Axel Vogt

Pi^2*(c+(1+Pi)/Pi)^2+Pi^2)/((c-(-1+Pi)/Pi)^2*Pi^2+Pi^2);

                         2 /    1 + Pi\2     2
                       Pi  |c + ------|  + Pi
     ...

Is there a direct command to give the (first) index in a list,
for which the entry coincides with some given value (without
coding a loop, to run through the list)?

---

PS: when I enter that question I automatically get an info,
that similar questions exists. But clicking on those links do
not give usefull infos, they just lead to a page of old threads
(Page 529 of 569 for the first link ...)

I want to use the Bits package, but have troubles - may be a bug?

I do not understand the following (Maple 15), where the help says "The And
command computes the bit-wise logical and of the inputs ... "

  with(Bits);
  Settings(defaultbits=4); # poor help text for that ...

  4; Split(%);
                     ...

Is there a way to have interval arithmetics for complex inputs
(maple seems to name that range arithmetics in the help)?

x:=Pi/5;
shake(x);

              INTERVAL(0.628318529462 .. 0.628318531974)

shake(x*I);

    Error, (in evalr/shake) not a real number

Usually Maple gives solutions in terms of radicals only up to degree=4
(for example using RootOf + allvalues).

Using 'irreduc' (to test first) and 'galois' (to check for the Galois
group, if degree <= 9) I have cases, where the result implies, that by
theory the roots can be given through radicals:

Though the results are difficult to read in my case they are 'C(6)' or
'C(8)', the cyclic groups of that order - thus abelian and IIRC those
groups are solvable.

How can I use 'evalr' and 'shake' for functions (in a relative or absolute sense)?

What I see in the help is the result for disturbing the input to a function (by decimal digits).

But I want ranges for the output, if the function itself is disturbed, not only the input
(giving resulting error ranges, even for exact input).

Any idea?

The following works:

  u+v*w; 
  patmatch(%,a::name*b::name +c::name,'p'); 
  p;

                                 true
                        [a = v, b = w, c = u]

Testing a numerical implementation I want to access data, which are
suggested as maximal errors through plotting (with care) to examine
that in more detail (so plotting is considered just a help)

For univariate functions I am aware how to look into data pairs for
the command plot.

My function is bivariate and real valued.

P:= plot3d( f(x,y), ...) lets me save the result and 

  op(P);
  op(1,P);
  arr:=op(3, %);

  arr; Arr:=convert(%, Matrix);
  plots[matrixplot](Arr, axes=boxed);

Is there a method to work with Reals or Complex modulo Integers (need not
to be modulo a discrete group, circle or torus is fine for me)?

Where the residue class is represented in the unit interval or square (as
the command modp does in the finite case)?

What I have in mind is to modify 'argument' to 'argument modulo 2*Pi', but
mod is for integer cases.

Especially in old books (but not only there) the authors prefer the notion
of 'argument' ( = polar coordinates and using the angle).

Sometimes it comes to something like 

                | arg(-z) | < Pi and | arg(1 - z) | < Pi

which I prefer to have in terms of interval notation 'z in ... ' or its
complement  'not (z in .. )'.

I do not even know how to get | arg(z) | < Pi  <==> z is not a negative Real. 

How can I do it in Maple?

With Maple 12 the compiler accepts complex complex floats.
However there is some limitation in using compiled results:

  # a simple function to be called by another
  foo1:=proc(z::complex[8])::complex[8]; return z*I end proc;
  foo:=proc(z::complex[8])::complex[8]; return foo1(z); end proc;

Now compile:

  cp1:=Compiler:-Compile(foo1);
  cp:=Compiler:-Compile(foo);

The first call works, the second gives an error:

    Error, (in printtab[CodeGeneration:-Names:-FunctionCall])

There is a very nice sheet by Sergej Moiseev Orthogonal Functions, Orthogonal Polynomials, and Orthogonal Wavelets series expansions of function at the Application Center, www.maplesoft.com/applications/app_center_view.aspx.

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 a continous anti-derivate (cos(2*u*m)-alpha*u*sin(2*u*m))/(4*u^2+1)
w.r.t. u, for alpha and m Reals, 0 < u.

What I get with Maple in terms of Ci and Si jumps in m=0 (and for m=0 it
is not defined, due to Ci).

The best I got was

  Si(-conjugate(v))-Si(v); eval(%, v=m*(2*u+I));
  psi:= unapply(%, u,m);
  chi:= (u,m) -> piecewise(0 <= m, -Ci((2*u-I)*m)+Ci(m*(2*u+I)), 

I wanted to use (one of the variouos) cosine transforms DCT, but only find FFT in Maple12.

Googling did not give me more (except there seem to recipes to reduce my theme in some
brute (?) ways to a FFT problem).

Is there any Maple solution around (even if I can use Clenshaw's algorithm having only a
moderate size - but want to see some generalisation ...)?