Product Tips & Techniques

Tips and Tricks on how to get the most about Maple and MapleSim

MapleSim is a fantastic tool to model multi-domain physical systems at a level that was unthinkable not so long ago. This post is about a simple problem that can be solved by hand, but where I failed with MapleSim using online resources.

For some time, I have been looking for answers to two questions:

  • How to control which variables (and parameters) are included in MapleSims equation exports? This question is crucial to derive forward and inverse kinematics.
  • Can the Equation Extraction App (in principle) provide a similar set of equations than the Multibody Analysis App? This question is rather academic until multidomain exports are desired (which the Multibody Analysis can’t provide).

The attached model helped me to clarify a few things and discover a real hidden secret (at least it was for me). I hope it can help others.

The model is a rather simple 3DOF mechanism. The task was to get a set of equations to derive the two rotations and the one displacement of the mechanism as a function of x,y,z coordinates.

After watching videos and inspecting models from the model gallery on inverse kinematics, I placed motion drivers for the input variables, added sensors for the output variables and wrapped the mechanism into a subsystem. However, as explained in more detail in the attachment, the set of exported variables was incomplete in both apps (AEs exports in the Equation Extraction Export and Position Constraints in the Multibody Analysis Export). Furthermore, the number of extracted equations did not match the three degrees of freedom.

After numerous trials it turned out that in addition to the motion drivers and sensors, initial conditions (ICs) had to be set. This is the hidden secret.  The crucial initial conditions (detailed in the attachment) are not required to assemble and run the model. So, introducing them temporarily for equation extraction is not obvious and never came to my mind. Setting ICs is, if I am not completely mistaken, also not highlighted in the documentation. This little trick of additionally setting initial conditions answered the above questions positively (at least for this 3DOF mechanism). In fact, it worked so well that all other failed attempts of conditioning the model for equations extraction worked immediately:

  • Immobilizing the assembly with a Fixed Frame (using parameters for the fixed frame position to represent input variables; the fixed frame can be inside or outside the subsystem model).
  • Using one Prescribed Translation component Instead of 3 motion drivers
  • Using variables to pass motion signals into the model subsystem instead of using signals and ports (using From variable and To Variable components)

These attempts underline the effort and the time spend to get the relevant equations for that simple problem. As it turned out, all approaches work but are not even required for the mechanism. The key to success was setting the ICs of the joints.  One can even strip the model down to its skeleton (removing all motion drivers and sensors as in the screen shot bellow) and still get the desired simple set of equations, provided the ICs are set.


It has to be noted, that the mechanically coupled (highlighted in yellow) prismatic joints contributed to the problems: MapleSim does not seem to take this mechanical constraint into account (as I would have expected). The ICs of both coupled components must be set to get the three equations containing all desired in and output variables.

If my finding is correct and of general relevance, I like to suggest including such kind of tips and tricks in training or reference material.  From an application engineer or developers’ perspective, knowing the underlying algorithms, its probably obvious what has to be done. But from a user’s perspective MaplsSim is a black box that works magically well in most cases. If it does not, trial and error is often the only alternative to make it work, because models are either too complex or too confidential to be shared with others.   

What I am addressing here is only the initial step of getting the desired equations. There is more to master. Save manipulation of equations too big to be inspected visually is also important. This has been well covered in several videos. Unfortunately, the quality of some of the footage does not allow to capture details of Maple commands. If possible, such material should be updated or replaced.

Overall, a collection of tips&tricks and dos&don’ts could establish some kind of best practice in deriving kinematics. If others would share their experience and findings, we all could save allot of time. A collection of valuable posts, questions, models, videos, and webinars could be a start. This collection not necessarily has to meet the high Maple standards of mathematical exactness and consistency. Engineers also accept pragmatic solutions to solve a problem.

If my findings are incorrect or you have better advise, please let us know.


A user of ours came up with an interesting request: taking a procedure name as an argument and then within the procedure, return a set containing the names of all variables within the procedure. This task can be accomplished in one of two ways, one with local variables, one with global variables.

One method is:

find_vars_in_proc(f :: procedure, $)
  return {op(2, eval(f))};
end proc;

for variables that Maple unambiguously determines to be local variables. For global variables, a slight variation appears as:

find_vars_in_proc(f :: procedure, $)
  return {op(2, eval(f)), op(6, eval(f))};
end proc;

As always, typing ?procedure directly in the worksheet brings up the help guide containing more information on operands of a procedure!

