## 12 Badges

15 years, 247 days

Dr. Robert J. Lopez, Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books including Advanced Engineering Mathematics (Addison-Wesley 2001). For over two decades, Dr. Lopez has also been a visionary figure in the introduction of Maplesoft technology into undergraduate education. Dr. Lopez earned his Ph.D. in mathematics from Purdue University, his MS from the University of Missouri - Rolla, and his BA from Marist College. He has held academic appointments at Rose-Hulman (1985-2003), Memorial University of Newfoundland (1973-1985), and the University of Nebraska - Lincoln (1970-1973). His publication and research history includes manuscripts and papers in a variety of pure and applied mathematics topics. He has received numerous awards for outstanding scholarship and teaching.

## min[index]...

The following two steps worked for me.

bb:=abs~(b);

min[index](bb);

The first command produces a list of real numbers; the second, returns the "location" of the minimum.

You could combine both into one step: min[inded](abs~(b))

The tilde maps the abs command onto each element of the list b. (The tilde is a newer construct than the older map command.)

## Equation Manipulator...

In addition to the LinearSolveSteps command, there are other tools in Maple to help with solving such linear equations.

For example, bring up the Context Menu (right-click in Windows, etc., elsewhere) and select "Manipulate Equation." An interactive tool pops up. In this tool, you can apply the various transformations you see in the stepwise solution provided by the LinearSolveSteps command.

You can also select terms in the equation and wait for Maple to provide suggestions for transformations (i.e., a next step).

If you know what steps you want to apply, you can also implement them stepwise from the keyboard. For example, to add 3 to both sides of the equation x-3=7, write (x-3=7)+3 and Maple will return x=10.

If you want to start out knowing what the solution is (so that you can recognize it when you find it stepwise) bring up the Context Menu and select the Solve option.

## Try Explore...

If you executed plots:-implicitplot(y=x+c,x=-1..1,y=-1..1); you would have gotten an error message indicating that "c" needed a value. But  you report that you got empty axes. So, we are now guessing what it was that you actually tried.

My suggestion would be to try the Explore command:

Explore(plots:-implicitplot(y=x+c,x=-1..1,y=-1..1,view=[-2..2,-2..2]),c=-1..1.0);

This draws a line segment whose location is controlled by the value of c, and the value of c is controlled by a slider under the graph.

If you used any form of the plot command applied to the equation y=x+c, or an equation of that form with c given a value, you would have obtained an error message. (The plot command graphs expressions, not equations.) Again, you do not report that you got an error message. Hope some of this helps.

## Context Menu...

Bring up the Context Menu (right-click in Windows) and select the option Standard Operations->Determinant.

If you do such a calculation using 1d input at a red prompt in a worksheet, Maple will write the underlying code that gets executed. That would show the Determinant command is part of the LinearAlgebra package.

## Wilhelm Werner's package...

In four Tips & Techniques articles (Maple Reporter series) between December 2006 and April 2007, I compared how to create and explore Fourier series with built-in Maple commands, and with three different packages contributed by Maple users. The first package is the one referenced by the OP, the one by Khanshan. I always found the second package, the one written by Prof. Wilhelm Werner, to be the best of the three. I believe Prof. Werner has maintained his package over a longer period of time than did Khanshan. I would recommend that the OP consider Werner's package.

The following link is to the Maple Application Center where Werner's contribution can be found.

https://www.maplesoft.com/applications/author.aspx?mid=162

The link to my T&T article describing this package is also in the Application Center:

https://www.maplesoft.com/applications/view.aspx?sid=4885

Since I wrote that sequence of articles, the Maple OrthogonalExpandsions package has been written and made available for direct download and installation from the Cloud [or link in the Application Center, for Maple versions older than 2017]. This package generalizes to the extent that it can deal with expansions in terms of a basis of orthogonal functions, not just orthogonal polynomials.

