@Carl Love You are of course correct. Don't know what I was thinking...

It would be interesting to know what the OP gets if he just loads CUDA.

On second thought, maybe his libname got messed up? If that gets overridden e.g. by assigning his private library area then Maple likely cannot find the system packages anymore.

M.D.

@Carl Love Ok, I understand that specfunc({sum,Sum}) selects an expression of the form sum() or Sum(). I do not really see why/how patfunc(`+`,anything) applies to the argument of the sum or Sum, i.e. restricts selection to expressions like Sum(A+...+B). I have not actually tried this; but off-hand I would suspect the And never can be True… (implying that Sum() is not of type `+` which I think is the case).

M.D.

@Carl Love Uhh, you got me there... It actually did work in my sheet; but only because I had a local definition of your original function masking my version, which is in a library. Since I really needed the result, first and foremost, I did not double-check this. The problem of course is the factor 2 in front of the sums.

Now, my DistSum still works in my case when I map it over the expression, so all is not lost (and I got where I needed to get already). I'll study your modification to see if I can figure out what exactly it does. I tend to get queasy if I just adopt something without understanding it so I need to do that before it becomes a part of my library. I know the help page you refer to, and yes, it is dense, and I won't claim to understand it.

Many thanks,

M.D.

@Axel Vogt 

@Carl Love

@acer

Thanks much all three of you; all answers/comments were helpful.

The suggestion to use the inert Sum rather than sum is absolutely correct; I had already gotten there (after posting my question) but that in itself did not solve my problem. I actually did check SumTools but did not find anything in there that looked like it would help. It seems like it should have such (rather elementary but useful) functions.

I voted Carl's solution best since it is terse but quite understandable, and I was able to easily modify it to add some checks for validity (as it was; it would merrily distribute the Sum across the factors of a product...No!). This in no way is meant to disregard or disparage Axel's solution. Incidentally, I do not use a range here as the whole computation is done in a general context where the range is not known (and not relevant either). Application of the formulae generated of course will involve ranges.

In case someone is interested, here is the "final" version of Carl's procedure with some added validity checks; coded as a function. Casual testing implies that it works at least for simple cases, and it can be mapped over the terms of simple expressions. It is still a one-liner although I break these up to avoid awkward line breaks.

DistSum:=(xpr)-> `if`(op(0,xpr)='Sum' or op(0,xpr)='sum',\
                                 `if`(type(op(1,xpr),`+`),\
                                       subsindets[flat](xpr, specfunc({sum,Sum}),\
                                                               xpr-> map(op(0,xpr), op(xpr))),\
                                       xpr),\
                                 xpr);

Thanks much,

M.D.

@jbail I just copy-pasted the commands into Maple 15 (fresh sheet, restart on top) and get a plot like Kitonum's.

Are you by any chance in Document mode (i.e. typeset input)? You should be in Worksheet mode whe you paste (red Courier font, Maple prompt at begining of a line.

M.D.

Well, even if it does not print, Maple still handles the expression and you can work with it. Simplify often expands along the way which may cause the long expression. You can try all the usual tricks of the trade to reduce this (I often like collect); and sometimes it helps adding an assumption if you know the domain of some of your variables.

M.D.

@Carl Love Interesting, the use of Record in your example. I had not thought about that.

Below is what I came up with for the exponential averager I need. I want it to return the average after each sample added. I don't need the ability to give a list as argument---I can always map the add function over the list---but I do need a reset function.

The nice thing about doing it this way---besides running several averagers in parallel---is that I can replace the exp. averager with e.g. a douple exp. averager without changing the code that uses it at all, just need to change the constructor. This is one of the features in Maple I cherish.

