Re: Second TI-Nspire report
- From: timite_h <timiteh@xxxxxxxxx>
- Date: 8 May 2007 07:51:51 -0700
parisse@xxxxxxxxxxxxxx a écrit :
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.
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).
Well,it is rumored that they will completely give up the AMS code to
focus exclusively on Derive code.
When you think about it,it would have been smarter to use Derive as
the CAS base from the start.
* Points 1, 2, 3 of your Qualitat der Algorithm are not
math-related improvements.
But the first point as an impact on math performance as it can
strongly reduce the problem solving capability of the calculator and
significantly slow down some computations.
* point 4 is because the size of an integer in base 2^8 is coded
on 8 bits: try 256*log(256.)
If they had used Derive code from the start,they wouldn't have this
limitation anymore.
i sincerily don't understand them.
The NSpire will be incompatible with the TI89T/V200 and will be be
available on both the handheld and the PC.It would have been simpler
and smarter to start from the Derive code.
* point 5 would require something like MPFR on PC
* 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).
Well,i thought that the TI89T/V200 also target colleges(thought
certainly not engineering schools and advanced math/sciences college
classes).
At least i bought a TI92 when i was in college and i should thank Jean
Michel Ferrard for its excellent book related to the TI92(i don't
remember the title) which helped me significantly increase the math
capabilities of the calculator and thus make it much more useful for
my studies.
* 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.
Especially if the CAS like to use autosimplification for everything.
Anyway,in this case the C.A.S use inappropriate algorithms for small
matrix.
The C.A.S seems to use the comatrix divided by the determinant formula
to compute the inverse of a matrix thus i think that in this case the
problem come from the computation of the determinant.
And the C.A.S is incredibly slow to compute the determinant of this
matrix.
I wrote a fast determinant function which run circles around the built-
in function for such cases and which used the exact formula for 2*2
and 3*3 matrix and reducing the matrix to a pseudo diagonal matrix for
bigger matrix.
As for the comparison with the 49g, the CAS software is not
15 years old, 10 (or even less) would be more correct.
Well,it was available 8 years ago,so it is even younger from a
customer point of view ;-)
.
- References:
- Second TI-Nspire report
- From: Michael Kuyumcu
- Re: Second TI-Nspire report
- From: parisse
- Second TI-Nspire report
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