Thanks for the hint, however I just had in mind some routines to produce Gauss quadrature rules (for given weight functions for example), there are some standard ways (sketched in the cited document) - certainly easier then the theory around Koepf's work.

Thx for your outing, no reason to blame you :-)

My interest was for some stand-alone package to have routines for specific quadratures without carrying together from books & papers and coding (& testing) it

Thx for your outing, no reason to blame you :-)

My interest was for some stand-alone package to have routines for specific quadratures without carrying together from books & papers and coding (& testing) it

so if a senior does not post one month he receives an award as new motivation ... nice thought :-)
Anyway: Gratuliere!

Changing periodics to 2*Pi and taking the derivative one wants the zeros of
-6*sin(2*xi-13/10)-5*sin(xi+1/2), where the first zero stands for the maximum.

The following is a symbolic solution for it (but my Maple falls into agony
if trying to convert that to Reals only), check it by numerical evaluation.

May be I say a bit more about that later.

-I*ln(I*(1/24*((-50*(cos(1)+I*sin(1))^(23/5)*(-202\
5*(cos(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^\
(46/5)+3*(4144227*(cos(1)+I*sin(1))^(69/5)+455625*\
(cos(1)+I*sin(1))^(46/5)+455625*(cos(1)+I*sin(1))^\
(92/5))^(1/2))^(1/3)*((-25*(cos(1)+I*sin(1))^(23/5\
)*(-2025*(cos(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*s\
in(1))^(46/5)+3*(4144227*(cos(1)+I*sin(1))^(69/5)+\
455625*(cos(1)+I*sin(1))^(46/5)+455625*(cos(1)+I*s\
in(1))^(92/5))^(1/2))^(1/3)+8*(-2025*(cos(1)+I*sin\
(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+3*(41442\
27*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)+I*sin(1\
))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))^(1/2))^\
(2/3)-2856*(cos(1)+I*sin(1))^(23/5))/(-2025*(cos(1\
)+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+3\
*(4144227*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)+\
I*sin(1))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))^\
(1/2))^(1/3))^(1/2)-8*((-25*(cos(1)+I*sin(1))^(23/\
5)*(-2025*(cos(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*\
sin(1))^(46/5)+3*(4144227*(cos(1)+I*sin(1))^(69/5)\
+455625*(cos(1)+I*sin(1))^(46/5)+455625*(cos(1)+I*\
sin(1))^(92/5))^(1/2))^(1/3)+8*(-2025*(cos(1)+I*si\
n(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+3*(4144\
227*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)+I*sin(\
1))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))^(1/2))\
^(2/3)-2856*(cos(1)+I*sin(1))^(23/5))/(-2025*(cos(\
1)+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+\
3*(4144227*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)\
+I*sin(1))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))\
^(1/2))^(1/3))^(1/2)*(-2025*(cos(1)+I*sin(1))^(23/\
5)+2025*(cos(1)+I*sin(1))^(46/5)+3*(4144227*(cos(1\
)+I*sin(1))^(69/5)+455625*(cos(1)+I*sin(1))^(46/5)\
+455625*(cos(1)+I*sin(1))^(92/5))^(1/2))^(2/3)+285\
6*((-25*(cos(1)+I*sin(1))^(23/5)*(-2025*(cos(1)+I*\
sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+3*(41\
44227*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)+I*si\
n(1))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))^(1/2\
))^(1/3)+8*(-2025*(cos(1)+I*sin(1))^(23/5)+2025*(c\
os(1)+I*sin(1))^(46/5)+3*(4144227*(cos(1)+I*sin(1)\
)^(69/5)+455625*(cos(1)+I*sin(1))^(46/5)+455625*(c\
os(1)+I*sin(1))^(92/5))^(1/2))^(2/3)-2856*(cos(1)+\
I*sin(1))^(23/5))/(-2025*(cos(1)+I*sin(1))^(23/5)+\
2025*(cos(1)+I*sin(1))^(46/5)+3*(4144227*(cos(1)+I\
*sin(1))^(69/5)+455625*(cos(1)+I*sin(1))^(46/5)+45\
5625*(cos(1)+I*sin(1))^(92/5))^(1/2))^(1/3))^(1/2)\
*(cos(1)+I*sin(1))^(23/5)+2880*I*(cos(1)+I*sin(1))\
^(23/10)*(-2025*(cos(1)+I*sin(1))^(23/5)+2025*(cos\
(1)+I*sin(1))^(46/5)+3*(4144227*(cos(1)+I*sin(1))^\
(69/5)+455625*(cos(1)+I*sin(1))^(46/5)+455625*(cos\
(1)+I*sin(1))^(92/5))^(1/2))^(1/3)-250*I*(cos(1)+I\
*sin(1))^(69/10)*(-2025*(cos(1)+I*sin(1))^(23/5)+2\
025*(cos(1)+I*sin(1))^(46/5)+3*(4144227*(cos(1)+I*\
sin(1))^(69/5)+455625*(cos(1)+I*sin(1))^(46/5)+455\
625*(cos(1)+I*sin(1))^(92/5))^(1/2))^(1/3))/(-2025\
*(cos(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^(\
46/5)+3*(4144227*(cos(1)+I*sin(1))^(69/5)+455625*(\
cos(1)+I*sin(1))^(46/5)+455625*(cos(1)+I*sin(1))^(\
92/5))^(1/2))^(1/3)/((-25*(cos(1)+I*sin(1))^(23/5)\
*(-2025*(cos(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*si\
n(1))^(46/5)+3*(4144227*(cos(1)+I*sin(1))^(69/5)+4\
55625*(cos(1)+I*sin(1))^(46/5)+455625*(cos(1)+I*si\
n(1))^(92/5))^(1/2))^(1/3)+8*(-2025*(cos(1)+I*sin(\
1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+3*(414422\
7*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)+I*sin(1)\
)^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))^(1/2))^(\
2/3)-2856*(cos(1)+I*sin(1))^(23/5))/(-2025*(cos(1)\
+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5)+3*\
(4144227*(cos(1)+I*sin(1))^(69/5)+455625*(cos(1)+I\
*sin(1))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5))^(\
1/2))^(1/3))^(1/2))^(1/2)+1/24*((-25*(cos(1)+I*sin\
(1))^(23/5)*(-2025*(cos(1)+I*sin(1))^(23/5)+2025*(\
cos(1)+I*sin(1))^(46/5)+3*(4144227*(cos(1)+I*sin(1\
))^(69/5)+455625*(cos(1)+I*sin(1))^(46/5)+455625*(\
cos(1)+I*sin(1))^(92/5))^(1/2))^(1/3)+8*(-2025*(co\
s(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1))^(46/5\
)+3*(4144227*(cos(1)+I*sin(1))^(69/5)+455625*(cos(\
1)+I*sin(1))^(46/5)+455625*(cos(1)+I*sin(1))^(92/5\
))^(1/2))^(2/3)-2856*(cos(1)+I*sin(1))^(23/5))/(-2\
025*(cos(1)+I*sin(1))^(23/5)+2025*(cos(1)+I*sin(1)\
)^(46/5)+3*(4144227*(cos(1)+I*sin(1))^(69/5)+45562\
5*(cos(1)+I*sin(1))^(46/5)+455625*(cos(1)+I*sin(1)\
)^(92/5))^(1/2))^(1/3))^(1/2)+5/24*I*cos(23/10)-5/\
24*sin(23/10)))-1/2;