Mac Dude

--------------

ExpAvg:=proc(lambdap)
 
  return module()
  export add,samples,reset;
  local lambda:=lambdap;
  local avg:=0;
  local n:=0;

    add:=proc(sample) # add sample, return average
      local i;
      avg:=`if`(n>0,lambda*sample+(1-lambda)*avg,sample);
      n:=n+1;
      return avg;
    end proc; # add

    samples:=proc() # return number of samples
      return n
    end proc; # samples

    reset:=proc() # reset this averager
      n:=0;
      avg:=0;
    end proc; # reset

  end module; # the generated module

end proc: # the constructor

ExpAvg.mw

@tomleslie Yeah, I was thinking along those lines initially, too. But I want this to be general & would be concerned tht it is a bit fragile a construct. So I think the module factory is the way to go.

Thanks,

M.D.

@bfathi Ok, without orbit.sav I cannot really run the code. G and Mz are undefined; I assume orbit.sav sets these as well as the arrays XS and YS.

For me the code gets stuck in the loops.

One observation: You use arrays X and Y without declaring them beforehand. While this can be done it leaves Maple to decide what kind of array to use, and I have found I disagreed with Maple's decision. I suggest you do something like
X:=Vector(329,datatype=float);

and the equivalent for any other array you plan to use. With the datatype you also force an evalf and avoid storing symbolic expressions of ever increasing length. If the evalf cannot fully proceed you will get an error and know where the code goes wrong.

Also note that you want to set the starting point for the loop involving n. Not a big deal; but better to know exactly what is being done.

I don't have time right now to continue but hopefully can get back to this later, in the evening.

M.D.

It may not be clear what you mean by "corner". The diagram suggests you are referring to the angles against the vertical axis (what I guess you call the "neutral axis").

I'd first see how to get the angles between the vectors a, b and c from the "corner" angles and the known values of k. That part you can debug by itself. Once you have those, you will be able to solve your problem. It is likely that you get multiple solutions, and you need to settle on the one(s) you want in order to be able to continue.

As far as solving the equations in your worksheet (whatever they mean); you may be able to make progress by replacing the cosine terms with constants, trying to solve, and putting the cosine terms back into the solution. It is probably easier using freeze and thaw for that (rather than subs); or use frontend (which I am having a very hard time with, so I rarely use it). Check the docs for these; it is a bit too detailed to explain here and in any case I would need to fiddle with it to get it right (& I really do not have the time for that right now). It is better you do this on your own.

Yes, there are several obvious errors.

"whit(plots)" on line 1 should be "with(plots)"

Further down there are a number of semicolons (;) missing.

I'd watch out for the
i:='i'; j:=i+1;

construct and make sure it does what you want. If it fails, consider defining j as a function:

j:=ix-> ix+1;

and then reference j(i) when you use it. Note that I deliberately use another name as argument to make clear what this is.

You need to do some basic checking on your code. While Maple's error messages can be cryptic, these ones you should be able to find yourself. Do note that, if Maple returns a function unevaluated (e.g. returns "whit(plots)") it means the function is not (yet) defined; either by design or by error.

M.D.

@shzan I'd argue Maple is doing the correct thing. After all; without specifying f(x) there is no way of telling what f'(x)|{x=1} would result in. It may need to be a limit, or whatever. As Maple writes it; you can work with it. f'(-1), if undefined, is useless even if the limit exists.

M.D.

@Preben Alsholm I'd like to add that, when you formulate the problem as a differential equation and dsolve that, the constant is carried (as it has to in order to be able to solve for a particular initial condition).

M.D.

@acer Hmm, I was not aware that I could index into the Record. I use the :- syntax to get at its members.

(Having said this; I now recognize the indexing syntax in use for members of Packages; esp. Maple-supplied ones. I guess I never made the connection...)

I'll certainly try that.

Thanks,

M.D.

@nm My .mapleinit (name on OS X) file has the statement print("Maple Init loaded..."); at its end.

Very reassuring when it comes up.

Also interesting when I played with Maple's Grid functions (Grid:-Seq et al.) and it showed up 4 times...

M.D.