Dear Maple Community,

It has been a year since the passing of Stefan Vorkoetter, who started contributing to the Maple project in the 80s and was a long term member of our development team. 

Here are a few recently published articles about Stefan, that I'd like to share with you:

https://mapletransactions.org/index.php/maple/article/view/18269
https://mapletransactions.org/index.php/maple/article/view/18681

we shall not forget

We are pleased to announce that the registration for the Maple Conference 2024 is now open.

Like the last few years, this year’s conference will be a free virtual event. Please visit the conference page for more information on how to register.

This year we are offering a number of new sessions, including more product training options and an Audience Choice session.
You can find an overview of the program on the Sessions page. Those who register before September 10th, 2024 will have a chance to vote for the topics they want to learn more about during the Audience Choice session.

We hope to see you there!

Maple Learn has so much to offer, but it can be tricky to know where to start! Even for those experienced with Maple Learn, sometimes, we miss an update with new features or fall out of practice with older ones. Luckily, we have the perfect solution for you–and it shows up right when you open your first document.

Introducing our brand-new Walkthrough Tutorial!

The tutorial covers all the main features of Maple Learn: from assigning functions, to using the Plot commands and Context Panel operations, all the way to creating your own visualizations with the Geometry commands. Stuck? Hints are provided throughout, or just click "Next" and the step will be completed automatically. 

If you're just starting out with Maple Learn, try the Beginner tutorial and work up to Advanced. This will introduce you to a holistic view of Maple Learn's capabilities along with some Maple Learn terminology. If you have some experience, starting with the Beginner tutorial is still a great option, but you may wish to begin with the Intermediate and Advanced tutorials. The Intermediate and Advanced sections cover how to use newer features of Maple Learn and you might discover something you haven't seen before!

How do I access the tutorial?

The tutorial will automatically launch when you open a new document. Head to https://learn.maplesoft.com and click "Open new document".

If the tutorial doesn't open automatically, it may have been disabled. You can manually open it by clicking the "Help" button in the top right, then clicking "Walkthrough Tutorial". 

There you have it! I had been using Maple Learn for the past few months and only recently discovered these two incredible features:

Silencing Groups (Intermediate - 6/7)

Live Sessions (Advanced - 6/6)

I found these features thanks to the Walkthrough Tutorial and my experience on Maple Learn hasn't been the same since! The Walkthrough Tutorial is a great introduction for new users, and a quick refresher for experts, but isn't the end of exploring Maple Learn's capabilities. See our How to Use Maple Learn (maplesoft.com) collection and our Getting Started with Maple Learn (youtube.com) video for more. You can also challenge The Treasure of Maple Learn (maplesoft.com) – a collection of documents designed to gamify exploring Maple Learn's features. Check out our blog post on The Case of the Mysterious Treasure - MaplePrimes to learn more about this collection. 

Hope you enjoy our new tutorial and let us know what you think!

This is a reminder that presentation applications for the Maple Conference are due July 17, 2024.

The conference is a a free virtual event and will be held on October 24 and 25, 2024.

We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page.

I encourage all of you here in the Maple Primes community to consider joining us for this event, whether as a presenter or an attendee!

Kaska Kowalska
Contributed Program Co-Chair

The Proceedings of the Maple Conference 2023 is now out, at

mapletransactions.org

The presentations these are based on (and more) can be found at https://www.maplesoft.com/mapleconference/2023/full-program.aspx#schedule .

There are several math research papers using Maple, an application paper by an undergraduate student, an engineering application paper, and an interesting geometry teaching paper.

Please have a look, and don't forget to register for the Maple Conference 2024.

A simple visual way to show that the parametric equation of a circle is a helix in our three-dimensional space.
Parametric equation of a circle f1 and f2.
The helix is ​​defined by the intersection of two mutually perpendicular cylindrical surfaces f1 and f2.

