One decade on MaplePrimes

Always I Wish A Wonderful Year In Mathematics As Annus mirabilis

Fereydoon Shekofte

Aleksandrov_3dnew.mws

Hare in the forest

The rocket flies

Быльнов_raketa_letit.mws

Plotting the function of a complex variable

Plotting_the_function_of_a_complex_variable.mws

Animated 3-D cascade of dolls

3d_matryoshkas_en.mws

It is a very good computational tool to perform modeling and simulation using our world as a reference. You can also teach math knowing how to choose the right icons.
I recommend this software to everyone who wants to simulate objects or multibodies. In any case, knowledge of physics and mathematics, especially vector mechanics, is necessary.
Very grateful to the Maplesoft company for sharing their projects through the MapleSim gallery.

From now on all projects will be with Maple and MapleSim.

Lenin AC

Ambassador of Maple

Download QCT2019_PrimesV17_05.05.19.mw

I am a highschool teacher and we just started using Maple. It is a great program, but the students  had a few problems with the worksheet-mode in the editor. Here is a list of small problems that are hopefully easy to fix.

In text editors such as Word you can highlight a piece of text and select "insert->equation" to turn the text into an equation. Maple doesn't supprt this, so if the students have written an equation in textmode, then they have trouble turning it into math-mode. (the answer is: highlight, ctrl-X, F5, ctrl-v but that is difficult to guess for beginners)

Once in a while the students place two equations next to eachother with no space in between. When this happens they cannot place the cursor between the two eqations, and therefore they cannot place a newline between the equations. In other words the two equations are glued together. (I think that you can solve this by pressing f5 in the right place, but it would be better to mirror the behavior of word)

It would be great to allow the user to delete the pink error messages by pressing delete. Sometimes the students use math mode to write text inside a large paragraph and the result is an error message a few lines below. This error message cannot be deleted unless you trace down the math field and delete it. In one situation a student had deleted all the letters in the math field, but the error message could not be deleted until the empty mathfield had been found and deleted. (One solution is to highlight all math fields on the page whenever the user is editing text in math mode. That would make them easier to find and understand)

If a student pressed enter or alt-enter inside an equation in worksheet mode, then the student stays in worksheet mode after executing the equation. I would prefer to switch to text-mode after pressing enter. This would mirror the behavior of word. Sometimes the students end up writing a long paragraph because they expect Maple to mirror the behavior of word. Once the text has been written in math mode then it is difficult to convert it into textmode again (This requires highlight, ctrl-X, F5, ctrl-v)

It would be great to write an equation that isn't meant to be executed by the kernel.  In other words the equation should only be for display. You can solve this by writing ":"  at theb end of the equation, but that makes the math look weird. It would be nice to have a way to do this.

If mac users havent installed a printer then they cannot export to pdf. It would be great to solve this problem (or at least write a helpful error message)

All of these problems are beginner problems, but if I you want to sell Maple in highschools then I think that you can gain from focusing on making Maple approachable so that the students have an early succes-story with the program. In my class we switched to Maple from another math program, and it was a hard sell because the other math program had an easier editor.

I recently had a wonderful and valuable opportunity to meet with some primary school students and teachers at Holbaek by Skole in Denmark to discuss the use of technology in the classroom. The Danish education system has long been an advocate of using technology and digital learning solutions to augment learning for its students. One of the technology solutions they are using is Maple, Maplesoft’s comprehensive mathematics software tool designed to meet the unique and complex needs of STEM courses. It is rare to find Maple being used at the primary school level, so it was fascinating to see first-hand how Maple is being incorporated at the school.

In speaking with some of the students, I asked them what their education was like before Maple was incorporated into their course. They told me that before they had access to Maple, the teacher would put an example problem on the whiteboard and they would have to take notes and work through the solution in their notebooks. They definitely prefer the way the course is taught using Maple. They love the fact that they have a tool that let them work through the solution and provide context to the answer, as opposed to just giving them the solution. It forces them to think about how to solve the problem. The students expressed to me that Maple has transformed their learning and they cannot imagine going back to taking lectures using a whiteboard and notebook.

Here, I am speaking with some students about how they have adapted Maple to meet their needs ... and about football. Their team had just won 12-1.

