@krismalo That should be *~ rather than ~*.

@Markiyan Hirnyk Thank you.

I think that the term "p-value" is nearly universal (well, I only know about English language) for this concept. Do you think that this would be a suitable replacement for P(>|t|)?

@taro Let me know if you need any further explanation. I thought that sort(..., key= ...) was the year's best new feature for whichever year it was added---Maple 18 I think.

@tomleslie I think that the problem is that isolating R/R[0] results in a much more complicated expression, with an especially nasty looking RootOf. This explains why the plotting is slow---there's an fsolve required for every point. It doesn't explain the inaccuracy. But it looks like some catasthropic cancellation may be occuring.

The lesson is that you should trust implicitplot: It's a very fast and usually very accurate command suitable for almost any relation between two variables. If you read its help page, I think that you'll see at least that it's well designed.

@taro My command is easy to study by taking it apart like this:

indets(hh);
%[];
[%];
`[]`~(%);
map2(solve, hh, %); #These are all possible substitutions.
select(s-> nops(s)=1, %); #These are the 7 injective substitutions.
op~(%);
map2(eval, nb, %);
simplify~(%);
sort(%, key= length);
%[1];

@fatyplus Is it appropriate to assume r > 0? Then does the following give you what you expect?

Y:= evalc(f1*(Re(Z)+Re(diff(Z,x)))+f2*(Im(Z)+Im(diff(Z,x)))) assuming r > 0;

f1*(cos((1/2)*x)*A0/r^(1/2)+cos((1/2)*x)*r^(1/2)*A1+cos((3/2)*x)*r^(3/2)*A2-(1/2)*sin((1/2)*x)*A0/r^(1/2)-(1/2)*sin((1/2)*x)*r^(1/2)*A1-(3/2)*sin((3/2)*x)*r^(3/2)*A2)+f2*(-sin((1/2)*x)*A0/r^(1/2)+sin((1/2)*x)*r^(1/2)*A1+sin((3/2)*x)*r^(3/2)*A2-(1/2)*cos((1/2)*x)*A0/r^(1/2)+(1/2)*cos((1/2)*x)*r^(1/2)*A1+(3/2)*cos((3/2)*x)*r^(3/2)*A2)

@nidojan Thank you. Calling it a workaround makes it seem as if there is a bug or as if display wasn't the intended way to do it. There isn't a bug, and using display is the official, designed way.

All attached worksheets are read only. There is no problem. It just means that you need to change the name if you want to save it after modification.

I see that you keep bumping this Question to the top of the stack. Please don't change the Products list in the header again, unless it's to select your version of Maple. Your Question is about Maple alone; checking off other boxes is disrespectful.

I think that your problem is too general to be solved by a little bit of Maple code. Perhaps it could be the subject of a whole package with hundreds of lines of code. In particular, your iteration requires as an initialization the solution of a PDE, and it requires two indefinite integrations at each step. These are difficult things even in specific cases, let alone with the generality that you specify here. After the PDE and the indefinite integration are handled, the rest of your iteration is straightforward.

@Markiyan Hirnyk 

It's just a triviality based on the random function used, which should have no effect on the OP's problem. However, by randomizing the initial point (away from the default (0,0), which is likely a critical point), the example can be improved. I updated the code to do this, so please try again.

I have no idea where all that Typesetting junk that you show comes from. Let's see if it goes away. If not, try 1-D input.

@Kitonum I'm somewhat skeptical about using algsubs in this context, even though I don't have at hand an example where it doesn't work. I'd use simplify with side relations:

subs(t= a^4*b*c, collect(simplify(S, {a^4*b*c= t}), t));

or

thaw(collect(simplify(S, {a^4*b*c= freeze(a^4*b*c)}), t));

@emendes Please show me an executed example of what you mean by "the extra messages that come with Vector". You can attach a Maple worksheet to one of these posts. If you are trying to use op on a Vector, then that is the problem, for the same reason that nops won't work.

If you have an ordered one-dimensional structure whose contents don't need to be modified, then it's usually best to store it as a list rather a Vector.

A help file just starts as a Maple worksheet. Typically one would write one worksheet for each proc. Then use the commands in the HelpTools package to collect the worksheets, index them, and turn them into a help database.

@nm Fortunately, it's very difficult to write large Maple programs in anything other than plain text, and there's no good reason why one would want to. The majority of the Maple Programming Guide reflects this.

@emendes Note that interface(rtablesize= ...) only affects how rtables (Vectors, Matrices, Arrays) prettyprint in the GUI. It has nothing to do with programmatic access to these structures or how they print with lprint or printf.

I have interface(rtablesize= 25) set in my initialization file. You probably don't want a 1000x1000 Matrix to fully display in your GUI.

@emendes The most general command for the number of elements is numelems. It works for new- and old-style vectors, matrices, arrays, tables, lists, sets, and strings.

The operands of a new-style Vector (or Matrix, Array, or rtable) are details refering to its internal representation (such as the dimensions, datatype, indexing, storage order); nops stands for number of operands, and it returns a count of these details.

LinearAlgebra:-ColumnDimension is probably too specific, and in the long run, you may regret that you used it. It also bothers me that these low-level operations on Vectors and Matrices are not linear algebra, so they shouldn't be part of LinearAlgebra.

Why are you using row vectors? It's generally easier to use the default column vectors. It you're choocing row simply for display reasons, considering transposing before display. If v is a Vector, than its transpose is v^+ or v^%T (your choice). If LV is a list of vectors, then you can use LV^~%T.