There is an interesting preprint here, on a method for integration of some pseudo-elliptic integrals.

It was mentioned in a (sci.math.symbolic) usenet thread, which can be accessed via Google Groups here.

Inside the paper, the author mentions that the following is possible for some cases -- to first convert to RootOf form.

Download int_pe.mw

I’m extremely pleased to introduce the newest update to the Maple Companion. In this time of wide-spread remote learning, tools like the Maple Companion are more important than ever, and I’m happy that our efforts are helping students (and some of their parents!) with at least one small aspect of their life.  Since we’ve added a lot of useful features since I last posted about this free mobile app, I wanted to share the ones I’m most excited about. 

(If you haven’t heard about the Maple Companion app, you can read more about it here.) 

If you use the app primarily to move math into Maple, you’ll be happy to hear that the automatic camera focus has gotten much better over the last couple of updates, and with this latest update, you can now turn on the flash if you need it. For me, these changes have virtually eliminated the need to fiddle with the camera to bring the math in focus, which sometimes happened in earlier versions.

If you use the app to get answers on your phone, that’s gotten much better, too. You can now see plots instantly as you enter your expression in the editor, and watch how the plot changes as you change the expression. You can also get results to many numerical problems results immediately, without having to switch to the results screen. This “calculator mode” is available even if you aren’t connected to the internet.  Okay, so there aren’t a lot of students doing their homework on the bus right now, but someday!

Speaking of plots, you can also now view plots full-screen, so you can see more of plot at once without zooming and panning, squinting, or buying a bigger phone.

Finally, if English is not you or your students’ first language, note that the app was recently made available in Spanish, French, German, Russian, Danish, Japanese, and Simplified Chinese. 

As always, we’d love you hear your feedback and suggestions. Please leave a comment, or use the feedback forms in the app or our web site.

Visit Maple Companion to learn more, find links to the app stores so you can download the app, and access the feedback form. If you already have it installed, you can get the new release simply by updating the app on your phone.

Download log_misinterpretation2.mw

One of the forums asked a question: what is the maximum area of a triangle inscribed in a given ellipse x^2/16 + y^2/3 - 1 = 0? It turned out to be 9, but there are infinitely many such triangles. There was a desire to show them in one of the possible ways. This is a complete (as far as possible) set of such triangles.
(This is not an example of Maple programming; it is just an implementation of a Maple-based algorithm and the work of the Optimization package).
MAX_S_TRIAN_ANINATION.mw

This app shows the modeling and simulation of DNA carried out entirely in Maple. The mathematical model is inserted through the combination of trigonometric functions. It shows the graphs of the curvature vs time for its interpretation. Made for engineering and health science students.

MV_AC_R3_UNI_2020.mw

Lenin Araujo Castillo

Ambassador of Maple

I have recently taken some questions about MaplePrimes reputation scores, and coincidentally, there was a discussion about it within MaplePrimes yesterday. I wanted to address these issues, and thought that doing so as a separate post made sense.

Reputation was added back in 2010 as a mechanism to track how fellow users value your contributions, and I believe it has largely worked. It's become a great way to acknowledge the time and effort our members put into the community, and I know that many of you greatly value the scores that you have earned. I also know that it is never fun to see it drop, even by just a few points.

To be clear, there are only two ways to lose reputation:

• If someone upvoted your answer/reply and then later rescinded the upvote
• If someone marked your answer as the "best" answer, and then later changed their vote to another answer

This means you can only lose reputation points if someone undoes an action that gave you points in the first place. This is going to happen occasionally. For example, the user may have voted your answer “best”, but as the discussion continued, someone else posted a different solution that the user felt was even better. So you can expect to see small fluctuations from day to day, but the overall trend will be upward. 

That said, members get understandably concerned when their reputation drops, and want to know why. We have always been able to track when reputation changed, but “why it changed” was obscured. Starting today, we have added enhanced logging for reputation shifts. This will allow us to better diagnose the causes when a member is concerned about a change to their reputation points. As well, in the very unlikely event that there is malicious behavior on MaplePrimes, this will give also us the data we need to take action to protect the community.  

With the new features added to the Student[LinearAlgebra] package I wanted to go over some of the basics on how someone can do Linear Algebra in Maple without require them to do any programming.  I was recently asked about this and thought that the information may be useful to others.
 

This post will be focussed towards new Maple users. I hope that this will be helpful to students using Maple for the first time and professors who want their students to use Maple without needing to spend time learning the language.
 

In addition to the following post you can find a detailed video on using Maple to do Linear Algebra without programming here. You can also find some of the tools that are new to Maple 2020 for Linear Algebra here.

The biggest tools you'll be using are the Matrix palette on the left of Maple, and the Context Panel on the right of Maple.

First you should load the Student[LinearAlgebra] package by entering:

with(Student[LinearAlgebra]);

Once you have a Matrix you can use the context panel on the right to apply a variety of operations to it:

The Student Linear Algebra Menu will give you many linear algebra commands.

You can also access Maple's Tutors from the Tools Menu

Tools > Tutors > Linear Algebra

?Student[LinearAlegbra]

Maple_for_Beginners.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Over the past weeks, we have spoken with many of our academic customers throughout the world, many of whom have decided to continue their academic years online. As you can imagine, this is a considerable challenge for instructors and students alike. Academia has quickly had to pivot to virtual classrooms, online testing and other collaborative technologies, while at the same time dealing with the stress and uncertainty that has resulted from this crisis.

