Product Tips & Techniques

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

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]

(1)

eliminate(sys, [x,y]);

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

(2)

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,

 

eval(sys,[a=1,b=3,c=2]);

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

(3)

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

[0, 0, 0]

(4)

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]]

 

1

(5)

Now, the correct result (also by hand):

solve(sys[[1,2]], {x,y});
eval(sys[3],%);
numer(simplify(%));

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

 

c/(a-b)-2*a/(a-b)

 

c-2*a

(6)

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]

(7)

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

[2*a-c]

(8)

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]

(9)

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.

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!

Happy Valentine’s Day! Love is celebrated all around the world on this day, but did you know of some other love celebrations, and some of the mythology around the holiday?

First of all, Cupid. We all know of the image of Cupid and his bow, shooting arrows to make couples fall in love. But where exactly did this come from?

Cupid is a Latin deity, the son of Venus and Mars. With his parents being love and war, it’s no surprise that he ended up with a bow! In one legend, he shoots a golden arrow at Apollo, which makes him fall in love with a nymph. Unfortunately for Apollo, he also shoots a lead arrow at the nymph, making her repulsed by him.

Roses are another popular tradition with Valentine’s Day. Red roses persist as a symbol of Aphrodite, the mother of Cupid, and are a symbol of love. Did you know you can draw them in Maple Learn with our geometry palette? See one rendition below of a stained glass rose. The link to the document is HERE.

Now, there are a few other love traditions around the world. Did you know that not everyone celebrates love only on Valentine’s Day? There are other important days around the world, and some pre-date Valentine’s Day.

For example, in China, the Miao people celebrate the Sister’s Meal Festival, likely our earliest form of a Valentine’s Day tradition in the world. This occurs in March. Young women make dyed rice representing the different seasons, and when the men come by to sing, they give them packages of the rice. Inside the rice are objects, each with different meanings. A pair of red chopsticks means the woman returns the man’s affection, while one red chopstick is a polite refusal. A clove of garlic or a chili pepper means a strong refusal, and pine needles mean that she is waiting for him to woo her.

We’ve created a document to join in on the fun, even if you’re not participating in this Festival this year. Follow the link HERE to work with fraction tiles to pack your own rice packages, and your own responses to declarations of love. 

We hope everyone has a lovely Valentine’s day!

You heard us right! With the new update of Maple Learn, we’ve added a few more interesting features, perfect to keep your math learning going.

Before we dig too far into these exciting features, we just have one quick thing to let you know about. We have updated the font sizes for Maple Learn text, adding 20 and 22 point font, and removing 36 and 120 point font.

Now, let’s talk new features. First, we’ve added support for partial derivatives, allowing you to calculate derivatives for functions with two or more variables. How does this work? Well, take a look at our example document HERE. The button for entering a partial derivative is located in the functions palette. You can plot them too (shown below)!

We’ve also added support for shaded Geometric Primitives. Remember our earlier post about MAPLE LEARN ART? Well, now you can color in your shapes! This allows for further math-related art, or ease of communication while teaching about area, or really, anything else you can think of! See how to use this HERE. In essence, with the shaded command, you can now place a geometric primitive inside the shaded command, which shades it! As well, you can assign a variable to a geometric primitive, and then place that inside the shaded command. This allows for a different color outline than the shaded section.

Ever wanted to create a sequence in Maple Learn? Well, now you can easily, with our new sequence support. The syntax is simple, focusing on the start, end, and steps. See how to use this HERE. We hope this can be used for all kinds of documents!

We hope you enjoy all the new features we’ve added to Maple Learn. Let us know in the comments what you think of them, and show us what you’re working on! Simply leave a comment with a link to a Maple Learn document, and we’ll gladly take a look at your ideas.

We have just issued a critical fix to Maple, MapleSim, and Maple Flow running on macOS.

We have heard from some users who were experiencing serious problems with doubled characters while using Maplesoft products on macOS, including these reports on MaplePrimes. Further investigation determined that these problems appear specifically on macOS 11 and macOS 12.  I am happy to report that we have now corrected the problem, and a patch is available. 

Anyone who uses macOS 11 or macOS 12 should install this update immediately. We also strongly recommend that all macOS users install this update, to avoid problems that may be triggered by future updates to your operating system.

To obtain this update:

For those who have experienced problems, we apologize for the inconvenience and thank you for your patience while we worked to find a solution.

Maple users may notice unexpected results when calculating standard deviations with weights.

This is because the notion of weights used by Maple is not exactly the commonly used notion of repeated measurements.

