13*SIN(1)^8+
91945674412720128000*COS(1)^15*
SIN(1)^6+52226296442191872000*
COS(1)^17*SIN(1)^4+
17030314057236480000*COS(1)^19*
SIN(1)^2+2432902008176640000*COS
(1)^21)/(51090942171709440000*
SIN(1)^21)*h^21-(443861162*SIN(1
)^20+37776932168*COS(1)^2*SIN(1)
^18+620404499106*COS(1)^4*SIN(1)
^16+4391471022960*COS(1)^6*SIN(1
)^14+17051306990760*COS(1)^8*SIN
(1)^12+40351310017200*COS(1)^10*
SIN(1)^10+60941527571925*COS(1)^
12*SIN(1)^8+59200602961500*COS(1
)^14*SIN(1)^6+35885700600750*COS
(1)^16*SIN(1)^4+12374379517500*
COS(1)^18*SIN(1)^2+1856156927625
*COS(1)^20)/(37123138552500*SIN(
1)^20)*h^20+(443861162*COS(1)*
SIN(1)^18+12444357002*COS(1)^3*
SIN(1)^16+116614285620*COS(1)^5*
SIN(1)^14+544057084980*COS(1)^7*
SIN(1)^12+1471434155100*COS(1)^9
*SIN(1)^10+2464400238300*COS(1)^
11*SIN(1)^8+2602548073125*COS(1)
^13*SIN(1)^6+1691165200725*COS(1
)^15*SIN(1)^4+618718975875*COS(1
)^17*SIN(1)^2+97692469875*COS(1)
^19)/(1856156927625*SIN(1)^19)*h
^19-(6404582*SIN(1)^18+443861162
*COS(1)^2*SIN(1)^16+6000247920*
COS(1)^4*SIN(1)^14+34871263260*
COS(1)^6*SIN(1)^12+109860823800*
COS(1)^8*SIN(1)^10+206398171980*
COS(1)^10*SIN(1)^8+238734896400*
COS(1)^12*SIN(1)^6+167162670675*
COS(1)^14*SIN(1)^4+65128313250*
COS(1)^16*SIN(1)^2+10854718875*
COS(1)^18)/(195384939750*SIN(1)^
18)*h^18+(6404582*COS(1)*SIN(1)^
16+145818860*COS(1)^3*SIN(1)^14+
1112558268*COS(1)^5*SIN(1)^12+
4186924560*COS(1)^7*SIN(1)^10+
8950261320*COS(1)^9*SIN(1)^8+
11440529100*COS(1)^11*SIN(1)^6+
8683775100*COS(1)^13*SIN(1)^4+
3618239625*COS(1)^15*SIN(1)^2+
638512875*COS(1)^17)/(
10854718875*SIN(1)^17)*h^17-(
929569*SIN(1)^16+51236656*COS(1)
^2*SIN(1)^14+557657112*COS(1)^4*
SIN(1)^12+2595050640*COS(1)^6*
SIN(1)^10+6427561140*COS(1)^8*
SIN(1)^8+9178369200*COS(1)^10*
SIN(1)^6+7605397800*COS(1)^12*
SIN(1)^4+3405402000*COS(1)^14*
SIN(1)^2+638512875*COS(1)^16)/(
10216206000*SIN(1)^16)*h^16+(
929569*COS(1)*SIN(1)^14+16769029
*COS(1)^3*SIN(1)^12+101470005*
COS(1)^5*SIN(1)^10+298242945*COS
(1)^7*SIN(1)^8+482206725*COS(1)^
9*SIN(1)^6+439864425*COS(1)^11*
SIN(1)^4+212837625*COS(1)^13*SIN
(1)^2+42567525*COS(1)^15)/(
638512875*SIN(1)^15)*h^15-(21844
*SIN(1)^14+929569*COS(1)^2*SIN(1
)^12+7919730*COS(1)^4*SIN(1)^10+
28543515*COS(1)^6*SIN(1)^8+
53153100*COS(1)^8*SIN(1)^6+
53918865*COS(1)^10*SIN(1)^4+
28378350*COS(1)^12*SIN(1)^2+
6081075*COS(1)^14)/(85135050*SIN
(1)^14)*h^14+(21844*COS(1)*SIN(1
)^12+302575*COS(1)^3*SIN(1)^10+
1402401*COS(1)^5*SIN(1)^8+
3075930*COS(1)^7*SIN(1)^6+
3513510*COS(1)^9*SIN(1)^4+
2027025*COS(1)^11*SIN(1)^2+
467775*COS(1)^13)/(6081075*SIN(1
)^13)*h^13-(1382*SIN(1)^12+43688
*COS(1)^2*SIN(1)^10+280731*COS(1
)^4*SIN(1)^8+747780*COS(1)^6*SIN
(1)^6+977130*COS(1)^8*SIN(1)^4+
623700*COS(1)^10*SIN(1)^2+155925
*COS(1)^12)/(1871100*SIN(1)^12)*
h^12+(1382*COS(1)*SIN(1)^10+
14102*COS(1)^3*SIN(1)^8+47685*
COS(1)^5*SIN(1)^6+72765*COS(1)^7
*SIN(1)^4+51975*COS(1)^9*SIN(1)^
2+14175*COS(1)^11)/(155925*SIN(1
)^11)*h^11-(62*SIN(1)^10+1382*
COS(1)^2*SIN(1)^8+6360*COS(1)^4*
SIN(1)^6+11655*COS(1)^6*SIN(1)^4
+9450*COS(1)^8*SIN(1)^2+2835*COS
(1)^10)/(28350*SIN(1)^10)*h^10+(
62*COS(1)*SIN(1)^8+440*COS(1)^3*
SIN(1)^6+1008*COS(1)^5*SIN(1)^4+
945*COS(1)^7*SIN(1)^2+315*COS(1)
^9)/(2835*SIN(1)^9)*h^9-(17*SIN(
1)^8+248*COS(1)^2*SIN(1)^6+756*
COS(1)^4*SIN(1)^4+840*COS(1)^6*
SIN(1)^2+315*COS(1)^8)/(2520*SIN
(1)^8)*h^8+(17*COS(1)*SIN(1)^6+
77*COS(1)^3*SIN(1)^4+105*COS(1)^
5*SIN(1)^2+45*COS(1)^7)/(315*SIN
(1)^7)*h^7-(2*SIN(1)^6+17*COS(1)
^2*SIN(1)^4+30*COS(1)^4*SIN(1)^2
+15*COS(1)^6)/(90*SIN(1)^6)*h^6+
(2*COS(1)*SIN(1)^4+5*COS(1)^3*
SIN(1)^2+3*COS(1)^5)/(15*SIN(1)^
5)*h^5-(SIN(1)^4+4*COS(1)^2*SIN(
1)^2+3*COS(1)^4)/(12*SIN(1)^4)*h
^4+(COS(1)*SIN(1)^2+COS(1)^3)/(3
*SIN(1)^3)*h^3-(SIN(1)^2+COS(1)^
2)/(2*SIN(1)^2)*h^2+COS(1)/SIN(1
)*h+LN(SIN(1))' :Remain: 'h^21'
}
1: 'h=X-1'

