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MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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  •        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

    Si vous aimez les mathématiques, vous connaissez le symbole mathématique pi. Vous devriez aussi savoir que le jour de pi est le 14 mars ou 3/14. Le jour de Pi était donc ce lundi donc vous vous demandez peut-être pourquoi je publie ce post aujourd’hui ? Et bien pour ce poste, j’ai pensée que je pourrai vous donner plus d’information au sujet de pi, l’histoire de pi et l’histoire de la célébration du jour de pi.

    Commençons avec une vue d’ensemble de pi. Il est le symbole mathématique qui représente la proportion entre la circonférence d’un cercle et son diamètre. Comme il a une connexion avec les cercles, pi est utilisé pour calculer les volumes des solides, l’aire et le périmètre d’un cercle et bien plus.

    Comment a t’il été découvert ?

    Le premier calcul de pi a été effectué par Archimède qui a fait une approximation de l’aire d’un cercle en utilisant le théorème de Pythagore. Il trouve l’aire de deux polygones réguliers : Celui qui s’inscrit dans le cercle et celui que le cercle circonscrit. Avec cette méthode, il a pu trouver une approximation de l’aire entre les deux polygones et ainsi une approximation de l’aire du cercle.

     Le symbole de Pi a été introduit et popularisé au 16e siècle. Avec cela, George Buffon a trouvé une méthode de calcul de pi basée sur des probabilités au même siècle.

    Tout mène à une de mes plus grandes interrogations : Comment le jour de pi a été créé ? Je sais que la date est symbolique, mais pourquoi nous célébrons pi ?

    Le jour de pi a été introduit en 1988 par un physicien nommé Larry Shaw.  Le 14 mars est aussi la date d’anniversaire d’Albert Einstein et ce qui ajoute quelque chose de plus a célébré supplémentaire pour les physiciens. Le premier jour de pi fut célébré avec une parade circulaire et des tartes aux fruits.  À Maplesoft, nous l’avons célébrer avec des tartes ainsi qu’en faisant de l’art avec Maple Learn.

    Peut-être que qu’un jour d’autres jours célébrants des concepts mathématiques ajouterons à notre calendrier, mais en attendant, commencez planifier le jour de pi pour l’année prochaine ! Peut-être que vous pouriez créer quelque chose de plus grand que la première célébration en 1988. J’espère que votre jour de pi c’est bien passé !

    If you know math, you’re aware of the mathematical sign of pi. If you’re really into math, you know of Pi Day, occurring on March 14, or 3/14. Pi day this year occurred on Monday, so you may be wondering why we’re posting today as well! Well, I thought I’d give a bit more information about pi, the history of it, and the history of celebrating Pi Day.

    Let’s start with a brief overview of pi. Pi is a mathematical sign representing the ratio of a circle’s circumference to its diameter, typically approximated to 3.14. Because of its connection to circles, pi is used to calculate the volumes of solids, area and perimeter of circles, and many other applications.

    So how did we come up with this?

    The first calculation of pi is attributed to Archimedes, who approximated the area of a circle using the Pythagorean Theorem. He found the area of two regular polygons: the one inscribed into the circle, and the one which the circle is circumscribed. This way he could find an approximation between the areas of those two polygons, and therefore an approximation of the area of the circle.

    In the 1700s, the symbol for Pi was introduced and popularized. Along with that, Georges Buffon found a way to calculate Pi based on probability in the same century.

    This leads to what was my biggest question: How did Pi Day come about? I know the digits of the date are significant, but why do we celebrate pi?

    Pi Day was founded in 1988 by a physicist named Larry Shaw. March 14 is also Albert Einstein’s birthday, adding a bit of extra celebration to the date by physicists. The first Pi Day featured a circular parade and fruit pies. Here at Maplesoft, we celebrated with pie, and learning how to make art with Maple Learn.

    Maybe someday we’ll have more days celebrating mathematical concepts, but for now, start planning for next year’s Pi Day! Perhaps you can make it bigger and better than the first celebration in 1988. I hope your Pi Day this year went well, and happy Friday!

    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.


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    #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

    Hi, just some ideas for improvement!

    - since MapleFlow uses Maple as its engine, more integration of MapleFlow and Maple would be nice. Some commands that work very well in Maple not always work the same in MapleFlow. For example, BodePlot plots magnitude and phase in Maple but plots only magnitude in MapleFlow

    - a better Help documentation would also help. ?command/function works in Maple but not in MapleFlow. It's a bit anoying to have to open Maple just to get help documentation

    - a lot of palettes are not enabled in MapleFlow. Again, it is a little anoying to have to open Maple to get some of the palettes copied and pasted into MapleFlow

    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.

    One way to show all solutions of a polynomial in one variable.
    The root is the intersection of curves representing the imaginary part of the equation (red) and the real part (blue). These equations are obtained after representing the variable as the sum of its imaginary and real parts. The circle limits the area where all the roots are located (according to theory).
    Example      -15*x^7+x^2+I*x+2=0;

    Explorer 1 was the first satellite sent into space by the United States. It was a scientific instrument that led to the discovery of the Van Allen radiation belt. In order to keep its orientation, the satellite was spin stabilized. Unexpectedly, shortly after launch, Explorer 1 flipped the axis of rotation. The animation below shows, on the left, Explorer 1 in its initial state after launch, rotating about the axis of minimum moment of inertia. On the right side, 100 minutes later in the simulation, Explorer 1 rotates about the axis of maximum moment of inertia. This unintended behavior could not be explained immediately. Finally, structural damping in the four whip-like antennas was made responsible for the flip (explained here).

