lopez@maplesoft.com@alecjacobson 

The help page for the EulerLagrange command specifically states that the argument for this command is an expression in t, x(t), and x'(t). The Description section suggests that for higher-order functions, use variables to represent derivatives, and gives an example of how this might be done.

Alternatively, using Physics:-diff, you can differentiate with respect to a function such as x'(t). Hence, it is possible to implement the Euler-Lagrange equation from first principles. Decidedly more tedious, but certainly possible.

rlopez@Noor2015 Note that the syntax solve({sin(x)+y=0,y^2-x=0},{x=0..6,y=0..6}); is not valid. The solve command does not take any specification for location of roots. That syntax would work with the fsolve command, the numeric solver. The exact solver, the solve command, does not have that capability.

The solve command will not return "points" in the form (a,b) or [a,b]. Maple just does not do that. Ever.

Executing solve({sin(x)+y=0,y^2-x=0},{x,y}); returns solutions in the form of a RootOf construction. Applying the allvalues command to this expression yields two complicated, but complex, solutions, and a real third solution of the form {x=0,y=0}. This is how Maple indicates that the real solution is the point (0,0).

Assuming this last form of solve has had allvalues applied, and the result is called SOL. One way of picking out the real solution is by executing remove(has,[SOL],I)[]. This will result in the set {x=0,y=0}.

If you have a command that returns a set of equations such as {x=a,y=b} and you needed to have this result in the form [a,b], the simplest way to do that is to execute eval([x,y],{x=a,y=b}), that is, evaluate the template [x,y] using the information in the set of equations.

@tazatel Use the options shown in the following form of the PlotPositionVector command.

PlotPositionVector(R,x=-1..1,y=-1..1,vectorfield=F,vectorfieldoptions=[width=.05,color=green],vectorgrid=[3,3],scaling=constrained);

The help page is dense with descriptions of how the graph of curves and surfaces, along with associated vector fields, can be adjusted.

@vv The first appearance of a true bivariate limit functionality in Maple is in Maple 17. Check ?updates,Maple17,BivariateLimits. Initially, the algorithm worked for isolated singularities. Eventually, it was updated to allow for non-isolated singularities. And soon, the restriction to rational functions will disappear.

@pacew Your observation that after the graph has been constructed in the Plot Builder and inserted into the worksheet, the "system exhibits the same behavior." Once the graph is in the worksheet, the connection to the computational engine is lost, and the GUI is able to manipulate just the existing plot data-structure. It can't add new data to the structure, but only manipulate the data that the math engine generated.

This is a shortcoming that our developers have discussed for many releases, and correcting it will require a great change in how graphs are generated and then rendered.

Once a graph has been inserted into the worksheet, connection between the graph and the computational engine of Maple needed for doing more computing is lost. Hence, when the image is moved by the pan operation, it is the GUI that is changing the display, not the math engine. This situation holds for all changes made to the graph via the context menu for the graph.

It would be much better to use the Plot Builder to obtain the graph. In this Assistant, the graph can be manipulated because there is still a connection to the math engine. The Preview button in the Plot Builder lets you see what your graph will look like when you select Plot.

RJL Maplesoft

@Mac Dude In Maple 2016, document block management is available through the Edit menu option "Document Blocks". With this option, document blocks can be created, removed, edited, etc. It also helps to make the "Marker Column" visible by selecting the View menu option "Markers". This column on the left of the workspace shows pairs of opposing triangles that delineate each document block.

@peter2108 Not sure what version of Maple you are using, and not sure just what you tried. But I just tried this: On a graph, select Drawing and open a text box. In that text box, swith to Typeset math. Type sqrt and press Esc. The dialog listing things that start with "s" appears, and selection of the radical inserts the square-root template. I get the same dialog with Control+Space.

@John Fredsted 

Perhaps NullSpace(M) is even simpler?

The collection of steps is contained in a hidden table. The ultimate value of the integral sits outside that table. Hence, only the final result, the value of the integral, is being sent to the Math Container. This is merely by way of explanation. The functionality is obviously deficient.

Also, in Maple 2016, the MultiInt command can be accessed through the Context Menu once the Student MultivariateCalculus package has been loaded. This provides some measure of "syntax-free" access to the MultiInt command, but does not fully address the issue raised in the post.