How long TI-NSPIRE CAS device uses to make series expansion of
'LN(SIN(X))' around point 1 up to 20th order? I don't kmow because I
don't the device.

Taylor series of 'X^X' around point 0+ up to 4th order with real HP
50G:

'X^X' 'X=0+0' 20 SERIES

-->

2:{ :Limit: 1 :Equiv: 1 :Expans: '
1/(2432902008176640000*(-1/LN(h)
)^20)*h^20+-1/(
121645100408832000*(-1/LN(h))^19
)*h^19+1/(6402373705728000*(-1/
LN(h))^18)*h^18+-1/(
355687428096000*(-1/LN(h))^17)*h
^17+1/(20922789888000*(-1/LN(h))
^16)*h^16+-1/(1307674368000*(-1/
LN(h))^15)*h^15+1/(87178291200*(
-1/LN(h))^14)*h^14+-1/(
6227020800*(-1/LN(h))^13)*h^13+1
/(479001600*(-1/LN(h))^12)*h^12+
-1/(39916800*(-1/LN(h))^11)*h^11
+1/(3628800*(-1/LN(h))^10)*h^10+
-1/(362880*(-1/LN(h))^9)*h^9+1/(
40320*(-1/LN(h))^8)*h^8+-1/(5040
*(-1/LN(h))^7)*h^7+1/(720*(-1/LN
(h))^6)*h^6+-1/(120*(-1/LN(h))^5
)*h^5+1/(24*(-1/LN(h))^4)*h^4+-1
/(6*(-1/LN(h))^3)*h^3+1/(2*(-1/
LN(h))^2)*h^2+-1/(-1/LN(h))*h+1'
:Remain: 'h^21' }
1:'h=X'

NSPIRE can not do the series expansion of 'X^X' around point 0+!

