Re: Second TI-Nspire report
- From: Yao Konan <KonanYao@xxxxxxxxx>
- Date: 8 May 2007 09:31:57 -0700
Hi Mr Parisse,
On 7 mai, 20:17, pari...@xxxxxxxxxxxxxx wrote:
Fairly interesting report from what I could understand,
it would be nice to have it translated in English!
On your CAS algorithms remarks, I can give you a few hypothesis
* there is most probably nobody at TI working on improving
the maths algorithms. My guess is that they have
concluded the CAS is good enough for the nspire, and
they are most probably right. Competition will not come
until PC CAS will be widely available on handhelds.
Unfortunately it won't be anytime soon.
The other problem is that handheld need to become almost as cheap as
calculator.
Though since symbian and windows mobile have become the dominant O.S
of this market,the price of handheld won't significantly decrease
anytime soon.
They will just get more and more powerful.
The math soft of the nspire is therefore most probably exactly
the same as the latest TI89/V200 AMS versions, just recompiled
(with a few improvements in the non math areas).
* Points 1, 2, 3 of your Qualitat der Algorithm are not
math-related improvements.
The 32 KB limit is indirectly math related.
Especially with algorithm as poor as the taylor one.
* point 4 is because the size of an integer in base 2^8 is coded
on 8 bits: try 256*log(256.)
This limit should have been removed since at least the TI92+ and the
TI89.Though the conversion of bigger integer to string(for display)
would be awfully slow unless strongly optimised with low level C or
even assembly.
* point 5 would require something like MPFR on PC
Or just use this capability from Derive.
* point 6 is because they use the Taylor formula instead of
arithmetic operations on expansion. That's what I find
the main weakness of the TI, but it's not apparent before
student are at the University, hence TI does not care
(same for arithmetic functions on polynomial or Bezout
identity for integers).
This is in fact a weakness of Derive not specifically of the A.M.S.
I have been quite disapointed when i find it out. It is distrurbing to
see a decades year old C.A.S having such limitations.
* point 10 is because it's hard to know exactly if a combination
of square roots is not 0. If you compute with sqrt of
2,3,5,6,7 and -1, you must work in an extension of degree
2^5=32 and most importantly you must check at each step
that it does not reduce further.
Well considering that the determinant of this matrix can be easily
compute with the formula:
m[1,1]*m[2,2]-m[2,1]*m[1,2],assuming m is the matrix i think like
Hassan that the problem come from the computation of the determinant.
However note that the C.A.S also has trouble with other
operations(REF,RREF) on this matrix.
i have chose the square to avoid any easy simplication from the
calculator and to clearly underline the trouble it has with such
matrix.Note that i have been kind,i could have used symbolic values
instead of number.
What do you think for example of this:
[1/(sqrt(n01)+i*sqrt(n02)),1/(sqrt(n03)+i*sqrt(n04));1/
(sqrt(n05)+i*sqrt(n06)),1/(sqrt(n07)+i*sqrt(n08))]
I haven't try but it would be quite naughty >:)
.
- References:
- Second TI-Nspire report
- From: Michael Kuyumcu
- Re: Second TI-Nspire report
- From: parisse
- Second TI-Nspire report
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