Bon vendredi à tous! Je suis de retour avec un autre article de mise à jour détaillant les nouveautés que nous avons apportés à Maple Learn cette semaine. Bonne lecture!

Tout d'abord, nous avons ajouté des permutations et des combinaisons, ainsi que la notation binomiale, à Maple Learn ! Gardez l’œil à l’affût des documents utilisant ces nouvelles fonctionnalités et consultez nos exemples ici et ici. Les opérations se trouvent dans la palette des fonctions. Nous espérons que cela permettra de rendre votre création de document avec Maple Learn encore plus agréable !

Nous avons également mis à jour la syntaxe des graphiques paramétriques pour utiliser l'opérateur tel que. Veuillez consulter notre page d’instruction pour plus de détails (ici). Remplacez simplement la virgule de l'ancienne syntaxe par le |. À partir de là, placez vos restrictions et le tour est joué ! Un graphique paramétrique utilisant l'opérateur tel que.

Enfin, quelques changements mineurs à Maple Learn. Nous avons ajusté la taille de police par défaut à une police de taille 20. De plus, nous avons fait en sorte qu'il remplace automatiquement <= ou >= par le symbole ≤ ou ≥.

J'espère que ces nouvelles fonctionnalités sont tout aussi intéressantes pour vous qu'elles le sont pour moi ! Faites-nous savoir ce que vous pensez dans les commentaires ci-dessous.

Happy Friday everyone! I’m back with another update post detailing the new changes we’ve made to Maple Learn this week. Just keep reading, and we’ll get right into them.

First, we’ve added permutations and combinations, along with binomial notation, to Maple Learn! Keep an eye out for documents using these new features, and check out our examples here and here.  The operations can be found in the functions palette. We hope that this allows even more fun with documents on Maple Learn!

We’ve also updated the syntax for parametric plots to use the such that operator. Please see our how-to page for more detail (here). Simply replace the comma from the old syntax with the |. From there, place your restrictions, and voila! A parametric plot using the such that operator.

Finally, some minor changes to Maple Learn. We’ve adjusted the default font size to 20 point font. As well, we’ve made it automatically change <= or >= to the ≤ or ≥ symbol.

I hope these new features are just as exciting to you as they are to me! Let us know what you think in the comments below.

Users often wonder how the length(expr) command works.

length(expr) returns the length of expr.

For more information, see the ?length help article in Maple, or Online Help version


Probability is a field of mathematics that sees extensive use outside of academics.  Whether one’s checking the likelihood of rain on a weather app or the odds of winning the lottery, probability is everywhere.  My favorite application of probability is dice games like Dungeons and Dragons.  The game can be played very simply (choose to attack a monster, roll a 20-sided-die, try to exceed a certain number) or with a complexity that rivals high school math courses.  There are spells and abilities that modify one’s dice rolls, such as adding additional rolls to the total or rerolling the die and using the higher result.  A good player regularly asks themself when to activate certain buffs and how likely they are to succeed with or without them.

All of these questions boil down to the basics of probability.  Things that one learns in an introductory statistics course extend into countless applications.  Currently, I’m adding some of that knowledge to the Maple Learn document gallery, and I’m here to give a sneak peek.

First, I’ve built tree diagrams in Maple Learn.  Tree diagrams are a way to map probability across multiple events occurring in sequence.  Each branching path represents a series of events that have a specified probability of occurring.

Here’s an example: one morning I flip a coin to decide if I buy a lottery ticket.  If it’s heads, I do.  If I buy the ticket, I have a one in a million chance of winning the cash prize.  Drawn as a tree diagram…

I drew this using Maple Learn line, point, and label operations.

My new D&D-themed documents are a bit more exciting.  In the first, we explore a tree diagram with variable probabilities.  A brave hero makes their way into a dungeon, attacking any random monster they see.  How likely are they to land an attack?  Adjust the details of the question and watch the diagram change.

In the second, I used Maple program scripting to add a live randomized dice roller.  Many probability techniques are at play to analyze which of two buffs will do more good for a dice-rolling adventurer.

I plan on making more documents like these; keep your eyes on the Document Gallery probability collection for updates.