The CAS of the HP 50g is more flexible, try to calculate this
expression with CASIO ClassPad, TI-NSPRE CAS and TI 89T/V200, you fail
in any way:

'ABS(\GS(K=1,+\oo,((1+i)/2)^K))' ('\GS' is the summation symbol and
'i' is the imaginary unit)

Using the HP 50g we can do it with these steps:

'\GS(K=1,N,((1+i)/2)^K)' EVAL SIMPLIFY

'(-(i*EXP((2*N*LN(2)+i*\pi*N)/4))+i*EXP(N*LN(2)))/EXP(N*LN(2))'
'N=\oo'
'lim'

result: 'i'
and finally we get 1 with ABS

Partial fraction:

HP 50g
'(3*X^3+2*X^2+X+1)/(4*X^2+2*X+1)' PARTFRAC --> '3/4*X+1/8+(7*i*\v/3/12/
(4*X+(1+i*\v/3))-7*i*\v/3/12/(4*X+(1-i*\v/3)))'

TI-NSPIRE CAS is unable to do the partial fraction expansion when the
denominator has complex roots!

expand((3*X^3+2*X^2+X+1)/(4*X^2+2*X+1)) = 7/(8*(4*x^2+2*x+1))+3*x/
4+1/8

In the TI89T/V200 calculators expand() is buggy :-P .

Regarding the programmability the HP 50g beats competitors:

HP Basic
User RPL
System RPL
Saturn assembly
ARM assembly
C/C++

====================================================================
AMD K7 1GHz - ASUS A7V - 1256 MB SDRAM 133 MHz
Windows XP PRO SP3
TI-NSPIRE CAS Computer Software Teacher Edition Version: 2.0.0.1188
EMU48 1.47+ HP 50g ROM 2.15
REAL HP 50G ROM 2.15
====================================================================

On 18 Feb, 11:39, Nelson Sousa <nso...@gmail.com> wrote:
> that's not a very significant test.
>
> I prefer to have them factor 2^67-1 to check integer arithmetic speed
> and the taylor series of ln(sin(x)) around point 1 up to 5th order,
> 10th order, ... the expression grows immensely when the order
> increases and you test both the symbolic manipulation routines and the
> memory management of the operating system (by the way, I have no idea
> how does the HPs behave with these two, I'm curious).
>
> Having a calculator compute 99999^999 is only a matter of
> specification: how many integer digits does it support. Not really
> speed, algorithm sophistication or pure power. And on top of that,
> having 999 digits instead of 610 of the TI-89 or 990 of the NspireCAS
> doesn't strike me as such an advantage.
>
> Cheers,
> Nelson
>

> On Thu, Feb 18, 2010 at 00:52, T Tran <themostwan...@gmail.com> wrote:
> > It's me who posted it.

> > Actually, the NspireCASderived from theCASof the Ti-89 family,

> > thus, you would expect predictable behavior between the two.

> > However, NspireCAShas been improved over time.

>
> > For example, in arithmetic calculation, we see that
>
> > HP 50g (OS 2.09 2006) still takes the lead.
> > It can compute 99999^999 and display every single digit without
> > scientific notation.
>

> > 2nd position.
> > It can compute 99999^198 without scientific notation.
>
>
> > Ti-89 Titanium comes last with 500^228

> > I have a classpad 300+ and Ti-NspireCAS. I found myself using the

> > Nspire more than the classpad for quick calculation.
>
> > On Feb 17, 5:40 pm, Ross <ross3...@gmail.com> wrote:
> >> I am curious to know who created and posted the document comparing the
> >> ti 89 and the hp 49.  If at all possible, I would really like to see

> >> how the TI NspireCASand the HP calcs perform in a competition like

### Nelson Sousa

Mar 24, 2010, 6:20:31 AM3/24/10

Ok, you have a few interesting test cases there (I knew some of them already).

