Axel Vogt

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20 years, 229 days
Munich, Bavaria, Germany

MaplePrimes Activity


These are replies submitted by Axel Vogt

I also got some: x1=Pi-x2, x3 = arccot(25/6) and the zeros of 
-3305*sin(x2)^4*661^(1/2)+1080*cos(x2)*sin(x2)^3+7920*sin(x2)^4
+1080*cos(x2)+9000*sin(x2)

[x1,x2,x3] = # alfa

       [2.59141396550604, 0.550178688083745, 0.235544980720863]
       [0.45685691213802, 2.68473574145177, 0.235544980720863]
       [0.12147192400544, 3.02012072958435, 0.235544980720863]
       [-3.02396720384266, 6.16555985743245, 0.235544980720863]

I convert at Digits = 15 (he uses only ~ 10 Digits).

Will send you a sheet later (sorry, upload does not work, I have given up for that)

Edited to add:

To see the problem use (EQ = convert(Eq, rational))

  subs(p=2/10, EQ): #sqrt(.283856826615611);
  plot( sign(%)*log10(abs(%)), omega=0.53 .. 0.54);

and then

  convert(.532782156810465, rational); # solution 15 Digits
  subs(p=2/10, omega=%, EQ): evalf(%);
  sign(%)*log10(abs(%));

                          -625.360654195823

I have not looked up 'condition number for polynomials and Maple',
but that should be the buzz word (leading to high Digits in general)

When I coded (in old days) I always refused polynomials of degree
higher than 16 (and those coefficients make it worse).

In educated terms I would say: the task is 'illposed'.

Yes, this is too extreme for 'usual' precision.

I converted to rationals (Digits=15), then observed symmetry and setting
omega = sqrt(t) has lower degree. Looking at q=1=t I made an attempt to
reduce magnitudes of coefficients, dividing by 10^636 (an average).

Let be Q the resulting polynomial (!), the one wants the positive roots
(and +- sqrt of them give one for the original task).

Now even with that low Digits one gets an implicit plot (feeding Q),
though it is shaped a bit differently than Markiyan's (t=sqrt(omega)).
But showing those 2 branches (one close to x axes, the other close
to y axes and then becoming a 'diagonal')

Ok, I looked again.

The problem seems to come through the *.js in the xhtm tag and for those
NoScript does not offer an activation. One has to find it out oneself and
allow it. How about adding some usual test before or having it in the FAQ?

The other thing 'needed' is WebGL (though it will still work, slower).

Have not checked whether those grafics are SVG - are they?

It does not use cookies (having all in the page itself, yes?),
have not checked carefully for other storage.

Saving as *.wm: one must save the whole stuff (before executing the js),
if I understodd correctly .

Revisiting 'deleting' I see - those which are not cleared may be graphics.

Looks nice!


For browser statistics you may check media sites (not only the w3 school's
data for their own site), http://www.web-stats.info/ (for Germany), it may
vary on countries and intended audience.

For the first link I get a text displayed (shortend by me using dots)

Welcome to Maple WWW Maple World Wide Worksheet LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Description ...
....
...2) end if else NULL end if end proc; JSFH

Looking at the source code it is a worksheet.

Saving as such and opening (with M18) it says: "the ws contains elements not recognized by this version of M. your ws may be incomplete". It executes on demand. But astonishingly it does not allow to delete output.

Using concurrent FF (not in a standard way, but without artifical proxy or such)

 

May be you want to give some more guiding?

 

PS I have some inhibitions because of security: I neither would allow IFrames (which you seem to expect to be allowed in some cases) nor would I usually blindly download and use mw sheets (having auto exec or such)

@Preben Alsholm 

For all cases I get

                        "Están en perspectiva"

with an accent (M18, classic or in my oldest version M15 as well)

@Preben Alsholm 

He means a full set of characters (like in keyboard settinngs), covering accents (like in French) or Umlaute (like in German) or that little circles over 'a' (like in Nordic languages) or ... a kind of typesetting

Though it is risky (if knowing not really) I like that.

And I like the silent twist for variable input types - the last 'convert' is nice!

thumb up/down: clicking once it counts up, another click resets - intended?

Sort by rating: Fine that some like that. I prefer logical ordering: that forum is for content, not for marketing ... oh ... sorry if I understood it wrong, stupid me ...

it does not (securely) update after posting - I have to open a new call myself

It still has that ugly sorting by ratings?

All requested to sort by date - the logical sort to follow discussions
(without enforcing it manually)

The results can be confirmed independently, using Prudnikov & Marichev
Vol 2, Formula 1.8.2.4 (~ page 40), which give the integral using some
Lommel functions (different from Maple's use, as series in Bessels)

Int(x^(nu+1)*exp(a*x^2)*BesselJ(nu,b*x), x=0..X)=

  'b^nu*exp(a*X^2)/(2*I*a)^(nu+1)*
    (u(nu+1,2*I*a*X^2,b*X) + I*u(nu+2,2*I*a*X^2,b*X))';

where

u := (nu, z, xi) ->
  Sum((-1)^k*(z/xi)^(2*k+nu)*BesselJ(2*k+nu,xi),k = 0 .. infinity);

covering higher precision as well (for Digits=15 I lost patients to
wait for the integration, it is quick for default, Digits=10)

For example it does not work using 'Tor', a standard for privacy.

And it does not work for anonymized browser profiles (with true IP, no SSL) - it looses login credentials.

Both ways of access do work for German government sites.

Same for me ... that mess has not been solved - may be it should be tested more carefully before release ..

Despite what was announced, see for example Alejandro's post

Integrate[r*(BesselI[1, a*r]* BesselK[1, a*r]), r] should return in terms of the parameter a
and the integration variable r.

What do you get for Integrate[r*(BesselI[1, a*r]* BesselK[1, a*r]), r = 0 .. t], 0 < t ?
Which is perhaps the practical task ...

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