    The flip can be reproduced with MapleSim using flexible beam components with damping enabled. Without damping and without slight angular misalignment at launch the flip does not manifest.

    The simulation is only of qualitative nature since data of the antennas could not be found. On images of Explorer 1, the antennas look prebend and show large deflections of about 45 degrees under gravity. Since rotation of the satelite stretches the antennas, no modeling of large deflections needed to be considered in the simulation and rather stiff antennas (2 mm in diameter) without spheres at their ends were used. (Modeling large deflections with high fidelity might only be considered if the unfolding process of the antennas at launch is of interest. This should be modeled with several flexible beam components.)  

    The graph bellow shows the evolution of the angular velocity in x direction. Conservation of angular momentum reduces the angular velocity when the satellite starts flipping towards a rotation about the axis of maximum moment of inertia.

    Not long ago such simulations would have been worth a doctoral thesis. Today its rather straight forward to reproduce the flip with MapleSim.

    Not so easy is the calculation of energy and angular momentum (for the purpose of observing how well numerics preserve physical quantities in rather long calculations. After all, the solver does not know the physical context). Such calculations would require access to the inertia matrix of the cylinder component including a coordinate transform into the frame of reference where the vector of rotation can be measured.

    In case such calculations are possible with MapleSim, it would be nice if someone can update the model or at least indicate how calculations can be done.


    On a side note: I learned from the flip in an excellent series of lectures on dynamics. Wherever our professor could, he came up with animation in hardware. In this case, he could only provide an exciting story about the space race and sometimes fruitful mistakes in science. That’s why I still remember it.

    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!


    It’s midterm season in North America! I know, I know, you see enough reminders at school. However, we’re here to help with those tough midterms, with tips good for those who are taking their first midterms or who have already taken many.

    I surveyed the co-op students working at Maplesoft, and collected some of their best study tips and mindsets surrounding midterms. Maplesoft hires many co-ops, as a piece of their education in work experience.

    Let’s start with studying! One thing many of the students brought up was the importance of notetaking. Even if the lectures are recorded, or PowerPoints are given, it’s important to take notes that you can study from, that are more succinct. As well, another discussed the importance of doing many different types of studying, in order to keep you interested and focused. For example, using flashcards and answering practice problems, instead of only using flashcards.

    So, how can Maplesoft help with your studying? Let’s start with a video. In this video, Justice explains how first year math can be explored using Maple Learn’s features. He walks through using the document gallery, which we’ll talk about later, along with the power of Maple Learn.

    You can also create your own study sheets in Maple Learn, to reference later, or to simply practice what you know! One suggestion would be to create a sheet as though you’re teaching someone else, as teaching can be a great way to learn concepts and cement them in your mind.

    These are just some of the many ways that Maple Learn can be used to improve your studying! Play around with introducing Maple Learn into your study routine, and I know you’ll find a method that works for you.

    Are you having trouble grasping some advanced concepts? We have many different documents in the document gallery, available here. These documents typically fall under 3 categories: explanation documents explaining theory, example documents showing how to apply the theory, and then practice problems for you to solve that include solutions.

    Proofs were a topic the students considered an advanced topic, and as such we’ll use that as an example. A simple search brings up many documents, ranging from the proof of the derivative of sine (here) to the Taylor’s Theorem proof (here). These documents are available for a wide variety of topics, from calculus to graph theory to kinematics.

    Time Management is another piece that many of the students identified. We know this can be hard, especially when there are so many things to juggle, so we’ve created a document to help you plan out your time, available here!


    Using the document, you can see how many hours in a day that you’re using for sleep, studying, and everything else you can think of. We hope this helps you to keep track of just how many hours in a day you can realistically study!

    Now, we know that studying isn’t the only hard part of a midterm. The mindset piece is critical, along with studying. Let’s see what the students had to say about it!

    One of the students surveyed responded with “I am going to fail at some point. It is inevitable, and that is okay”. This is a great mindset for everyone to have. Remember that even failure isn’t failure. Learning something from any experience is a success, even if the outcome wasn’t what you wanted. There’s always next time, and time to learn even more and improve.

    Another student discussed the importance of a positive mindset, saying “Stay calm, stay confident, and as long as you try your best you will do great!” Remember, in the end, the best you can do is all you can do.

    We know midterms are a stressful time. Take care of yourself as we at Maplesoft continue to support you.

    Auto paste last entry

    So maple uses % as the last expression entry.  My suggestion is to use Crtl+Space on the % command to re-display the last expression.  Yes one could easily use the mouse to select the last entry then Crtl+c and Crtl+v. 

    Or maybe the command Crtl+Shift+L to auto paste last entry. 

    **edit** actually I would prefer the Crtl+Shift+L option to auto paste the last entry.

    ** Appears to be a suggestion I made earlier

    Vous venez de découvrir vos résultats du bac blanc et n’avez pas obtenus les résultats espérés à l’épreuve de mathématiques ?

    Maple Learn pourrait vous aider à améliorer vos connaissances et vous préparer pour le vrai baccalauréat.

    Commencez par revoir les théorèmes et définitions essentielles en explorant les documents de la galerie Maple Learn. Si vous avez des doutes sur certaines définitions; n’hésitez pas à utiliser les outils graphiques de Maple Learn pour approfondir vos connaissances

    Consultez ces documents ici et ici.

    Ensuite entrainez-vous à faire vos exercices avec Maple Learn

    Consultez ce document ici.

    Et enfin vérifiez vos résultats avec la Calculatrice Maple pour voir les étapes de résolutions :

    N’hésitez pas à partager en commentaire vos astuces pour réviser avec Maple Learn ou la Calculatrice Maple!

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