So here are the results:

factor(2^67-1): less than 1sec on PC, ~2 secs on the handheld (compared to 25 seconds on the HP emulator software)
factor(2^256-1): I aborted the calculation after a few minutes, didn't get an answer on either one, nor I feel the need to. I'll just have to accept your claim that the sw didn't factor in 1 hour and I assume the handheld won't either. The issue has to do with the size of the last prime factor, it's beyond the Nspire CAS' algorithms. However, in ALL factorizations that the Nspire CAS does handle the result is almost instantaneous.
taylor(ln(sin(x)),x,10,1) : a few seconds on the software; 48 secs on the handheld (compared to 30 minutes on the HP50 handheld)
taylor or x^x around zero: Nspire CAS doesn't compute it. Why? beats me. If I compute the sum of the first 20 derivatives multiplied by x^n/n! I get the full answer in about 20 or 30 seconds.
Sum: the Nspire CAS isn't that powerful computing complex sums, so that fact that it doesn't compute doesn't surprise me;
Propfrac: yes, propfrac doesn't factor polynomials with no real roots. It's a design limitation, not a performance one.

Now, I'm pretty sure I could come up with some examples to make the Nspire CAS shine and claim that that proves the Nspire is better than the HP, but... what's the point? Are you that happy to know that the HP is much better than the Nspire computing things for which you have no use in real life? On the other hand, the Nspire is much faster than the HP in other stuff. So?...

I think it's much more relevant the fact that you take the HP to exams because or its wireless communication capabilities.

Nelson

Now, lets do the hones comparison, shall we?

Factoring of 2^67-1: Advantage TI-Nspire CAS
Factoring of 2^256-1: didn't try for long, I forfeit this one, just don't have the time.
Taylor(ln(sin(x)))to 20th order: well, it's comparing 48 seconds versus 30 minutes, you do the math.
taylor(x^x): Nspire doesn't compute.

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### supergems

Mar 24, 2010, 6:44:50 AM3/24/10
to tinspire
I just wanted to show that the CAS of the TI calculators is not the
best ever.

> On Wed, Mar 24, 2010 at 08:40, supergems <simone.cer...@gmail.com> wrote:
> > The FACTOR is time ;-)
>

> ...
>
> leggi tutto

### Nelson Sousa

Mar 24, 2010, 7:07:00 AM3/24/10

Oh, but I don't think nobody ever claimed it to be.

I do, however, have to change a statement I did before (I had woken up just a little earlier, half my brain was still sleeping).

About the taylor series expansion of x^x: the sum I did it totally meaningless (and wrong).
So, yes, it's true, the Nspire CAS doesn't compute that taylor series. And the reason is it doesn't exist!

The taylor series to n'th order around point x=a is defined as sum( f^(k)(a)*(x-a)^k/k! , k,0,n) = f(a) + f'(a)*(x-a) + f''(a)(x-a)^2/2 + ...

The series only exists if f(a) and ALL derivatives are well defined on x=a. With f(x)=x^x, f(0) is not defined, nor are any of its derivatives. This function cannot be expanded around x=0. The answer your HP returned is just wrong.

Nelson

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### Andy Kemp

Mar 24, 2010, 7:09:38 AM3/24/10
I think Nelson's point is that "Best Ever" is a relative term...  Best for what use it for it for is clearly a better question and for many people the Npsire CAS is the 'Best' for their required usage...  If it isn't for what you need to do then obviously you would consider other things...

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### joaquim.f.marques

Mar 24, 2010, 10:03:12 AM3/24/10
The taylor series to n'th order around point x=a is defined as sum( f^(k)(a)*(x-a)^k/k! , k,0,n) = f(a) + f'(a)*(x-a) + f''(a)(x-a)^2/2 + ...

The series only exists if f(a) and ALL derivatives are well defined on x=a. With f(x)=x^x, f(0) is not defined, nor are any of its derivatives. This function cannot be expanded around x=0. The answer your HP returned is just wrong.

Nelson

Not exactly...

Exists lots of functions with all derivatives in x=0 without expression of Taylor series at x=0.

Thanks to Cantor theory of infinity.

Remember that the set of all functions with all derivatives at x=0 is a numerable set and the set of all functions isn't numerable (it's like rationals and irrationals, the functions with all derivatives at x=0 play the role of the rationals!)

Joaquim

### Nelson Sousa

Mar 24, 2010, 10:34:33 AM3/24/10