## Solution exists...

It took only a minute to enter the coefficient matrix interactively. The determinant of that matrix is zero, so, since the equations are homogeneous, a nontrivial solution exists. It's easy enough to generate the equations from the coefficient matrix. The solve/solve option from the context menu then provides the solution w = 3*z*(1/2), x = -(1/2)*z, y = z, z = z. Check your worksheet for anything that might be causing your "solve" to come up empty.

## Control+Shift+R (or C)...

If the input form of the matrix is generated by the Matrix palette, then placing the cursor at the end of the row or column after which the insertion is to be made, and pressing Control+Shift+R (or C) will insert an additional row or column template into the existing input form of the matrix. This is the same device that works on the piecewise template in the Expression palette.

## CrossSection command...

Student:-MultivariateCalculus:-CrossSection( .8707945038*exp(-50.00000000*(m-.842e-1)^2+2.745342070*(m-.842e-1)*(a-2.3722)-.1046792095*(a-2.3722)^2), m = -.2, a = -4 .. 4, m = -4 .. 4, output = plot, planes = 1, axes = boxed, scaling = unconstrained,caption="");

Actually, if you use the Cross Section tutor from the Student MultivariateCalculus package, you will see this command at the bottom of the tutor. You get the desired graph in the tutor, and can copy/paste the command from the tutor to the worksheet and modify the command to suit.

My first reaction was to use the intersectplot command from the plots package, but the arguments for this command are either two expressions or two implicit representations. PP is an expression, but m=-0.2 is implicit. The mix of the two forms causes problems. Hence, the switch to the CrossSection command. The curve you want to see on the PP surface is a "plane section" in the language of multivariate calculus.

## Embedded Components?...

Perhaps Maple's embedded components will let you construct the "interface" mentioned. Embedded components can be accessed through the Components palette. Each such component has a help page describing its use.

## textplot or drawing tools...

The textplot command in the plots package is designed to code the writing of text or symbols on a Maple graph. It survives re-execution, but is tedious to implement.

An alternative is the set of drawing tools that can be accessed from the toolbar for plots. This tool makes it far easier to annotate a graph. The downside is that the annotations are not permanent. I usually get around this by then exporting the graph to some appropriate format (right click on the graph and select "Export"). The exported graph can then be re-imported into Maple as an image, and a re-execution of the worksheet will not damage the picture. But the graph is no longer interactive.

Others have addressed the issue of coloring curves.

## Visualizing region of integration?...

If this question arises from the task of visualizing a region of integration in 3D, perhaps the task template at

Tools/Tasks/Browse: Calculus-Multivariate/Integration/Visualizing Regions of Integration/Cartesian 3-D

might be of some help. The code for drawing the graph is visible by right-clicking on the Plot button and selecting "Click Edit Action."

The idea for coding this and related task templates stems from the work of Tim Murdoch who coded the package calcplot while at Washington and Lee University in the early '90s. Tim left academe and I have never been able to track him down since. His insight into graphics coding lives on in my rendering as found in these task templates.

## Atomic Variables...

If you color your variables, then convert them to atomic variables, they will retain their color upon output. This works in Maple 2017, but I believe that in some earlier versions of Maple certain properties of atomic variables were not preserved. If color is one such property, then there will exist a version of Maple below which the device advocated here will not work.

## rhs?...

Wouldn't rhs(Soln[1]) work? And to get it as a float, evalf(rhs(...

## Context Menu option - Join...

Right-click on a sequence of two lists and use the Join option.

The code executed by this step is map(op,[sequence of two lists]);

In other words, the op command extracts the elements of a list, and by mapping it onto the sequence of two lists, the elements of both lists are extracted, forming a new sequence, which is then made into a new list by the square brackets. I can't vouch for the efficiency of this approach, but it was coded by one of the best programmers at Maplesoft.

## Cursor behavior...

Me too.

Maple allows the cursor to "misbehave" in a number of situations, at the bottom of a screen, and within a worksheet or document, expecially when deleting large blocks of material or closing sections, etc.

My expedient is to add extra blank document blocks to the bottom of a Document to raise the last line of text to the middle of the window, very necessary when using Maple for a presentation.

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