We have been working with our customers to help them through this time in a variety of ways, but we know that there are still classes and students out there who are having trouble getting all the resources they need to complete their school year. So starting today, Maple Student Edition is being made free for every student, anywhere in the world, until the end of June. It is our hope that this action will remove a barrier for instructors to complete their Maple-led math instruction, and will help make things a bit more simple for everyone.

If you are a student, you can get your free copy of Maple here.

In addition, many of you have asked us about the best way to work on your engineering projects from home and/or teaching and learning remotely during this global crisis. We have put together resources for both that you can use as a starting point, and I invite you to contact us if you have any questions, or are dealing with challenges of your own. We are here to support you, and will be very flexible as we work together through these uncertain times.

I wish you all the best,

Laurent
President & CEO

Download Vectors_and_Spherical_coordinates_in_tensor_notation.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

A way of cutting holes on an implicit plot. This is from the field of numerical parameterization of surfaces. On the example of the surface  x3 = 0.01*exp (x1) / (0.01 + x1^4 + x2^4 + x3^4)  consider the approach to producing holes. The surface is locally parameterized in some suitable way and the place for the hole and its size are selected. In the first example, the parametrization is performed on the basis of the section of the initial surface by perpendicular planes. In the second example, "round"  parametrization. It is made on the basis of the cylinder and the planes passing through its axis. Holes can be of any size and any shape. In the figures, the cut out surface sections are colored green and are located above their own holes at an equidistant to the original surface.
HOLE_1.mwHOLE_2.mw

Hi, 

The present work is aimed to show how bayesian inference methods can be used to infer (= to assess) the probabilility that a person detected infected by the SARS-Cov2  has to die (remark I did not write "has to die if it" because one never be sure of the reason of the death).
A lot of details are avaliable in the attached pdf file (I tried to be pedagogic enough so that the people not familiar with bayesian inference can get a global understanding of the subject, many links are provided for quick access to the different notions).

In particular, I explain why simple mathematics cannot provide a reliable estimate of this probability of death (sometimes referred to as the "death rate") as long as the epidemic continues to spread.

Even if the approach presented here is rather original, this is not the purpose of this post. 
Since a long time I had in mind to post here an application concerning bayesian methods. The CoVid19 outbreak has only provided me with the most high-profile topic to do so.
I will say no more about the inference procedure itself (all the material is given in the attached pdf file) and I will only concentrate on the MAPLE implementation of the solution algorithm.

Bayesian Inference uses generally simple algorithms such as MCMC (Markov Chain Monte Carlo) or ABC (Approximate Bayesian Computation) to mention a few, and their corresponding pseudo code writes generally upon a few tens of lines.
This is something I already done with other languages but I found the task comparatively more difficult with Maple. Probably I was to obsess not to code in Maple as you code in Matlab or R for instance.
At the very end the code I wrote is rather slow, this because of the allocated memory size it uses.
In a question I posed weeks ago (How can I prevent the creation of random variables...) Preben gave a solution to limit the burst of the memory: the trick works well but I'm still stuked with memory size problems (Acer also poposed a solution but I wasn't capable to make it works... maybe I was too lazzy to modify deeply my code).

Anyway, the code is there, in case anyone would like to take up the challenge to make it more efficient (in which case I'll take it).

Note 1: this code contains a small "Maplet" to help you choose any country in the data file on which you would like to run the inference.
Note 2: Be careful: doing statistics, even bayesian statistics, needs enough data: some countries have history records ranging over a few days , or no recorded death at all; infering something from so loos date will probably be disappointing

The attached files:

• The pdf file is the "companion document" where all or most of it is explained.It has been written a few days ago for another purpose and the results it presents were not ontained from the lattest data (march 21, 2020 coronavirus)
• xls files are data files, they were loaded yesterday (march 28, 2020) from here coronavirus
• the mw file... well, I guess you know what it is.
   

Bayesian_inference.pdf

total-cases-covid-19_NF.xls

total-deaths-covid-19_NF.xls

Bayesian_Inference_ABC+MCMC_NF_2.mw

In maple plot, very many symbols like, diamond, star, solidcircle are available. Many of them may have been used also for teaching purposes.

Recently, someone encountered the need to draw graphs with arrowheads and many solutions may be available as well. But it requires a thorough understanding of maple's features which are infinitely many. My feeling was that an arrow symbol also could be added in the symbol feature so that the option can be used as a plot point in the graph at the graph end points very easily. It can be just like adding a solidbox symbol at any point on the curve.

Hope my suggestions are in order.

Thanks.

Ramakrishnan V

The following puzzle prompted me to write this post: "A figure is drawn on checkered paper that needs to be cut into 2 equal parts (the cuts must pass along the sides of the squares.)" (parts are called equal if, after cutting, they can be superimposed on one another, that is, if one of them can be moved, rotated and (if need to) flip so that they completely coincide) (see the first picture below). 
I could not solve it manually and wrote a procedure called  CutTwoParts  that does this automatically (of course, this procedure applies to other similar puzzles). This procedure uses my procedure  AreIsometric  published earlier  https://www.mapleprimes.com/posts/200157-Testing-Of-Two-Plane-Sets-For-Isometry  (for convenience, I have included its text here). In the procedure  CutTwoParts  the figure is specified by the coordinates of the centers of the squares of which it consists).

I advise everyone to first try to solve this puzzle manually in order to feel its non-triviality, and only then load the worksheet with the procedure for automatic solution.


For some reason, the worksheet did not load and I was only able to insert the link.

Cuttings.mw