Axel Vogt

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19 years, 354 days
Munich, Bavaria, Germany

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These are questions asked by Axel Vogt

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?
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