Alejandro, thank you for pointing to the poor replacement.

But it is overdue to have solutions. It is like treating users as guinea pigs
and ignoring their interests and desires.

So what. I am going to loose interest here, certainly being not the only one.
And there is no actual need to contribute resulting in annoyance.

For the concrete question that means: best to be discussed with Maple stuff,
as the board is not the adequate media.

doubling digits is a rule of thumb and will not always work:

After re-scaling one has something like 

 1.0 + large = large

since if 'large' is large enough, then adding 1.0 will not contribute
to the signifikant, leading digits (of course that will depend on the
precision used and both acer's and pagan's (+links) touches that).

It is not the vague help page per se: it just needs time to get used
to that and the whole problem (it affected Numerics for generations
and they are pretty aware, that also usual 'group rules' are not valid,
which is what acer's last example says).


There is a usefull approach within Maple: evalr and shake.

  S:=eval(exp(abs(tan(x)-x)),x=1/10^4)-1;

  shake(S,10);
                                   -8            -8
                 INTERVAL(-0.100 10   .. 0.100 10  )

This 'says': with 10 Digits one can not even be sure of the sign.

  shake(S,24);
                                  -12                      -12
       INTERVAL(0.3333333346567 10    .. 0.3333333346767 10   )

is close ... (working with Digits = 10)


The command also may give some insight on the first, original task:

  shake(4*Pi*(1391000/2)^2,2);
                                   13             13
                 INTERVAL(0.4926 10   .. 0.7354 10  )


I think Maple also has a package for 'interval arithmetics' (may be
it is outside, but free, have not looked for it now).


Finally just want to mention that may be quite helpful for experimental
data, as they are not accurate (though I am not from Physics).

The help is still not quite clear (in Maple 12 at least): "To specify the numeric precision for an evalf computation ..."

AFAIK evalf[n] uses n digits for computational precision, but that does not say, that the result is accurate to n digits.

If one wants that, then something like "evalf[2*n](expr); evalf[n](%);"is usefull.

The other thing: usually Maple remembers previous results, so decreasing n should not matter. Usually.

@hirnyk : I do not quite understand, your method works quite well (if using indexed variables),
its results are even more simple (have not thought about 'why').

Essentially it means to find a diagonal presentation of a quadratic form and that can be seen
as a general version of 'completing the square' (that's how I once learned that). And think, that
PolynomialSystem does something towards that

I append it as 'classical' sheet, since for various reasons I do not want to work with the other
format (nice, but unhandy and not save for input if not handled with care and copy+paste is
a mess).

Cholesky_hirnyk.mws

@hirnyk : I do not quite understand, your method works quite well (if using indexed variables),
its results are even more simple (have not thought about 'why').

Essentially it means to find a diagonal presentation of a quadratic form and that can be seen
as a general version of 'completing the square' (that's how I once learned that). And think, that
PolynomialSystem does something towards that

I append it as 'classical' sheet, since for various reasons I do not want to work with the other
format (nice, but unhandy and not save for input if not handled with care and copy+paste is
a mess).

Cholesky_hirnyk.mws

Alles Gute!

If I go 9 month back than Xmas is indeed for Love & Peace ...

Not sure about 'positive non-integer imaginary number', guess it is eta = r*I, 0 < r
and there is no special thing about assuming 'a non-integer', guess 0 < a is ok as well.

Then I would try recursion in the index (=first argument) and write Bessel as sum and
use termwise integration (justified?)

The simpliest case is eps=1 where it seems to work, but in general you may need to
consider Bessel * x^k * exp

Not sure about 'positive non-integer imaginary number', guess it is eta = r*I, 0 < r
and there is no special thing about assuming 'a non-integer', guess 0 < a is ok as well.

Then I would try recursion in the index (=first argument) and write Bessel as sum and
use termwise integration (justified?)

The simpliest case is eps=1 where it seems to work, but in general you may need to
consider Bessel * x^k * exp

@pagan thx for the suggestion (usually I only use the DLLs, not the lib)

  'cname'="gsl_sf_bessel_J0",
  'library'=" -LC:\\WINDOWS\\system32 -lgsl -lgslcblas"

results in the error message

Error, (in LinkDSO) linker exited with nonzero status 1: Open Watcom Linker Version 1.3
Portions Copyright (c) 1985-2002 Sybase, Inc. All Rights Reserved.
Source code is available under the Sybase Open Watcom Public License.
See http://www.openwatcom.org/ for details.
Error! E3033: directive error near '-lgsl'

What I find at the web for 3033 is not illuminating ...

Might it be, that there are different calling conventions? GSL is cdecl if I remember correctly.

PS: I am on Maple 12, Win XP

I partially can follow and tried to give it a go with GSL, but do not quite understand what to take for

  'cname'="j0",
  'library'=" -L/usr/lib -lm "

Any suggestions?

PS: I vote for Task B, of course :-) But do never use thumbs up/down (I hate such systems)

@Will thx - see my comment to your post (and you can delete our 3 posts if you wish, to keep the thread clean).

Will - thx for the improvement, it is a good thing!

It works for me (Firefox 3.6.6) now (well just some tests on some threads).

But also observed that problem with IE (IE6 at home and IE8 at work) or a slim browser like K-Meleon). May be others have time to check, whether the problem now is solved even for a greater number of browsers than FF.

Rgrds

For the current board I prefer posts without images:

Since the new board does not allow to print to a pdf or postscript
besides the first page only one can not simply archive discussions.

Thus I have to save the HTML page - which no reasonable man
does with all the pics.

All I have heared to this issue is 'we have a plan'. Fine.

@Alejandro Jakubi 

Have that. Does not work. Me stupid back woods man.

Or: thanks, I tried it through all the versions - and it never worked for me on WIN. It may be my fault, of course, but I would want to try it on a test version, before buying a new one and being faced with it again. But concerning Maple's reactions: "no answer is an answer as well" ...

@Alejandro Jakubi 

Have that. Does not work. Me stupid back woods man.

Or: thanks, I tried it through all the versions - and it never worked for me on WIN. It may be my fault, of course, but I would want to try it on a test version, before buying a new one and being faced with it again. But concerning Maple's reactions: "no answer is an answer as well" ...