Mathematics courses, and on a broader level, STEM courses, deal with a lot of complex materials and can be incredibly challenging. If we are able to start laying the groundwork for competency and understanding at a younger age, students will be better positioned for not only higher education, but their careers as well. This creates the potential for stronger ideas and greater innovation, which has far-reaching benefits for society as a whole.

Jesper Estrup and Gitte Christiansen, two passionate primary school teachers, were responsible for introducing Maple at Holbaek by Skole. It was a pleasure to meet with them and discuss their vision for improving mathematics education at the school. They wanted to provide their students experience with a technology tool so they would be better equipped to handle learning in the future. With the use of Maple, the students achieved the highest grades in their school system. As a result of this success, Jesper and Gitte decided to develop primary school level content for a learning package to further enhance the way their students learn and understand mathematics, and to benefit other institutions seeking to do the same. Their efforts resulted in the development of Maple-Skole, a new educational tool, based on Maple, that supports mathematics teaching for primary schools in Denmark.

Maplesoft has a long-standing relationship with the Danish education system. Maple is already used in high schools throughout Denmark, supported by the Maple Gym package. This package is an add-on to Maple that contains a number of routines to make working with Maple more convenient within various topics. These routines are made available to students and teachers with a single command that simplifies learning. Maple-Skole is the next step in the country’s vision of utilizing technology tools to enhance learning for its students. And having the opportunity to work with one tool all the way through their schooling will provide even greater benefit to students.

(L-R) Henrik and Carolyn from Maplesoft meeting with Jesper and Gitte from Holbaek by Skole

It helps foster greater knowledge and competency in primary school students by developing a passion for mathematics early on. This is a big step and one that we hope will revolutionize mathematics education in the country. It is exciting to see both the great potential for the Maple-Skole package and the fact that young students are already embracing Maple in such a positive way.

For us at Maplesoft, this exciting new package provides a great opportunity to not only improve upon our relationships with educational institutions in Denmark, but also to be a part of something significant, enhancing the way students learn mathematics. We strongly believe in the benefits of Maple-Skole, which is why it will be offered to schools at no charge until July 2020. I truly believe this new tool has the potential to revolutionize mathematics education at a young age, which will make them better prepared as they move forward in their education.

Last year, I read a fascinating paper that presented evidence of an exoplanet, inferred through the “wobble” (or radial velocity) of the star it orbits, HD 3651. A periodogram of the radial velocity revealed the orbital period of the exoplanet – about 62.2 days.

I found the experimental data and attempted to reproduce the periodogram. However, the data was irregularly sampled, as is most astronomical data. This meant I couldn’t use the standard Fourier-based tools from the signal processing package.

I started hunting for the techniques used in the spectral analysis of irregularly sampled data, and found that the Lomb Scargle approach was often used for astronomical data. I threw together some simple prototype code and successfully reproduced the periodogram in the paper.

After some (not so) gentle prodding, Erik Postma’s team wrote their own, far faster and far more robust, implementation.

This new functionality makes its debut in Maple 2019 (and the final worksheet is here.)

From a simple germ of an idea, to a finished, robust, fully documented product that we can put in front of our users – that, for me, is incredibly satisfying.

That’s a minor story about a niche I’m interested in, but these stories are repeated time and time again.  Ideas spring from users and from those that work at Maplesoft. They’re filtered to a manageable set that we can work on. Some projects reach completion in under a year, while other, more ambitious, projects take longer.

The result is software developed by passionate people invested in their work, and used by passionate people in universities, industry and at home.

We always pack a lot into each release. Maple 2019 contains improvements for the most commonly used Maple functions that nearly everyone uses – such as solve, simplify and int – as well features that target specific groups (such as those that share my interest in signal processing!)

I’d like to to highlight a few new of the new features that I find particularly impressive, or have just caught my eye because they’re cool.

Of course, this is only a small selection of the shiny new stuff – everything is described in detail on the Maplesoft website.

Edgardo, research fellow at Maplesoft, recently sent me a recent independent comparison of Maple’s PDE solver versus those in Mathematica (in case you’re not aware, he’s the senior developer for that function). He was excited – this test suite demonstrated that Maple was far ahead of its closest competitor, both in the number of PDEs solved, and the time taken to return those solutions.

