rlopez

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19 years, 340 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.

MaplePrimes Activity


These are replies submitted by rlopez

@C_R 

Sorry to have short-circuited your happiness, but as I expressed in my initial post, this is a problem that has plagued me (and Maple) for a long time. It probably makes no difference to someone using Maple for computations, but it's an irritant to an instructor trying to match notation to a subtle distinction in mathematical meaning.

By the way, in something like -3 - x, it's visual shock to see the first dash as long as the second.

Thanks for your response. I'm keeping score.

@Carl Love 

Great observation! Indeed, let's hope this is an easy fix that will be implemented soon.

@Carl Love 

Thanks, Carl. I'm deeply into an update of my AEM text, one that differs from the ebook version in that I'm re-creating the original text form of the work. The unary/binary issue is rampant and very tedious to correct. Try inserting a space between a too-long unary sign and what it negates. This changes the size of the sign in older versions of Maple. I don't know what it does in 2023, the version of Maple that induced me to bring the issue to the attention of R&D. Not having gotten to first base there, I've opted to work in earlier versions in the hope that one day, Maple will have the issue resolved.

@Carl Love 

But suppose the OP meant to write sin(x)/cos(x) not becoming tan(x) under "simplify." That was the case with all Maple up to and including 2022. That's fixed in Maple 2023. Just guessing.

Make the functionalities of all the Student packages available via the Context Panel.

Load the Student VectorCalculus package and define the vector q:=Vector(<1,0,0>).

Change to spherical coordinates:

MapToBasis(q,spherical) => (1)*e[r]+(Pi/2)*e[phi]+(0)*e[theta]

So, the Physics convention has been imposed, as it has been since at least Map;le 2016 (thee earliest version I can access). To reverse the meaning of the names phi and theta, do MapToBasis(q,spherical[r,theta,phi]) =>(1)*e[r]+(Pi/2)*e[theta]+(0)*e[phi]. Note that it's the position of the angle names in the triple of coordinate names that determines the meaning of these angle names.

However, MapToBasis(q,spherical_math) leads to an error (spherical_math is not one of the 5 coordinate systems supported by the Student package). Therefor try

VectorCalculus:-MapToBasis(q,spherical_math) => (1)*e[r]+(Pi/2)*e[theta]+(0)*e[phi], which is the same as if "spherical_math" were just "spherical."

The reason for this: the "changecoords" command applies only to scalars. To change coordinates in a vector in one of the VC packages, the MapToBasis command is essential. Otherwise, the basis vectors will not be subjected to the change.

Also, note again that in the VC packages, it's not the names of the spherical angles that matter. Perhaps for display purposes, yes. But the function (i.e., meaning) of the angles, no matter what their names, it's the position of the angles in the triple [name1, name2, name3]. The middle name in that triple is always the angle down from the z-axis; the third name always refers to the angle around the z-axis.

Perhaps the help page at ?coords could have mentioned these two issues - (1) the changecoords command is a top-level command, and has nothing to do with what happens in the VC packages. In those packages, the MapToBasis command is much more important but has been left ignorant of the option spherical_math; and (2) the meaning of the names used in spherical coordinates is determined by the position in the triple of coordinate names, not by the names themselves.

 

 

@JAMET 

It's easy enough to sketch a drawing with pencil and paper. Would that suffice, or do you want to see the Maple code that would draw such a figure? (I don't find it particularly easy to use Maple as a drawing tool.)

@Ahmed111 

In the LinearAlgebra package, the noncommutative multiplication operator is the period. I don't know if you used the period and it displayed like a centered bold black dot. I think you will have to figure out a proper entry for z1. If it continues to contain a mixture of ordinary multiplication and noncommutative products, I'm not sure how you can simplify and collect on lambda.

@Ahmed111 

Why is the LinearAlgebra package installed? Is it because you are taking dot products (see your bold black dots where the asterisk for ordinary multiplication is expected) between scalars? I see nothing to indicate that any of the quantities in z1 are vectors, so why the dot product symbol?

Inspect the result of lprint(z1) and you will see that there are some ordinary multipications (*) and some dot prodcts. That use of the dot product operator is why z1 is not simplifying, and why the coeff command utterly fails. Change all the dot product operators to ordinary multiplications and z1 simplifies and coeff will work.

@mmcdara 

https://youtu.be/_8nhHBEHEw0

Projection

Let me climb up on my soapbox and pontificate: (The 81-year-old lecturer in me can't resist, even if he can't be forgiven.)

There are times when one wants an efficiently obtained answer, and there are times when one wants Maple to implement  the computational steps that provide that answer. The efficient solution provided by the MultivariateCalculus package's Lines&Planes tools allow one to think conceptually. "What is the line onto which the projection is to take place, what is the projected point, and how far apart are the points?" According to this mode of thinking, the details of how one obtains the line, etc., are not as important as is the thought process "how is the answer to the question logically obtained?" Once the logical, i.e., conceptual framework is determined, and can be shown to lead to the solution, then the mundane details of the computation that implements the conceptualization can be pursued.

I added my solution to this discussion simply to remind readers that there are other tools in Maple that are worth knowing about. I do indeed appreciate the kind words you attached to my solution.

@FDS 

I am not familiar with the syntax of Mathcad. If you would state clearly what mathematics your Mathcad formula is supposed to encapsulate, perhaps we could tell you the equivalent in Maple. The common language between us should be standard mathematical notation. Then we could determine the Maple syntax that reproduces that mathematics.

I suspect Axel Vogt is right in opining that Mathcad is performing elementwise multiplications between vectors. If that is so, could you then detail what the resulting mathematical expressions would be?

@FDS 

In the Multiple_input worksheet, near the end you define a function f(p), but it contains vectors multiplied by vectors. I think you need to examine just what mathematical objects you are manipulating in that definition.

As far as I can tell, it works fine in Maple 2022.2 running in Windows10 on a 64-bit machine.

I no longer have access to Maple 2022, so couldn't tell if that version exhibits a bug.

RJL Maplesoft

I just checked: acer's code will cause f(cos(t),sin(t),z) to echo with the name "f" carrying the superscript cos(t) sin(t). (If the first two arguments to f are large expressions, the echo could be really difficult to read.) Is that what you really want?

@ I can but pass this along to Maplesoft, as I have just done.

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