 

restart; with(plots): 
R := 1.;
f1 := x1-R*cos(x3); 
f2 := x2-R*sin(x3); 
PT := implicitplot3d([f1, f2], x1 = -6 .. 6, x2 = -6 .. 6, x3 = -2 .. 12, numpoints = 10000, style = surface, color = [blue, green], transparency = .5):
IT := intersectplot(f1, f2, x1 = -1 .. 1, x2 = -1 .. 1, x3 = -2 .. 12, thickness = 3, axes = normal, grid = [10, 10, 30]): 
display(PT, view = [-6 .. 6, -6 .. 6, -2 .. 12]);
display(PT, IT, view = [-6 .. 6, -6 .. 6, -2 .. 12]); 
display(IT, view = [-R .. R, -R .. R, -2 .. 12], scaling = constrained)

We have just released an update to Maple. Maple 2024.1 includes improvements to the math engine, PDF export, the Physics package, command completion, and more. As always, we recommend that all Maple 2024 users install this update. In particular, please note that this update includes fixes to ODESteps and simplifying integrals, as reported on Maple Primes. Thanks for helping us, and other users, by letting us know!

At the same time, we have also released an update to MapleSim. MapleSim 2024.1.1 includes improvements to FMU import/export, plotting, co-simulation, and more, as well as enhancements to the Web Handling Library.

These updates are available through Tools>Check for Updates in Maple or MapleSim, and are also available from the Download Product Updates section of our web site, where you can find more details.

This post summarizes links for those who have not studied numerical integration methods from scratch and are interested in simulation settings in MapleSim (like me).

The MapleSim help pages simulation settings and advanced simulation settings give first guidance for the trained user but do not provide explanations or links for the terms used in the description of the settings (as for example: stiffness, constraint stabilization, constraint projection, events and event iteration,...).

It can easily be overlooked that Maple help pages provide further information for most of the terms. Under the assumption that MapleSim uses the same terminology as Maple, I recommend to first have a look at Maple help topics before consulting the web or other resources. Since searching and retrieving can be time consuming, I made a list of helpful links.

There are still some open points. I would be happy for more links and help in filling these gaps.

How Maple simulates

?MapleSimUserGuide,Chapter04:
section 4.1 How MapleSim Simulates a Model

?tasks,generatingCode

Solvers

An overview of solvers: ?dsolve,numeric

Differential Algebraic Equation introduction: ?MaplePortal,DAE

Overview of numeric differential-algebraic equation solvers (index reduction, constraint drift, projection):
 ?examples/numeric_DAE and ?dsolve,numeric,DAE_extension

Stiffness and stiff solvers

Stiffness and stiff IVPs: ?dsolve,Stiffness

Events

?dsolve,numeric,Events

Time events and state events

Event handling:

?MapleSimUserGuide,Chapter04:
section 4.1 How MapleSim Simulates a Model

Event iteration:

?MapleSimUserGuide,Chapter05:
section 5.5 Selecting the Code Generation Options

Iteration, hysteresis, Intermediate steps: ?tasks,generatingCode

Hysteresis:

Hysteresis in value or also in time?

Do variable solvers adapt the value of event hysteresis during runtime?

Baumgarte constraint stabilization, unconstrained dynamics, constrained dynamics

?MapleSim,Multibody,Dynamic_Exports
(in combination with ?MapleSim,Multibody,Kinematic_Exports)

?examples/numeric_DAE

?tasks,generatingCode

?MapleSimUserGuide,Chapter05:
section 5.5 Selecting the Code Generation Options

Error control

              ?dsolve,numeric,Error_Control

              Absolute error: ?dsolve,numeric,IVP

              Relative error: (relative to what?)

Index1 error control and Index1 Tollerance: see solvers

Scaling

scalemethod (this does not seem to exist in Maple)

Examples (Multibody)

Events

                            Catapult
                            (from MapleSim>Help>Examples>Physical Domains>Multibody)
                            contact events

                          Catapult_-_Events.msim

                            Throwing a ball
                            (from MapleSim>Help>Examples>Physical Domains>Multibody)

                            conditional events (with boolean logic)

                          Throwing_a_Ball_-_Events.msim

              Solvers

              Conservation of energy of a pendulum depends on solvers.
                           Euler increases energy, implict Euler dissipates energy.