Les probabilités sont  un domaine des mathématiques largement utilisé en dehors des universités. Que l'on vérifie la probabilité de l’apparition de la pluie sur une application météo ou les chances de gagner à la loterie, les probabilités sont partout. Mon application des probabilités préférée est les jeux de dés comme Donjons et Dragons. Le jeu peut se jouer très simplement (choisir d'attaquer un monstre, lancer un dé à 20 faces, essayer de dépasser un certain nombre) ou avec une complexité qui rivalise avec les cours de mathématiques du lycée. Il existe des sorts et des capacités qui modifient les lancés de dés, comme ajouter des lancés supplémentaires au total ou relancer le dé et utiliser le résultat le plus élevé. Un bon joueur se demande régulièrement quand activer certains « buffs » et quelle est la probabilité qu'ils réussissent avec ou sans eux.

Toutes ces questions se résument aux bases des probabilités. Les choses que l'on apprend dans un cours d'introduction aux statistiques s'étendent à d'innombrables applications. Actuellement, j'ajoute certaines de ces connaissances à la galerie de documents Maple Learn je voulais vous en donner un aperçu.

Tout d'abord, j'ai construit des arbres de probabilité avec Maple Learn. Ceux-ci permettent de représenter graphiquement la probabilité de plusieurs événements se produisant en séquence. Chaque chemin de branchement représente une série d'événements qui ont une probabilité de se produire spécifique.

Voici un exemple : un matin, je lance une pièce pour décider si j'achète un billet de loterie. Si c'est face, je le fais. Si j'achète le billet, j'ai une chance sur un million de gagner l’argent. Dessiné sous forme d'arbre de probabilité…

J'ai dessiné ceci en utilisant les fonctionnalités ligne, point et étiquette de Maple Learn.

Mes nouveaux documents sur le thème de D&D sont un peu plus intéressants. Dans le premier, nous explorons un arbre de probabilités variables. Un héros courageux se rend dans un donjon, attaquant n'importe quel monstre aléatoire qu'il voit. Quelle est la probabilité qu'ils lancent une attaque ? Ajustez les détails de la question et regardez le diagramme changer.

Dans le second, j'ai utilisé la fonction script de Maple pour ajouter un lanceur de dés aléatoire en direct. De nombreuses techniques de probabilité sont en jeu pour analyser lequel des deux « buffs » fera le plus de bien à un aventurier qui lance les dés.

Je prévois de faire plus de documents comme ceux-ci; gardez un œil sur la catégorie de probabilités dans la galerie de documents Maple Learn pour les mises à jour.

A user wondered why an example of integration by parts from the Calculus Study Guide was immediately showing the final answer instead of the parts steps shown in the Guide. 

We suggest users pay special attention to the "Initialize" rows of the Guide example(s) where converting the integral to inert form is discussed. 

Using an inert form of the integral ensures that Maple does not evaluate the integral unexpectedly. 


Int(exp(a*x)*cos(b*x), x)


Parts(Q, exp(a*x)) = sin(b*x)*exp(a*x)/b-(Int(sin(b*x)*a*exp(a*x)/b, x))



       The Standard Model of Particle Physics in Maple 2022


One of the most important mathematical formulations in human history is that of the Standard Model in particle physics. It describes all the elementary particles (leptons like the electron, quarks, bosons as the Higgs or the photon), which in different arrangements, form all the observable particles in nature. The formulation is not just a tremendous theoretical achievement that rendered Nobel prizes but also a practical one. Basically, all the measurements performed in the particle accelerators at CERN and the Fermilab take this mathematical, abstract formulation as the starting point. However, for computer algebra systems, the complexity of the model is somewhat extreme: is not only the number of terms in the corresponding Lagrangian impressively large but also the mathematical properties of each of these objects that represented a challenge for a long time. With hacks of different kinds, the computer algebra representation of only some aspects of the Standard Model was possible, with restricted computational capabilities.

Hidden among the novelties of Maple 2022, a breakthrough in computer algebra is the introduction of a new, fully computable representation of the Standard Model. This representation includes the accessory commands to calculate related scattering amplitudes  (the essence of the computations behind particle collision experiments) and related Feynman integrals . This is a remarkable achievement in computational physics. And from the educational point of view, it brings one more brick of knowledge from "the dark side" of the moon into "the bright side." Making the Standard Model computations be at the tip of one's fingers completely transforms the possible experience we can have with the underlying knowledge.

