I have run into a "funny" feature of 2-D input: It seems to convert something like k/2 into this k*`^`(2,-1). While this would often not be an issue (it is correct after all), it becomes a problem when used in an argument list to a procedure. It becomes even more of a problem when, by chance, I have overloaded `^` to act on specific types that I have defined.

Let me try to explain briefly. I have a package called "Lattice" that does whatever it does (not of relevance here). I am writing a little manual for this package, for which I use 2-D input so I can write it in Maple and have the examples right in it and "live".

Here is what happens:

with(Lattice) # load the package

QFh:=Quad(0,kf/2) # Define an element for Lattice

Error, invalid input: Lattice:-`^` expects its 1st argument, element, to be of type Element, but received 2

Copy-pasting kf/2 into a 1-d worksheet, I get

QFh := Quad(0, kf*Lattice[`^`](2, -1));

So it uses Lattice[`^`] which actually appears to bypass the overload I have in the Lattice package. `^` is defined like this in Lattice:

`^`:=proc(element::Element,n::algebraic) option overload; # Element is a defined type in Lattice
...
end proc;

How can I possibly rewrite `^` to fall-back to Maple's ^ operator when called as Lattice[`^`] ?? I know there is a function overload() but have no experience with it. Would it even help?

Or am I missing something completely here? I do not use 2-D input for my usual work, but in this case I want and need to use it. The reason for its bizarre rewrite of "/2" is beyond me. Note that I can replace /2 by *0.5; but that causes problems later on for algebraic work as 1/2 is not 0.5 in Maple. I tried *1/2 but that has the same problem.

Has anyone a clean solution for this? I assume this effect is not limited to my own package but would affect others as well.

M.D.

PS: I ran into this using Maple 15 but I doubt it is specific to this particular version.

I ran into a problem with the physics package that I subsequently solved. But I am wondering whether this would be a candidate for an SCR and/or be considered a bug.

The calculation I am trying is actually (so far) very simple.

I define a Hamiltonian H:

H := sqrt(p_^2*c^2+m^2*c^4); # note the square of vector p_

p_:=p1*_i+p2*_j+p3*_k;

H;

So far so good. Now I want to take the differentials of H against the components of p:

diff(H,p1) assuming c::real;

Hmm... I am not sure why the p2 and p3 still show up; but then, the product between the unit vectors should be 0 for different ones and one for equal unit vectors so maybe this is ok.

But H behaves weird: I can simplify it:

but if I try to do anything with it, it barfs:

dH+0;

Error, (in Physics:-Vectors:-+) invalid operation * between vectors _i and _j

As it turns out the issue is the square of the vector p_. Maple (or rather, Physics) does not recognize that it needs to expand p_^2 as p_.p_ and seems to treat is like p_*p_.

I would like Edgardo---& others more experienced with the Physics package than I am---to look at this. I do not understand the Physics package well enough to judge whether overloading the exponentiation operator to make this work is the right thing.

The example works once I replace p_^2 by p_.p_. But the ^2 notation is fairly standard usage so it feels slightly awkward.

Thanks,

Mac Dude.

Derivation_of_H.mw

I know this has been dealt with before here, but I have forgotten the proper way to trim a small imaginary round-off from a result. I cannot locate the proper answer in MaplePrimes; and the Mapledocs are either quiet about it or it is hidden in a difficult-to-find place.

What I want is to ignore ny imaginary part below a certain threshold. Ideally, it takes the threshold in relation to the real part but I am not particular about this.

Thanks in advance,

Mac Dude

Here is one I have been struggling with lately:

I have a relatively large module with many procedures inside (plus some other data structures). In one of the procedures, it turns out that it would be convenient to have a subprocedure defined inside to both shorten the code by avoiding duplication as well as make it more error proof (once the subprocedure is debugged it'll be correct everywhere it is used). Here is the skeleton

Lattice:=module() option package;
export Track;   ...
   Track:=proc(arguments) uses LinearAlgebra;
   local trackElement;
      ...

      for ... do
         result:=trackElement(parms); # This does not work
         ...
      end do

      trackElement:=proc(arguments) uses LinearAlgebra;
         ...
      end proc; # trackElement

   end proc; # Track;

end module; # Lattice

The problem I have is that procedure trackElement is not recognized as i found out running the code in the debugger. I can make it work by taking trackElement out of Track and make it local to the Lattice module. While functionally this works (and it is how I have it now programmed), I do  not like it as every proc in the Lattice module can see trackElement. That should not be so, I want it local to procedure Track, which is where it belongs.

I really thought I could define procedures within procedures. Am I wrong? Or is there something else ging on?

TIA,

Mac Dude

PS: The whole module is more than 100 kB of Maple code sitting in a library. I refrain from uploading it here as it would be non-trivial to get going even for a simple test case.

I am working on a problem involving sums in Maple and I find Maple's facilities lacking.

Specifically; I want to convert the square of a sum into a sum of squares plus the cross terms (which is a subtask of a larger problem). So I start with

sum(E[n],n=1..N)^2;

and immediately get stuck as I do not find any command that does anything with it. The expansion of this is known and easy to derive:

sum(E[n],n=1..N)^2 = sum(E[n]^2,n=1..N) + 2*sum(sum(E[m]*E[n],m=1..n-1),n=1..N);

Maple knows nothing about this relation. I have checked out packages like SumTools but have not found anything useful for this purpose. Quite some time ago I have had difficulty distributing a sum over the elements of its expression; this was answered here and involved a custom function.

Does a package exist that has these kinds of conversions, or do I need to roll my own? It seems a general enough issue that I would expect functions for this to exist.

TIA,

Mac Dude