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  restart; Digits:=14;     # using Maple 12.02
  J:=Int(arctan(z)^2/(1+4*z^2),z=0..infinity);


  evalf(J);
                           0.40325004753375

  value(J); evalf(%); Re(%);

                ...

Int(exp(-1/100+1/1000*I*u)/(4*u^2+1)*exp(1/2*I*u),u = 0 .. 1)

The integrand has positive real and imaginary parts over the
range (just use plot it) and numerical evaluation gives it as
0.53434219089626 + 0.98249392969436e-1 * I (using Digits:=14).

A symbolic integration and using evalf gives the same.

Now writes this as

  tstData:=[a=0, b=1, m=1/2, b0 = -1/100, b1 = 1/1000];

  J:=Int(exp(b0+b1*u*I)/(4*u^2+1)*exp(u*m*I),u = a .. b);
  eval(J,tstData...

I want the asymptotics for EllipticF(z,k) w.r.t. z (yes, not k).

My example is F:=I*EllipticF(c*I/x,k), c=2-2^(1/2),k=3+2*2^(1/2)
and I want the limit x ---> 0+.

  MultiSeries:-limit(E,x=0);

results in 0.54... + 0.54...*I (real = imag, positive value).

  MultiSeries:-series(E,x,3);

gives (after clearing the output) the same for setting x=0.


For Numerics my setting is Digits:=24 and eps:=1/10^18.

  subs(c=2-2^(1/2), k=3+2*2^(1/2), F...

  Int(phi(u-a*I)*exp(k*u*I),u = -infinity .. infinity);
  Change(%, u-a*I = s, s); subs(s=u,%): expand(%): combine(%,exp);

                   infinity
                  /
                 |
   ...

  restart; interface(version);

    Classic Worksheet Interface, Maple 12.00, Windows, Apr 10 2008 Build ID 347164

  Int(1/(u^2+1/4)*exp(I*u*k),u=-infinity...infinity); value(%);

                                  0

but

  Int(1/(u^2+1/4)*exp(I*u*k),u=-infinity...infinity...

This behaviour of 'assume' puzzles me ... 
and it needed some time to locate it
 
  restart; interface(version);

  Classic Worksheet Interface, Maple 12.00, Windows, Apr 10 2008 Build ID 347164

  assume(a::real); 
    #a:='a'; # activating removes the problem
  f0:=x+a; 
    #a:='a'; # that would not help - since is in use?
  assume(0<a);
  f:=collect(f0,x);

     ...

In this previous post, an example is shown that demonstrates the potential problems that can arise following symbolic conversions such as from sqrt(x^2)  to x^(1/2).

Here x is an unknown symbol. The difficulties include the fact that, while `sqrt` can be smart about simplifying numeric values (eg. integers, rationals) the `^` operator has no such opportunity. Once the conversion from `sqrt`...

> q := x^(1/2):

> type(q, `^`);
                                     true
> op(0,q);
                                       ^

> subsindets(q, `^`, f->subsop(0=H,f));
Error, (in unknown) improper op or subscript selector

What's wrong with that last one? It's modelled on the first Example in the ?subsindets help-page.

Are there cases where...

'Int(x^(k+v-1)/(1+x),x = 0 .. infinity)': '%'= value(%);

             infinity
            /          (k + v - 1)
           |          x
           |   ...

I am missing the F1-help to work properly after highlighting words
at least for the following

invfourier ---> completely missing (it is in inttrans)
invlaplace ---> completely missing
invmellin  ---> completely missing
fourier    ---> MTM[fourier], but not inttrans

Parts      ---> completely missing (expect it in IntegrationTools)
Flip       ---> ImageTools[Flip], but not...

  restart: interface(version); Digits:=14:

    Classic Worksheet Interface, Maple 11.02, Windows, Nov 10 2007 Build ID 330022

  Ei(1,1/2*Pi*(1+2*k)): 
  %=convert(%,Sum);
  subs(k=0,%);
  evalf(%);

                    Pi (1 + 2 k)
              Ei(1, ------------) = GAMMA(Pi k + 1/2 Pi)
                         2

                             Pi            Pi
                      Ei(1, ----) = GAMMA(----)
                             2            ...

This is a long shot, but I think Maplesoft should open up its bug database and allow MaplePrimes users to vote up or down on bugs, reddit style. This would provide direct feedback about which bugs really affect people. Behind the scenes you could cross-reference the votes with account data to get all kinds of useful information: like what bugs disproportionally affect new users, or what bugs annoy experienced Maple users the most, etc. This would allow you to focus attention...

The functionality to extend and augment the context-sensitive menus is quite nice. I especially like the submodule ContextMenu:-Test whose exports allow one to programmatically test the results and new menus.

But what about installing menus with items whose type checks relate to locals?

Here's a simple example.

> newCM:=ContextMenu:-New():
> newCM[Entries][Add]("local to global", "convert(%EXPR,`global`)", `local`):
> newCM[Entries...

Maple 11.00, Standard GUI, worksheet mode.

plot(sin(x),x=-10..10,legend="__never_display_this_legend_entry");

It's magic. The LEGEND() call is present in the PLOT structure, but it doesn't get displayed.

acer

The first example below seems OK. But, should I be expecting the different behaviour in the second example?


> restart:
> p := module() option package; export foo;
> foo:=proc(x) x; end proc;
> end module:

> foo := proc(x) cos(x); end proc:

> foo(3.2);
-0.9982947758

> p:-foo(3.2);
3.2

> evalhf(p:-foo(3.2)); # OK
3.20000000000000018

> restart:
> p := module() option package; export sin;