The illustration below of this new Maple 2022 StandardModel package is advanced in time with regards to the release of Maple 2022 days ago, and introduces a new command, Lagrangian, that increases one level the usability of the package. The so updated StandardModel is distributed as usual, within the Maplesoft Physics Updates for Maple 2022.

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



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

Background pattern


Today is one of my favorite days of the year. After months and months of hard work by a lot of people, it’s finally arrived:


It's Maple launch day!


Yes, I am very pleased to announce that Maple 2022 is here.


As we’ve done in years past, Samir and I started this release by spending many hours reviewing feedback from Maple Primes posts, support emails, sessions with staff who regularly talk with customers and who use Maple themselves, and our own direct conversations with customers. Of course a year is never enough to implement every good idea, but our goal was to identity a feature set that would appeal to, delight, and hopefully excite our customers.


Ultimately, you will be the judge, but I can tell that there are some things in Maple 2022 that I am personally very excited about. These are “quality of life” improvements that have been requested by customs and make some things in Maple that were frankly kind of annoying a lot better. The rest of this post will discuss my favorite improvements in more detail (or you can watch this video), and of course, you can get much more information about these and all the other improvements in What’s New in Maple 2022.


#1 – Did you ever find yourself jumping back and forth between your Maple document and Print Preview, again and again, as you prepare your worksheet for printing or export to PDF? It can be a pain, especially with long documents that include plots, tables, and sections. So I'm happy to announce that Maple 2022 includes a new Print Layout mode. This new layout mode lets you see the page boundaries as you edit the document, so you can adjust your content as you go. In Maple 2022, what you see on the page is what you get when you print or export to PDF. Hurray!





#2 – Are you tired of explaining to your students why the graph of tan(x) doesn’t look right in Maple?  Good news!  With Maple 2022, you won’t have to have that conversation ever again. Maple 2022's new adaptive plotting algorithm means that when you plot tan(x), 1/(1-x), floor and ceiling functions, and most other curves with discontinuities, you’ll get what you expect by default – no more vertical lines, no need to specify the discont option, and it’s still fast.


Description automatically generated


#3 – Did you ever run into a situation where zooming, panning, or resizing your plot didn’t actually give you the better view of the plot you were looking for? Now Maple recomputes and redraws when needed to give you what you wanted – a good look at your plot.



#4 – Are you a fan of the Plot Builder? If you are, I'm delighted to let you know that the Plot Builder in Maple 2022 now supports plotting multiple expressions together on the same axes. So don't hold back - use the Plot Builder to customize plots and animations of any number of 2-D and 3-D expressions plots and animations. (We also got rid of that annoying empty plot when you first open it, too.)



#5 - And, by popular demand, Maple 2022 now magnifies the text in the table of contents/search results when you magnify a help page. No more squinting to find the topic of interest. My eyes are much happier.


Those are my favorites, but there is a lot more in the release. To learn more about all the improvements in Maple 2022, visit What’s New in Maple 2022

La pandémie de COVID 19 nous a forcé à nous lancés dans l'apprentissage en ligne - mais après deux ans, il est clair que l'apprentissage en ligne est là pour rester. La bonne nouvelle est que de plus en plus de recherches sont disponibles et nous donnant plus d'informations sur les avantages et inconvénients des différentes méthodes d'enseignement ainsi que leur impact sur l'apprentissage de l’élèves. Tout cela conduit à une question : comment l'enseignement peut-il être plus efficace en ces temps difficiles ? Nous discuterons des recherches effectués et leur lien avec Maple Learn. Cependant, je tiens à préciser que je ne prétends pas être un spécialiste du sujet. Je suis simplement un étudiant qui veut améliorer l'apprentissage en ligne pour moi-même et mes pairs.

Dans ce contexte il existe trois principaux styles d'apprentissage, convenus par les psychologues : apprentissage passif, actif et interactif. Cependant, aujourd'hui, nous allons nous concentrer uniquement sur l'apprentissage interactif. L'apprentissage interactif est l'endroit où l'élève agit comme «un sujet d'activité éducative» (Kutbiddinova, Eromasova et Romanova, 2016). Dans la pratique, cela signifie généralement que l'étudiant collabore avec ses pairs. Cette pièce est plus difficile lorsque les cours sont en ligne et/ou asynchrones. Personnellement, j'ai eu du mal à établir des liens avec mes pairs pendant mes études en ligne, car notre principale forme de communication était les messages sur les forums de discussion. Nous discuterons des avantages de l'apprentissage interactif, puis discutons de la façon dont Maple Learn peut être utilisé dans le modèle d'apprentissage interactif.