He’s spent another release cycle working on pdsolve – it’s now more powerful than before. Here’s a PDE that Maple now successfully solves.

Maplesoft tracks visits to our online help pages - simplify is well-inside the top-ten most visited pages. It’s one of those core functions that nearly everyone uses.

For this release, R&D has made many improvements to simplify. For example, Maple 2019 better simplifies expressions that contain powers, exponentials and trig functions.

Everyone who touches Maple uses the same programming language. You could be an engineer that’s batch processing some data, or a mathematical researcher prototyping a new algorithm – everyone codes in the same language.

Maple now supports C-style increment, decrement, and assignment operators, giving you more concise code.

We’ve made a number of improvements to the interface, including a redesigned start page. My favorite is the display of large data structures (or rtables).

You now see the header (that is, the top-left) of the data structure.

For an audio file, you see useful information about its contents.

I enjoy creating new and different types of visualizations using Maple's sandbox of flexible plots and plotting primitives.

Here’s a new feature that I’ll use regularly: given a name (and optionally a modifier), polygonbyname draws a variety of shapes.

In other breaking news, I now know what a Reuleaux hexagon looks like.

Since I can’t resist talking about another signal processing feature, FindPeakPoints locates the local peaks or valleys of a 1D data set. Several options let you filter out spurious peaks or valleys

I’ve used this new function to find the fundamental frequencies and harmonics of a violin note from its periodogram.

Speaking of passionate developers who are devoted to their work, Edgardo has written a new e-book that teaches you how to use tensor computations using Physics. You get this e-book when you install Maple 2019.

The new LeastTrimmedSquares command fits data to an equation while not being signficantly influenced by outliers.

In this example, we:

• Artifically generate a noisy data set with a few outliers, but with the underlying trend Y =5 X + 50
• Fit straight lines using CurveFitting:-LeastSquares and Statistics:-LeastTrimmedSquares

LeastTrimmedSquares function correctly predicts the underlying trend.

We try to make every release faster and more efficient. We sometimes target key changes in the core infrastructure that benefit all users (such as the parallel garbage collector in Maple 17). Other times, we focus on specific functions.

For this release, I’m particularly impressed by this improved benchmark for factor, in which we’re factoring a sparse multivariate polynomial.

On my laptop, Maple 2018 takes 4.2 seconds to compute and consumes 0.92 GiB of memory.

Maple 2019 takes a mere 0.27 seconds, and only needs 45 MiB of memory!

I’m a visualization nut, and I always get a vicarious thrill when I see a shiny new plot, or a well-presented application.

I was immediately drawn to this new Maple 2019 app – it illustrates the transition between day and night on a world map. You can even change the projection used to generate the map. Shiny!

So that’s my pick of the top new features in Maple 2019. Everyone here at Maplesoft would love to hear your comments!

Recently, my research team at the University of Waterloo was approached by Mark Ideson, the skip for the Canadian Paralympic men’s curling team, about developing a curling end-effector, a device to give wheelchair curlers greater control over their shots. A gold medalist and multi-medal winner at the Paralympics, Mark has a passion to see wheelchair curling performance improve and entrusted us to assist him in this objective. We previously worked with Mark and his team on a research project to model the wheelchair curling shot and help optimize their performance on the ice. The end-effector project was the next step in our partnership.

The use of technology in the sports world is increasing rapidly, allowing us to better understand athletic performance. We are able to gather new types of data that, when coupled with advanced engineering tools, allow us to perform more in-depth analysis of the human body as it pertains to specific movements and tasks. As a result, we can refine motions and improve equipment to help athletes maximize their abilities and performance. As a professor of Systems Design Engineering at the University of Waterloo, I have overseen several studies on the motor function of Paralympic athletes. My team focuses on modelling the interactions between athletes and their equipment to maximize athletic performance, and we rely heavily on Maple and MapleSim in our research and project development.

The end-effector project was led by my UW students Borna Ghannadi and Conor Jansen. The objective was to design a device that attaches to the end of the curler’s stick and provides greater command over the stone by pulling it back prior to release.  Our team modeled the end effector in Maple and built an initial prototype, which has undergone several trials and adjustments since then. The device is now on its 7^th iteration, which we felt appropriate to name the Mark 7, in recognition of Mark’s inspiration for the project. The device has been a challenge, but we have steadily made improvements with Mark’s input and it is close to being a finished product.