Maple uses the NAG library from the Numerical Algorithms Group to compute the standard deviation in the presence of weights. The formula that is used is given in their documentation: https://www.nag.com/numeric/cl/nagdoc_cl25/pdf/g01/g01aac.pdf.

 

NULL

restart

with(Statistics)

V := `<,>`(seq(i, i = 57 .. 77), undefined)

_rtable[36893489755601713980]

(1)

W := `<,>`(2, 4, 14, 41, 83, 169, 394, 669, 990, 1223, 1329, 1230, 1063, 646, 392, 202, 79, 32, 16, 5, 2, 5)

StandardDeviation(V, weights = W)

HFloat(HFloat(undefined))

(2)

StandardDeviation(V, weights = W, ignore = true)

HFloat(2.7274213984819053)

(3)

NULL

Download standard-deviation-weights-help-example.mw

A user wondered how to have Maple produce a desired form of a solution

eq1 := `&sigma;__2` = P__2/(Pi*r^2)NULL

NULL

r := (1/2)*d

NULL

soln := `assuming`([solve(eq1, {d}, useassumptions)], [`&sigma;__2`::real, d > 0, P__2 > 0])

{d = 2*(Pi*sigma__2*P__2)^(1/2)/(Pi*sigma__2)}

(1)

NULL

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

Download question-better-spacing.mw

We suggested the closest they might be able to get is using simplify like so:

 

restart; eq1 := `&sigma;__2` = P__2/(Pi*r^2)
``

``

r := (1/2)*d

``

soln := `assuming`([solve(eq1, {d}, useassumptions)], [`&sigma;__2`::real, d > 0, P__2 > 0])

{d = 2*(Pi*sigma__2*P__2)^(1/2)/(Pi*sigma__2)}

(1)

``

`assuming`([simplify(soln)], [sigma__2::real, P__2 > 0])

{d = 2*P__2^(1/2)/(Pi^(1/2)*sigma__2^(1/2))}

(2)

NULL


Download suggestion.mw

Our user wondered about using PolynomialIdeals:

1.  If we have n+1 polynomials,  f, g1,...,gn,  how to determine if  f  is in the ideal generated by  g1,...,gn?

2.  If so, how to write  f  as a polynomial combination of   g1,...,gn? 

We suggested that;

The nicest interface to answer the first question is given by the ?PolynomialIdeals,Operators page: you can write

with(PolynomialIdeals):
with(Operators):
J := <g1, g2, ..., gn>;
f in J; # true or false

To answer the second question, you need to use the lower level  package (which underlies the  package). This will also answer the first question for you. In particular the  command. You can write:

(Edit Feb 1, 2022 - use  instead of 

with(Groebner):
G := [g1, g2, ..., gn];
ord := tdeg(x,y,z); # replace x, y, z with the appropriate variables; you can also use other variable orders -- see ?Groebner,MonomialOrders

b := Basis(G, ord);
n := NormalForm(f, b, ord, 'Q');
# if n = 0 then f is in the ideal; Q is the list of coefficients:
f - add(Q[i] * b[i], i = 1 .. numelems(b)); # this will be equal to n.

I’m looking for users’ favourite tips and tricks in Maple Learn. Specifically, small pieces of advice that most people don’t know about, but that helped you create better Maple Learn documents. For instance,

  • A favorite feature that you think is hard to discover;
  • Common techniques you use when creating documents;
  • Things about Maple Learn you wish you knew when you started.

These tricks could be for newbies or for experienced users.

To start off the discussion, let me share three of my own favorite tricks in Maple Learn.

1. Using Documents from the Document Gallery

Writing a Maple Learn document from scratch can seem overwhelming, especially for beginners. A much easier way to create documents is to start with a template from the Document Gallery.

There are hundreds of Maple Learn documents in the Document Gallery, available here. Instead of writing Maple Learn documents from scratch, I like to search the gallery for documents relating to my topic. I then select a document, and just modify it slightly to get what I want.

2. Toggling from Math Mode to Text Mode

If you want to write text in a group element, it’s best to toggle to text mode (otherwise Maple Learn will treat your text as math).

While this can be done using the toolbar, there is a nifty keyboard shortcut to toggle to text mode: place your cursor at the beginning of the group element, and press the space key.

3. Using Double Arrows in Plots to Show Distance

Here’s one for the advanced users. The Vector Command lets you draw arrows on a Maple Learn plot. Combine two such arrows of the same colour going in opposite directions, and you get a double arrow (see below), which I like to use to represent distances in my Maple Learn documents.

Indeed, here is an example document where I use double arrows to provide a visualization of the product rule in calculus (plot pictured below). Notice how the double arrows (created using the vector command) represent distances in the plot.