Le principal avantage de l'apprentissage interactif est qu'il encourage la participation active de toutes les personnes concernées. Lorsqu'ils sont encouragés à interagir avec leurs pairs dans des groupes plus petits, cela permet une plus grande participation des membres du groupe, par rapport au fait de poser des questions à toute la classe et de leur demander de lever la main pour répondre. Dans la même façon, l'apprentissage interactif crée plus d'engagement avec le matériel éducatif, ainsi que plus d'initiative de la part de l’étudiant (Ibid).

Dans un exemple discuté par Anderson en 2014, les étudiants se sont mis par paires et ils ont discuté de leur réponse à une question. Les étudiants, lors de l'exercice, devaient choisir sur une réponse, puis discuter de leur raisonnement qui a mené à ce choix,, dans le but de faire changer d'avis l'autre étudiant. Cela a créé une compréhension du matériel, ainsi qu'un investissement émotionnel dans le sujet.

Alors, comment Maple Learn peut-il aider à faciliter l'apprentissage interactif dans un environnement en ligne ? Commençons par recréer l'exemple d'Anderson, mais en ligne et avec une légère variation pour un cours de mathématiques.

À l'aide de Maple Learn, l'élève peut suivre toutes ses étapes, copier ses notes papier ou résoudre l'équation au fur et à mesure qu'il tape. Il peut également utiliser du texte pour expliquer son raisonnement pour chaque étape ou pour placer des formules à côté des mathématiques qu'il a utilisées.

À partir de là, l'élève peut utiliser la fonction de partage instantané pour échanger des documents avec quelqu'un d'autre dans la classe. Cela permet aux deux étudiants de voir le travail et le raisonnement de l'autre, sans avoir à lire des notes manuscrites numérisées. Cela signifie également que l'examen peut se produire de manière asynchrone, permettant aux étudiants de différents endroits et/ou fuseaux horaires de discuter. Contrairement à l'exemple original, puisque nous parlons de mathématiques, l'élève n'essaie pas nécessairement de convaincre l'autre élève. Les commentaires sur les mathématiques sont davantage utilisés pour donner des commentaires ciblés et soit comprendre soit d'autres façons de résoudre le problème, soit la bonne façon si elle a été mal résolue à l'origine.

S'éloignant de l'exemple, cette méthode peut également être utilisée pour l’annotation par les pairs. Maple Learn propose de nombreuses couleurs de police de texte différentes, permettant aux étudiants de laisser des commentaires sur le document, puis de générer un nouveau lien de partage instantané à renvoyer à l'étudiant d'origine.

Il existe bien d’autres façons d'utiliser Maple Learn pour l'apprentissage interactif, mais nous aimerions également connaître vos idées ! Veuillez nous faire savoir dans les commentaires si vous avez utilisé Maple Learn d'autres manières interactives, ou si vous avez des questions ou des suggestions à ce sujet.

The COVID 19 pandemic threw us for a spin with Online Learning – but after two years, it’s clear that Online Learning is here to stay. The good news is that more and more research is making its way to the classroom, giving us more information on the pros and cons of different teaching methods and how it impacts student learning. This all leads to one question: How can teaching be more effective during these tough times? Let’s discuss the research done and how it relates to Maple Learn. As a note, I do not claim to be an expert on this topic. I am simply a student attempting to improve online learning for myself and my peers.

There are three main styles of learning, in this context, agreed upon by psychologists: Passive, Active, and Interactive Learning. However, today we’re only going to focus on Interactive Learning. Interactive Learning is where the student acts as “a subject of educational activity” (Kutbiddinova, Eromasova, and Romanova, 2016). What this typically means in practice is the student collaborates with peers. This piece is much more difficult when classes are online and/or asynchronous. I know I struggled to make connections with my peers while in school online, as our main form of communication was discussion board posts. Let’s talk about the advantages of Interactive Learning first, and then discuss how Maple Learn can be used within the Interactive Learning model.