             Pendulum_for_solver_comparision.msim

Constraint dirft/projection

              2-d rigid slider crank

               (from MapleSim>Help>Examples>Physical Domains>Multibody)

              projection off leads to assembly desintegration after 2000 s simulation

             2D_Rigid_Slider_Crank_-_constraint_projection.msim

                         A stiff solver improves constraint drift, but only delays desintegration

                         Baumgarte constraint stabilization prevents simulation error but shows dislocated rigid body frames

We are happy to announce another Maple Conference to be held October 24 and 25, 2024!

It will be a free virtual event again this year, and it will be an excellent opportunity to meet other members of the Maple community and get the latest news about our products. More importantly, it's a chance for you to share the work you've been doing with Maple and Maple Learn. 

We have just opened the Call for Participation. We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. 

You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Applications are due July 17, 2024.

Presenters will have the option to submit papers and articles to a special Maple Conference issue of the Maple Transactions journal after the conference.

Registration for attending the conference will open in July.  Watch for further announcements in the coming weeks.

I encourage all of you here in the Maple Primes community to consider joining us for this event, whether as a presenter or an attendee!

Kaska Kowalska
Contributed Program Co-Chair

I’m excited to announce that we’ve just launched MapleSim 2024.

The new release has tools that are designed to drive innovation, and overall save you time when creating and developing simulations.

At Maplesoft we are looking to continually enhance our engineering software with new features based on customer feedback, and I’m pleased to share some of the fruits of that labor, and thank the developers, product management team, and  customers that contributed.

The new offering  helps engineers to

• Rapidly Tune Parameters
• Explore Design Concepts
• Expand Modeling Capabilities

For example, the new Rerun panel allows you to significantly cut the time between simulations as you quickly apply different parameter values, initial conditions and even simulation settings between runs. It does this by skipping the formulation steps when there are no structural changes made to the model, and you can even see the plots and results of the different iterations side by side.
You can see it in action in this short demo video.

There is now support for the latest Modelica feature set, so you can import Modelica Libraries that make use of MSL 4.0.0 features, and adds a range of new modeling components to the standard MapleSim libraries (electrical, 1-D mechanical, signal block and more).

MapleSim 2024 also includes more components in the Hydraulic library to support modeling of flow restrictions and adds a Scripting button to add and organize Maple worksheets.

We’ve also applied a whole series of updates to our MapleSim add-on products, including:

• The MapleSim Web Handling Library has new tools for modeling heavier webs, winding of multiple rolls on the same drum, and adding a Switching Nip Roller to swing the web contact points between rollers.
• The MapleSim Connector for FMI can now import and export FMI 3.0.
• The MapleSim CAD Toolbox supports recent software releases from NX™, SOLIDWORKS®, Solid Edge®, Parasolid®, and other CAD tools.
• The MapleSim Heat Transfer Library has gained a new T-junction component for the Water subpackage to improve flow/pressure-drop calculations for systems with branches.

We have an upcoming webinar for you to see the new 2024 features in MapleSim Web Handling Library – you can sign up to register here.

You can find out more about the other new features at the MapleSim What’s New web page, and as always, we are happy to hear your comments and product suggestions.

And if you are new to MapleSim and would like to try building and running a model yourself, you can request a free trial, or contact Maplesoft sales team with any questions.