Comment your favourite tips and tricks down below!

A user would like to know if it is possible to specify a data set say, x:=[1,2,3,4,5,6] and then extract a random sample from that data set, i.e. xsample:=[3,2,4] for a bootstrapping-type calculation.

We suggested they use something like the following:

restart; with(Statistics); my_data := [1, 2, 4, 5.5, 5.5, 6]; X := RandomVariable(EmpiricalDistribution(my_data)); s := Sample(X, 10); Bootstrap(Mean, X, samplesize = 4, replications = 10000)

HFloat(3.9984625)

(1)

NULL

Download array-random-sample.mw

A user wonders if there is a straightforward way to show US states with names using the WorldMap Data Set in Maple

We suggest something like the attached: map-of-us-with-states.mw

 

restart; with(DataSets:-Builtin); r := Reference("GeoNames"); states := r[[Country = "United States", Type = "first-order administrative division"]]; w := WorldMap(); w:-AddPoints(w, states); Display(w, mapdata = fine, style = polygonoutline, size = [2000, 1500])

 

 

Although not mentioned in the documentation, the flexible beam component of MapleSim allows for simulation of large deflections.  

In the animation, a flexible beam is loaded with a moment (red arrow) at its free end. Assuming an Euler-Bernoulli beam and slow loading (i.e., no dynamic forces), the beam should deform to an arc of constant radiusNot only the deformation of the beam can be described analytically, also the path (red trace) of the free end follows an analytical curve.

 

I used this test case to get a better understanding of nonlinearities observed in an oscillating system using flexible beams (https://www.mapleprimes.com/posts/215718-Mode-Coupling-With-Flexible-Beams-). The system required tuning of the structure to develop mode coupling. This could not be explained by linear theory. It was unclear whether the large deflections (nonlinear kinematics of the beam) themselves or the implementation of the flexible beam component were responsible for that.  

 

What I have learned so far with the test case using only default settings: 

  • For moderate deflections there is no difference to textbook formulas.
  • Up to 15 degrees rotation of the end frame, the difference between observed displacement and the Bernoulli beam stays bellow 5%.  
  • Up to 30 degrees rotation of the end frame (as in the mode coupling example) the trace of the end frame conforms well with the analytical path.
  • To simulate very large deflections beyond 45 degrees rotation, the beam needs to be segmented to closely follow the analytical path.  

For those that are unsure about the fidelity of their models, I can suggest increasing the numbers of flexible beam components and to compare. I did this in the case of the mode coupling example and noticed no difference. So, the component was not responsible for the nonlinearities. It were the kinematics.

It's unclear whether this good performance in large deflections was intended or is a byproduct of the sophisticated multibody dynamics under the hood.  Maybe an expert can tell more.

Overall, to what I have seen the (static) performance was very satisfying. Judging dynamic performance is much more difficult. Has anyone experience to share with that?

Flexible_beams_const_moment_curve_MP.mw

Flexible_beams_const_Moment_single_beam_MP.msim

Flexible_beams_const_Moment_7_beams_MP.msim

is what I have used.

We’ve been busy! We have just released the 2021.2 updates for Maple, Maple Flow, and MapleSim. Here’s a quick overview. These updates are freely available to all customers who have the 2021 version of these products.

Maple

The Maple update includes a variety of corrections and improvements to the math engine and interface. It is available through Tools>Check for Updates in Maple, and is also available from the Maple 2021 download page, where you can also find more details.

In particular, this update includes fixes to the bug in the combine command when working with double summations, and the problems when performing context menu operations on values with units while in Document mode, both of which were reported on MaplePrimes. As always, we appreciate the feedback!

Maple Flow

The Maple Flow 2021.2 update offers a richer range of formatting features for creating professional-looking engineering documents, which have been requested by customers. Highlights include sections, controlling the display of commands, annotating images, and disabling automatic evaluation while making a series of changes.  This update is available from the Maple Flow 2021.2 download page, which also contains more details.

MapleSim

Lots of good stuff here that makes it easier to build and analyze models, including productivity features that speed up the creation of models that use hydraulics, support for the latest CAD file formats in the MapleSim CAD toolbox, the ability to model drift conditions with the MapleSim Tire Library, tools for simulating 3-D winding effects with the MapleSim Ropes and Pulleys Library, and a new MapleSim Web Handling Library add-on (which, I am sad to say, has nothing to do with Spiderman). See What’s New in MapleSim for details, and the MapleSim 2021.2 download page for instruction on how to obtain your update.

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