The main advantage of Interactive Learning is that it encourages the active participation of all involved. When encouraged to interact with peers in smaller groups, this allows more participation of the members of the group, compared to asking questions to the entire class and asking for them to raise their hands for answering. At the same time, Interactive Learning creates more engagement in the material, along with more student initiative (Ibid).

In one example discussed by Anderson in 2014, the students got into pairs and discussed their answer to a question. The students, in the exercise, had to commit to one answer and then discuss their reasoning behind the answer, in an attempt to change the other student’s mind. This created understanding of the material, along with emotional investment in the topic.

So, how can Maple Learn help to facilitate Interactive Learning in an online environment? Let’s start with recreating Anderson’s example, but online and with a slight twist to accommodate a math class.

Using Maple Learn, the student can go through all their steps, copying from their paper notes, or solving the equation as they type. They can also use text to explain their reasoning behind taking each step, or to place formulas beside the math they’ve used.

From there, the student can use the snapshot share feature to swap documents with someone else in the class. This allows both students to see the other’s work, and reasoning, without having to read scanned handwritten notes. This also means the review can happen asynchronously, allowing students from different places and/or time zones to discuss. In contrast to the original example, since we’re discussing Math, the student is not necessarily trying to convince the other student. The comments on the math are used more for giving targeted feedback, and understanding either other ways of solving the problem, or the correct way if originally solved wrong.

Taking a step away from the example, this method can also be used for peer marking. Maple Learn offers many different text font colors, allowing students to leave comments on the document, then generate a new snapshot to send back to the original student.

There are many other ways Maple Learn could be used for Interactive Learning, but we’d like to hear your ideas too! Please let us know in the comments if you’ve used Maple Learn in other Interactive ways, or if you have any questions or suggestions for us.


Works cited:

Anderson, Jill. “The Benefit of Interactive Learning.” Harvard Graduate School of Education, 2014,

Kutbiddinova, Rimma, et al. “The Use of Interactive Methods in the Educational Process of the Higher Education Institution.” INTERNATIONAL JOURNAL OF ENVIRONMENTAL & SCIENCE EDUCATION, 2016, Accessed 2022.

Adeptes de Maple Learn, nous avons de bonnes nouvelles pour vous! Nous avons fait une mise à jour de Maple Learn avec quelques fonctionnalités supplémentaires que nous sommes ravis de partager avec vous.

Tout d'abord, nous avons ajouté des fonctionnalités de Conception réactive à Maple Learn. Cela signifie que lorsqu'un écran est plus petit ou rétréci, l'interface de Maple Learn change pour refléter cela. Cela vous permet d'avoir encore plus d'espace disponible, quelle que soit la taille de votre écran ! Par exemple, lorsque votre écran est suffisamment petit, et que vous cliquez dessus sur les palettes, une petite boîte de dialogue contextuelle s’ouvrira en dessous d'elles, au lieu d’avoir tout leur contenu dans la barre d'outils.


Parallèlement à cela, une icône de redimensionnement d'image a été ajoutée à la barre d'outils pour faciliter le redimensionnement des images insérées dans votre document.

Comme note finale sur la conception réactive, plusieurs de nos menus ont été combinés en un seul, désigné par le menu latéral dans le coin supérieur gauche (illustré ci-dessous, à gauche). C'est là que vous trouverez les menus  fichier, édition, exemples et aide. Si vous cherchez le menu des paramètres, vous le trouverez entre le symbole premium et votre photo de profil en haut à droite. Ceci est désigné par trois points empilés les uns sur les autres (illustrés ci-dessous, à droite).


Nous avons également ajouté plus de raccourcis clavier et augmenté la prise en charge du clavier AZERTY. La liste mise à jour est disponible ici. Nous espérons que ces nouveaux raccourcis vous aideront à créer des documents plus facilement.

Parallèlement à la prise en charge du clavier AZERTY, nous avons renforcé la prise en charge de nos utilisateurs francophones. De nombreux autres documents sont désormais disponibles en français et nous avons résolu un problème où les caractères latins étendus ne s'affichaient pas correctement.

Les graphiques cliquables sont là ! Maple Learn inclut désormais une fonctionnalité qui permet aux utilisateurs de colorier nos graphiques cliquables. Ces documents sont créés à l'aide de Maple et permettent de générer des documents de coloriage par numéro ou différentes visualisations pour les théorèmes qui impliquent des graphiques, comme ce document. D'autres documents seront disponibles ultérieurement dans la galerie de documents, située ici.