Currently, wheelchair curlers use a device that keeps the stone static before it’s thrown. Having the ability to pull back on the stone and break the friction prior to release will provide great benefit to the curlers. As a curler, if you can only push forward and the ice conditions aren’t perfect, you’re throwing at a different speed every time. If you can pull the stone back and then go forward, you’ve broken that friction and your shot is far more repeatable. This should make the game much more interesting.

For our team, the objective was to design a mechanism that not only allowed curlers to pull back on the stone, but also had a release option with no triggers on the curler’s hand. The device we developed screws on to the end of the curler’s stick, and is designed to rest firmly on the curling handle. Once the curler selects their shot, they can position the stone accordingly, slide the stone backward and then forward, and watch the device gently separate from the stone.

For our research, the increased speed and accuracy of MapleSim’s multibody dynamic simulations, made possible by the underlying symbolic modelling engine, Maple, allowed us to spend more time on system design and optimization. MapleSim combines principles of mechanics with linear graph theory to produce unified representations of the system topology and modelling coordinates. The system equations are automatically generated symbolically, which enables us to view and share the equations prior to a numerical solution of the highly-optimized simulation code.

The Mark 7 is an invention that could have significant ramifications in the curling world. Shooting accuracy across wheelchair curling is currently around 60-62%, and if new technology like the Mark 7 is adopted, that number could grow to 70 or 75%. Improved accuracy will make the game more enjoyable and competitive. Having the ability to pull back on the stone prior to release will eliminate some instability for the curlers, which can help level the playing field for everyone involved. Given the work we have been doing with Mark’s team on performance improvements, it was extremely satisfying for us to see them win the bronze medal in South Korea. We hope that our research and partnership with the team can produce gold medals in the years to come.

Over the holidays I reconnected with an old friend and occasional
chess partner who, upon hearing I was getting soundly thrashed by run
of the mill engines, recommended checking out the ChessTempo site.  It
has online tools for training your chess tactics.  As you attempt to
solve chess problems your rating is computed depending on how well you
do.  The chess problems, too, are rated and adjusted as visitors
attempt them.  This should be familar to any chess or table-tennis
player.  Rather than the Elo rating system, the Glicko rating system is
used.

You have a choice of the relative difficulty of the problems.
After attempting a number of easy puzzles and seeing my rating slowly
climb, I wondered what was the most effective technique to raise my
rating (the classical blunder).  Attempting higher rated problems would lower my
solving rate, but this would be compensated by a smaller loss and
larger gain.  Assuming my actual playing strength is greater than my
current rating (a misconception common to us patzers), there should be a
rating that maximizes the rating gain per problem.

The following Maple module computes the expected rating change
using the Glicko system.

Glicko := module()

export DeltaRating
    ,  ExpectedDelta
    ,  Pwin
    ;

    # Return the change in rating for a loss and a win
    # for player 1 against player2
    DeltaRating := proc(r1,rd1,r2,rd2)
    local E, K, g, g2, idd, q;

        q := ln(10)/400;
        g := rd -> 1/sqrt(1 + 3*q^2*rd^2/Pi^2);
        g2 := g(rd2);
        E := 1/(1+10^(-g2*(r1-r2)/400));
        idd := q^2*(g2^2*E*(1-E));

        K := q/(1/rd1^2+idd)*g2;

        (K*(0-E), K*(1-E));

    end proc:

    # Compute the probability of a win
    # for a player with strength s1
    # vs a player with strength s2.

    Pwin := proc(s1, s2)
    local p;
        p := 10^((s1-s2)/400);
        p/(1+p);
    end proc:

    # Compute the expected rating change for
    # player with strength s1, rating r1 vs a player with true rating r2.
    # The optional rating deviations are rd1 and rd2.

    ExpectedDelta := proc(s1,r1,r2,rd1 := 35, rd2 := 35)
    local P, l, w;
        P := Pwin(s1,r2);
        (l,w) := DeltaRating(r1,rd1,r2,rd2);
        P*w + (1-P)*l;
    end proc:

end module:

Assume a player has a rating of 1500 but an actual playing strength of 1700.  Compute the expected rating change for a given puzzle rating, then plot it.  As expected the graph has a peak.

