Re: Second TI-Nspire report

10) I don't agree. Mathematica doesn't need a single second to print
the correct answer. It must be a matter of (non-existent!)
algorithmic quality.

It might be because Mathematica does not check that the
det of the matrix is non 0. How is the inverse returned
by mathematica? Is it relatively compact or huge and
without sqrt in the denominator of the matrix elements?
How much time do you need to check that A*inv(A) is indeed
identity?
I have done the experience with Xcas (fixing a few bugs
on the fly), and it requires intensive computation
because you have first to find the minimal algebraic
extension of Q containing all the sqrt, then each
computation will be translated on polynomials of degree 16 with
complex rational coefficients (or degree 32 with rational
coefficients). After that you must translate back the
polynomial as a symbolic expression in terms of the generator
of the extension (e.g. sqrt(2)+sqrt(3)+sqrt(5)+sqrt(7)) and
depending how you rewrite it, it can be time costly as well.
I would guess that computing the inverse on an arm 70 Mhz
should take around 10 minutes with the current Xcas algorithm.
On the 49, I used a recursive representation for sqrt,
but it works only for sqrt, not for more general algebraic
extensions.
Or maybe mathematica has a better algorithm, if that is the
case, I'm curious to know how it works...
.

Relevant Pages

  • Re: Second TI-Nspire report
    ... It might be because Mathematica does not check that the ... without sqrt in the denominator of the matrix elements? ... extension of Q containing all the sqrt, ... should take around 10 minutes with the current Xcas algorithm. ...
    (comp.sys.hp48)
  • Re: Second TI-Nspire report
    ... It might be because Mathematica does not check that the ... without sqrt in the denominator of the matrix elements? ... extension of Q containing all the sqrt, ... should take around 10 minutes with the current Xcas algorithm. ...
    (comp.sys.hp48)
  • Re: 0^0 oh no!
    ... you'd use SetPrecision to tell the system to ... in Mathematica one would typically use SetPrecision if coding ... For languages that work in fixed precision (I think ... think typically one would, at the finish of an iterative algorithm, ...
    (sci.math.symbolic)
  • Re: Non-restoring binary square root and convergence
    ... I took the algorithm from "Algorithms for Extracting Square Roots and Cube ... % sqrt 9 16 ... int main ...
    (comp.programming)
  • Re: Non-restoring binary square root and convergence
    ... I took the algorithm from "Algorithms for Extracting Square Roots and Cube ... % sqrt 9 16 ... int main ...
    (sci.math)