Consider the equation  (2^x)*(27^(1/x)) = 24  for which we need to find the exact values ​​of its real roots. This is not difficult to solve by hand if you first take the logarithm of this equation to any base, after which the problem is reduced to solving a quadratic equation. But the  solve  command fails to solve this equation and returns the result in RootOf form. The problem is solved if we first ask Maple to take the logarithm of the equation. I wonder if the latest versions of Maple also do not directly address the problem?

restart;
Eq:=2^x*27^(1/x)=24:
solve(Eq, x, explicit);

map(ln, Eq); # Taking the logarithm of the equation
solve(%, x);
simplify({%}); # The final result

We've just launched Maple Flow 2024!

You're in the driving seat with Maple Flow - each new feature has a straight-line connection to a user-driven demand to work faster and more efficiently.

Head on over here for a rundown of everything that's new, but I thought I'd share my personal highlights here.

If your result contains a large vector or matrix, you can now scroll to see more data. You can also change the size of the matrix to view more or fewer rows and columns.

You can resize rows and columns if they're too large or small, and selectively enable row and column headers.

If the vector or matrix in your result contains a unit, you can now rescale units with the Context Panel (for the entire matrix) or inline (for individual entries).

A few releases ago, we introduced the Variables palette to help you keep track of all the user-defined parameters at point of the grid cursor.

You can now insert variables into the worksheet from the Variables palette. Just double-click on the appropriate name.

Maple Flow already features command completion - just type the first few letters of a command, and a list of potential completions appears. Just pick the completion you need with a quick tap of the Tab key.

We've supercharged this feature to give potential arguments for many popular functions. Type a function name followed by an opening bracket, and a list appears.

In case you've missed it, the argument completion list also features (when they make sense) user-defined variables.

You can now link to different parts of the same worksheet. This can be used to create a table of contents that lets you jump to different parts of larger worksheets.

This page lists everything that's new in the current release, and all the prior releases. You might notice that we have three releases a year, each featuring many user-requested items. Let me know what you want to see next - you might not have to wait that long!

In our recent project, we're diving deep into understanding the SIR model—a fundamental framework in epidemiology that helps us analyze how diseases spread through populations. The SIR model categorizes individuals into three groups: Susceptible (S), Infected (I), and Recovered (R). By tracking how people move through these categories, we can predict disease dynamics and evaluate interventions.

Key Points of the SIR Model:

• Susceptible (S): Individuals who can catch the disease.
• Infected (I): Those currently infected and capable of spreading the disease.
• Recovered (R): Individuals who have recovered and developed immunity.

Vaccination Impact: One of the critical interventions in disease control is vaccination, which moves individuals directly from the susceptible to the recovered group. This simple action reduces the number of people at risk, thereby lowering the overall spread of the disease.

We're experimenting with a simple model to understand how different vaccination rates can significantly alter the dynamics of an outbreak. By simulating scenarios with varying vaccination coverage, students can observe how herd immunity plays a crucial role in controlling diseases. Our goal is to make these abstract concepts clear and relatable through practical modeling exercises.

It can happen when an operation is interrupted by  that Maple does not return to  and still shows .

This can give the false impression that the Maple server in charge of the evaluation did not get the message to stop whatever it was doing.

By giving Maple an impossible task to solve analytically

f1 := x1 - x1*sin(x1 + 5*x2) - x2*cos(5*x1 - x2);
f2 := x2 - x2*sin(5*x1 - 3*x2) + x1*cos(3*x1 + 5*x2);
solve({f1, f2});

I have noticed in the Windows Task Manager that freeing allocated memory can take much longer than one might think.

In one case it took 30 minutes to free 24 Gb of total allocated memory (21 Gb of it in RAM/physical memory). In this case the interrupt button became active (turned from grey to red ) two times and memory continued piling up  again.

Lessons learned for me:

• The task manager is not only a valuable indicator for task activity but also for the interruption/memory freeing process.
• Before killing a whole Maple session and potentially losing the last state of a worksheet it can pay off to wait and repeatedly interrupt an operation.

Suggestion: When the maple server gets an interrupt request, it could report to the GUI that it is in an interruption state and is no longer evaluating input. For example changing the message in the status bar from Evaluating... to Interrupting...

Download integral.mw