Dites-nous ce que vous pensez des nouvelles fonctionnalités ci-dessous ! Nous espérons que vous apprécierez les utiliser pour créer de nouveau documents Maple Learn.


Works cited:

Anderson, Jill. “The Benefit of Interactive Learning.” Harvard Graduate School of Education, 2014,

Kutbiddinova, Rimma, et al. “The Use of Interactive Methods in the Educational Process of the Higher Education Institution.” INTERNATIONAL JOURNAL OF ENVIRONMENTAL & SCIENCE EDUCATION, 2016, Accessed 2022.

Maple Learn enthusiasts, we’ve got some exciting news for you! We’ve updated Maple Learn with a few more features that we’re excited to share with you.

First, we’ve added responsive design features to Maple Learn. This means that when a screen is smaller or shrunk the Maple Learn interface changes to reflect that. This lets you have even more canvas space, regardless of your screen size! For example, when your screen is small enough, the palettes, when clicked on, give a small pop-up dialogue below them, instead of their options also appearing in the toolbar.


Along with that, a resize image icon has been added to the toolbar to make it easier to resize the images you’ve inserted into your document.

As a final note on responsive design, several of our menus have been combined into one, designated by the hamburger icon in the top left corner (Shown below, left). This is where you’ll find the file, edit, examples, and help menus. If you are looking for the settings menu, it can be found between the premium symbol and your profile picture in the top right. This is designated by three dots stacked on top of each other (shown below, right).


We’ve also added more keyboard shortcuts, and increased support for the AZERTY keyboard. The updated list can be found here. We hope these new shortcuts will help you create documents more easily.

Along with the support for the AZERTY keyboard, we’ve increased support for our French language users. Many more documents are now available in French, and we’ve resolved an issue where Latin extended characters weren’t being displayed properly.

Clickable plots are here! Maple Learn now includes functionality which allows users to color our clickable plots. These documents are created through Maple scripting, and allow for colour-by-number documents, or different visualisations for theorems that involve graphics, such as this document. More documents will be available in the document gallery later, located here.


Let us know what you think of the new features below! We hope you enjoy using them in new and exciting ways.

About eliminate(...)


This post is motivated by a recent answer where I needed a necessary and sufficient condition for three straight lines in space be concurrent. I had to use determinants because the eliminate command did not provide the correct answer.
Investigating the cause, I saw that eliminate uses an heuristic algorithm, instead of using Groebner bases (when possible).

Here is an example.

We want to eliminate the unknowns x an y in the system

a*x + y = 0,  b*x+y+1 = 0, c*x+2*y = 0


sys:=[a*x + y, b*x + y + 1, c*x + 2*y];

[a*x+y, b*x+y+1, c*x+2*y]


eliminate(sys, [x,y]);

[{x = 0, y = 0}, {1}]


So, apparently, the elimination is not possible, i.e. for each triple (a,b,c), the system in x and y is incompatible.
This is not true. For example,



[x+y, 3*x+y+1, 2*x+2*y]


eval(%, [x=-1/2, y=1/2]);

[0, 0, 0]


eliminate  obtained its result this way (just like a superficial human):

solve(sys[[1,3]], [x,y]);
eval(sys[2],%[]); # The result obtained by eliminate

[[x = 0, y = 0]]




Now, the correct result (also by hand):

solve(sys[[1,2]], {x,y});

{x = 1/(a-b), y = -a/(a-b)}






So, for c = 2*a  (and a <> b)  the system in x,y  is compatible.


This result can be obtained with Groebner bases.

Groebner:-Basis(sys, plex(x,y,a,b,c));

[2*a-c, 2*b*y-c*y-c, c*x+2*y, b*x+y+1]


remove(has, %, {x,y});



Note that it is more efficient to use lexdeg([x,y], [a,b,c])  instead of plex(x,y,a,b,c).

Groebner:-Basis(sys, lexdeg([x,y], [a,b,c]));

[2*a-c, 2*b*y-c*y-c, c*x+2*y, b*x+y+1]


The conclusion is that eliminate should use internally Groebner:-Basis for polynomial systems.
Until then, we can use it ourselves!


1 2 3 4 5 6 7 Last Page 2 of 61