If the DEplot command in your post is copied and pasted into Maple as 2D math, it "looks" correct, but does not evaluate. If it is pasted into a worksheet as 1D math (i.e., the red stuff), then you will see that the spaces after DEplot, and after diff, translate to multiplications (an explicit asterisk can be seen). Remove these two spaces (or asterisks) and your command draws the graph you hoped for.

RJL Maplesoft

The interactiveparams command in the plots package will generate an animation on one parameter with control of other parameters by sliders. For example, to animate the graph of x+a+b, with a being the animation parameter and b being under the control of a slider, use

interactiveparams(animate,[plot,[x+a+b,x=0..1],a=0..1],b=0..1);

One way to discover this syntax is to launch the Plot Builder on the expression x+a+b, and to select Interactive Animation with 1 parameter in the "Select Plot Type anbd Functions" section. Then, check the box at the bottom, to the right of "On 'Plot" return command". The syntax for the appropriate use of the interactiveparams command will be returned. Of course, if this box isn't checked, the Plot Builder itself will generate the graph with the sliders. The one disadvantage of the interactiveparams command is that it launches a Maplet, which can't be saved or embedded in the worksheet. It's ephemeral, living only as long as it's "up."

The alternative is to use the animate command, and simply change the value(s) of the parameter(s) in each different animation.

RJL Maplesoft

The question asks for help graphing standing waves. Then it goes on to "clarify" by stating "what would happen if different types of waves traveling..."

Well, you either want to graph standing waves, in which case nothing moves, or you want to graph traveling waves where you can see two waves interacting. And for this, you need to add two waves, not multiply them. For the traveling waves, you also have to decide if they are traveling on an infinite line, or are they reflecting off a fixed endpoint.

RJL Maplesoft

I believe you want to complete the square in both x and y. If you type the equation of the circle in text form (1D math mode) then you need to include explicit multiplication, even between constants and variables. Thus, use x^2+y^2+2*x-4*y-4=0. If you enter this in math mode (2D math) then explicit multiplication will appear as a centered dot. Implied multiplication can be implemented with a space. Between a constant and a variable, you don't have to enter anything. Maple will understand that to mean multiplication.

Completion of the square is available in the Context Menu (right-click in Windows). The command upon which this is based is the CompleteSquare command in the Student[Precalculus] package. To use that command, either load the package (use the Tools menu with the Load Package option, or execute the command with(Student[Precalculus])) or issue the command in the long form: Student[Precalculus][CompleteSquare](x^2+y^2+2*x-4*y-4=0,[x,y]);

RJL Maplesoft

A solution clearly exists - at least that's what can be concluded from either calculation. But do you know if the solution is unique? The equations are nonlinear, and therefore could certainly have multiple solutions.

RJL Maplesoft

I believe this is a known bug introduced in Maple 15 when the plot code was modified to automatically label the horizontal axis of a trig plot in multiples of Pi.

If it hadn't already been listed in our bug data-base, it is now. Thanks for posting it.

RJL Maplesoft

After generating the desired graph in the ODE Analyzer Assistant, select "Plot" as the item to be returned upon pressing the "Quit" button. Press the Quit button.

Immediately, assign the inserted plot to a name such as "a". For example, as soon as the plot is inserted into the worksheet, execute the command a:=%, where the percent symbol references the (chronologically) (last) Maple computation.

Then,your previous technique of op([1,1],a); etc., will give the results you want.

RJL Maplesoft

with(VectorCalculus):

R:=PositionVector([cos(t),sin(t),t],cartesian[x,y,z]);

PlotPositionVector(R,t=0..2*Pi,tangent,normal,binormal);

This, however, generates an error in Maple 14, but the error has been fixed in Maple 15. Maple 14 will allow this command, provided it is restricted to a curve in the plane, in which case, omit binormal. The 3D case works in Maple 13, 12, and 11.