RJL Maplesoft

I believe that any "1D" math (which I prefer to think of as textual input) is equivalent to its "2D" counterpart (which I prefer to think of as typeset input). Of course, I have not tested each and every instance of this in the whole of AEM, so this is a conjecture on my part, based on feedback and information from the developers of typeset math notation.

There are many places where typeset math as input is easier to read. For example, I find reading a raised exponent easier than reading syntax such as x^2. On the other hand, there are lines of Maple code in the AEM book that lean toward "programming" and it's not at all a generally accepted position that typeset math is appropriate for coding.

So much for the pro & con on whether the ebook should have all its "red code" simply changed to typeset "black code."

The bigger issue is whether or not the format of the ebook is optimal. Apparently, there's some voices being raised to the contrary. No doubt, Maplesoft has, in the years since the AEM book was first written, developed many new features in Maple itself that would all for a different paradigm in an ebook. I'll be retiring at the end of the year and meanwhile, I'm contemplating a complete rewrite of the ebook to take into account the new tools available in Maple.

But for now, let me just point out a few details of the evolution of the text and its ebook form. The materials grew from worksheets written in the early '90s for use in my classes at RHIT. These worksheets were exported to LaTex, massaged so that the obvious Maple was removed, and given to Addison Wesley as the deliverable for the text. The worksheets themselves went into the back of the book on a disk. When the text went out of print, I got the copyright back, and at the suggestion of Maplesoft itself, morphed the worksheets that accompanied the book and upon which the book itself was built, into the ebook.

So, the worksheets in the ebook still have the flavor of their classroom roots, namely, to capture the mathematics, and to show users how to implement that mathematics in Maple. In the Maple content projects I've worked on directly for Maplesoft, I've moved in the direction of separating the presentation of mathematics from the implementation in Maple. So, for example, in the calculus study guides I've written, examples are presented in three forms. First, there's a mathematical form where no Maple appears. Then, there's a Maple version using syntax-free techniques. Finally, there's a version using Maple commands.

Would a similar separation of mathematical presentation and implementation in Maple be appropriate for AEM? I really don't know. I wouldn't mind hearing from users of AEM what they think. And for anyone who bought a copy of the ebook and was less than satisfied, I apologize for having failed. But I would appreciate hearing from anyone with suggestions for improvements that I'd like to spend my retirement making.

Go to the View menu and select "Markers" so that you can see the column of opposing triangles that delineate document blocks. Be sure you are entering typeset math in a document block in "math mode."

If you are still having trouble, post some form of display showing what you are doing. Otherwise we are all left to guess at the problem.

RJL Maplesoft

Seems to me that you have values for E, the independent variable. You also need the corresponding values of epsilon, the dependent variable. Given such pairs, there are a  number of ways to obtain a least-squares fit. The easiest way is to use the Curve Fitting Assistant available from the Tools menu. This Assistant is an interactive tool for obtaining a least-squares fit, and a graph of the data points along with a graph of the fitting function.

There are other built-in tools for obtaining least-squares fits in the Statistics package, but these are given in the form of commands whose syntax can be found in their help pages.

RJL Maplesoft

I brought this post to Primes to the attention of Maplesoft's Tech Support group, and received back the following answers. It appears that the scrolling issue has been fixed in the next version of Maple. The sticking cursor problem couldn't be replicated, so it seems that it was fixed in Maple 2015.1.

RJL Maplesoft

@Carl Love I admit that the paradigm Carl enunciates was not in focus as I wrote the blog. The issue to me has been that the examples from which I learned the material all made decisions based on the characteristics of the particular matrix A. I was looking for a process that uniformized these choices. I don't think I completely succeeded in that regard. My process still has points at which choices of basis vectors have to be made.

I've looked at the code Maple uses for producing the transition matrix. If any choices have to be made, it seems that Maple has been coded to make those choices. But I have to admit that so far, I've only scanned the code, I haven't gone down that tedious path of copying and pasting it so that I can execute it, analyze it, etc.

As I mentioned to the development team yesterday afternoon, it's really too bad that the design specs for Maple code didn't require that coded algorithms be accompanied by a mathematical description of the algorithm. I have always found it difficult to extract an algorithm from its code.

If anyone has more facility with this process and chooses to apply that skill to the algorithm by which Maple produces the transition matrix to Jordan form, I, for one, would be happy to benefit by such.