splitting the periodics manually also works

Optimization:-Maximize(y,x=0..1/2);

          [5.78110318870717600, [x = 0.0512129818925790292]]

Acer,

for me it is not clear what's the motivation ... would you mind to add some more comments?

Your linked comment from above reads for me as "remind Bezout's Theorem!", ok, but my
feeling is you might have something else in mind.

jakubi,

I guess you got me a bit wrong, I was talking about commercial issues (initiated by "why is such nice stuff not
baked into Maple?"). There is no problem in personal use. The main background is: those guys work for 'free'.
And do not want to see that others turn their results into moneymaking. That's essentially all for that point.

Hope that makes it clear enough and there is no need to argue about it in this thread: I use it as well, certainly.

a warm-up with oparam:=1000 gives .125, 1179432, 1729044 and with 50001 i have 3.094, 24899120, 5598698
with solR+I*solI = .318175350197958762e-7-.779830112408352940e-7*I, for 300000 the real parts needs 27.483 sec

computed on a Acer with 2.2 GHz Athlon, Win XP and GSL 1.3 (i think, but forgot which of the libs, there
are severals)

As long as it is not for sure (and is not cleared) a reasonable company would not take the risk, see this discussion
(my personal opinion ... and I am not a laywer ... and asking 2 of them you will hear 3 different & vague replies ...):

groups.google.com/group/microsoft.public.pocketpc/browse_thread/thread/4c196e0b8c995ac4/2642e2ea831d8839

But as a non-commercial person you can publish the possibility (I guess even as a commercial company), but you
have a risk in bundling that into a software

If you mean why Maple has not built in that connection to GSL then the answer may be:
licence problems with the GNU General Public Licence GPL

As soon as you link to software under GPL you are forced to publish the code and there
are discussions whether linking means linking like it is doen through compiling or if it
is already linked by calling through a fixed code

no idea however how they solved that for the multiprecision library GMP ... I think it is under
the Lesser General Public License ...

this is a chaotic thread ...

a) On WIN the usual directory is the system directory, like C:\WINDOWS\system32
Then usually one does not need to type in the path and just uses the file name

b) jakubi uses the classical interface and there input=red, output=blue

c) You use the standard interface

There are lots of differences between the both, they have different file extensions:
*.mws versus *.mw. Open the original sheet in classical mode, the it works.

Generally (not even for beginners) it is easier to use the classical interface,
but I am quite sure it was said quite often at this board

this is a chaotic thread ...

a) On WIN the usual directory is the system directory, like C:\WINDOWS\system32
Then usually one does not need to type in the path and just uses the file name

b) jakubi uses the classical interface and there input=red, output=blue

c) You use the standard interface

There are lots of differences between the both, they have different file extensions:
*.mws versus *.mw. Open the original sheet in classical mode, the it works.

Generally (not even for beginners) it is easier to use the classical interface,
but I am quite sure it was said quite often at this board

I like that very much (GSL is a actively maintained project, so it
is quite reliable, the code shows a sophisticated use of the NAG
routine in Maple and I was not aware of the 'option hfloat'). 
Thx, a nice shot!


The 'underlying problem' considered here can be seen as 

  Int( exp(omega*I*x) * BesselJ(0,c*sqrt(x)) , x = 0 .. 1)

with 1 < omega and 1 << c: so it is a rapidly oscillating Fourier
integral of a highly oscillating function ( omega = 20 .. 200 and
c = 15000 .. 50000 or even more).

I am not aware of any Maple code to handle this.

The problem however is not (only) numerics for Bessel: since it is used for large arguments one might think of using
asymptotics - and sees that the problem would be at least similar if using sin(50001*x) instead.

B.T.W. that thread is a bit chaotic