RJL Maplesoft

Acer's device of taking the arccosine of the cosine has gone into my Little Red Book of Maple Magic. It's one of those things that make you want to say "Now why didn't I think of that?" But if you think about it for a bit, you see that the elementary trig that then takes place squares the numerator and denominator of the argument of the arctangent...

The following is a brute-force path through the radical choke-point. It works because the argument of the arctangent is positive, so squaring to remove the radical in the numerator, then later taking the square root after rationalizing, doesn't introduce a sign error. The map command has to be used three times because the transformations are on the argument of the arctangent.

q := arctan(sqrt(10+2*sqrt(5)) / (sqrt(5)-1));

q1 := map(x->x^2,q);

q2 := map(normal,q1,expanded);

q3 := map(sqrt@expand@rationalize,q2); (Interesting! The at-symbol for composition is inducing the interpretation that I've typed an email address, but I assure you that I didn't.) 

simplify(q3);

This is not the first time I've resorted to simplifying the square, then taking the square root. The danger is the introduction of a sign error.

RJL Maplesoft

q:=arctan(1/(5^(1/2)-1)*(10+2*5^(1/2))^(1/2));

map(rationalize,q) => arctan((1/4)*(10+2*5^(1/2))^(1/2)*(5^(1/2)+1))

Now, if that argument could be factored to the form (1/4)*2^(1/2)*(5+5^(1/2))^(1/2)*(5^(1/2)+1), that is, if  sqrt(10+2*sqrt(5)) could be written as sqrt(2)*sqrt(5+sqrt(5)), then arctan of the resulting expression immediately evaluates to 2*Pi/5.

I have not been able to figure out a transformation of the key radical. That's probably why Maple needs the various tricks being reported here. What seems to be missing is a "simplification" of the radical to the form that arctan then recognizes.

RJL Maplesoft

 If I understand your question correctly, you are asking if it is possible to build a new embedded component in Maple. If that is the question, the answer is "no." The embedded components in Maple are what are available through the Components palette. New components are constructed by the Maple programmers as they see the need for same.

Also, I'm not sure of the distinction between "Big Time" and "small things" but I think that you could answer your own question by looking at the task templates that contain embedded components. Some of the early task templates are command-based, and did not make significant use of components. Many of the newer ones added later make use of embedded components. Whether the usage is "Big Time" or "small things" is something observers will have to answer for themselves.

RJL Maplesoft

 The Maple help system contains a pdf version of the programming guides, and a getting-started guide. Under Help, see Manuals, Resources and more,,,/Manuals

These should be enough to get  you started converting your code to Maple.

RJL Maplesoft

 The "white paper" http://www.maplesoft.com/applications/view.aspx?SID=33840 in the Applications Center might provide a streamlined introduction to using the DifferentialGeometry package for tensor calculus.

RJL Maplesoft

 The red code in the AEM ebook captures the calculations that have been off-loaded to Maple. Getting rid of the red code would remove that which makes the book interactive. Changing the text-form of the input (what Maplesoft calls 1D math) to typeset math input (2D math) would change the color from red to black, but the same issue prevails. The code shows how to capture in Maple the math under discussion. Maple then implements the calculations. The code can be modified as the text is read, allowing experiments, and what-if scenarios to be be explored. Much of the red code can also be converted to use in solving the exercises included with the ebook.

So, getting rid of the red code isn't the thing that caught my eye. It's the second part, converting it to something more meaningful. Well, what would be more meaningful? The intent of the ebook was to provide a mechanism for capturing the math in a format that was live, computable, and adaptable. It is its own meaning.

The alternative would be to have a completely discoursive text with no math, and no live calculations. I don't think that's what I set out to do when I wrote the text.

But I would welcome additional comment on just what it is that the questioner would like the ebook to be.

RJL

RJL Maplesoft

 If the equations are interpreted as they were by longrob, then the sum of squares of aa, bb, and cc is not 1. Hence, h cannot be 1 under this interpretation of the original expressions. Definitely, the original set of expressions are ambiguous as they stand.

RJL Maplesoft