Ept := Glicko:-ExpectedDelta(1700,1500,r2):
plot(Ept,r2 = 1000...2000);

Compute the optimum problem rating

fsolve(diff(Ept,r2));

                     {r2 = 1599.350691}

As your rating improves, you'll want to adjust the rating of the problems (the site doesn't allow that fine tuning). Here we plot the optimum puzzle rating (r2) for a given player rating (r1), assuming the player's strength remains at 1700.

Ept := Glicko:-ExpectedDelta(1700, r1, r2):
dEpt := diff(Ept,r2):
r2vsr1 := r -> fsolve(eval(dEpt,r1=r)):
plot(r2vsr1, 1000..1680);

Here is a Maple worksheet with the code and computations.

Glicko.mw

Later

After pondering this, I realized there is a more useful way to present the results. The shape of the optimal curve is independent of the user's actual strength. Showing that is trivial, just substitute a symbolic value for the player's strength, offset the ratings from it, and verify that the result does not depend on the strength.

Ept := Glicko:-ExpectedDelta(S, S+r1, S+r2):
has(Ept, S);
                    false

Here's the general curve, shifted so the player's strength is 0, r1 and r2 are relative to that.

r2_r1 := r -> rhs(Optimization:-Maximize(eval(Ept,r1=r), r2=-500..0)[2][]):
p1 := plot(r2_r1, -500..0, 'numpoints'=30);

Compute and plot the expected points gained when playing the optimal partner and your rating is r-points higher than your strength.

EptMax := r -> eval(Ept, [r1=r, r2=r2_r1(r)]):
plot(EptMax, -200..200, 'numpoints'=30, 'labels' = ["r","Ept"]);

When your playing strength matches your rating, the optimal opponent has a relative rating of

r2_r1(0);
                       -269.86

The expected points you win is

evalf(EptMax(0));
                       0.00956

Fourteen year old Lazar Paroski is an exceptional student. Not only is he an overachiever academically, but he has a passion to help struggling students, and to think of innovative ways to help them learn. Lazar is particularly fond of Math, and in his interactions with other students, he noticed how students have a hard time with Math.

Putting on his creative cap, Lazar came up with the idea of an easily accessible “Math Wall” that explains simple math concepts for students in a very visual way.

“The Music Wall on Pinterest was my inspiration,” says Lazar. “I thought I can use the same idea for Math, and why not a Math Wall”?

"The math wall is basically all the tools you'll have on the wall in your classroom outside," said Lazar. Making the Math Wall and getting it set up, took time and effort. But he had help along the way, which, fueled by his passion and enthusiasm, helped turn his creative dream into reality. Lazar received a grant of $6000 from the local government to implement the project; his teachers, principal and family helped promote it; and the community of parents provided encouragement.

The Math Wall covers fundamental math concepts learnt in grades 1 to 6. Lazar engaged with over 450 students in the community to understand what would really be helpful for students to see in this Math Wall, and then he carefully picked the top themes he wanted to focus on.

The three meter Math Wall is located in the Morrison community park, and was officially inaugurated by the Mayor of Kitchener in July 2018. Many students have already found it to be useful and educative. Parents who bring their children to the park stop by to give their kids a quick math lesson.

At Maplesoft, we love a math story like this! And that too in our backyard! We wanted to appreciate and encourage Lazar and his efforts in making math fun and easy and accessible to students. So we invited Lazar to our offices, gifted him a copy of Maple, and heard more about his passion and future plans. “In many ways, Lazar embodies the same qualities that Maplesoft stands for – making it easy for students to understand and grasp complex STEM concepts,” said Laurent Bernardin, Maplesoft’s Chief Operating Officer. “We try to impress upon students that math matters, even in everyday life, and they can now use advanced, sophisticated technology tools to make math learning fun and efficient.”

We wish Lazar all the very best as he thinks up new and innovative ways to spread his love for math to other kids. Well done, Lazar!

I have recently visited the Queen's House at Greenwich  (see wiki),  an  important building in British architectural history (17th century).
I was impressed by the Great Hall Floor, whose central geometric decoration seems to be generated by a Maple program :-)

Here is my code for this. I hope you will like it.

restart;
with(plots): with(plottools):
n:=32: m:=3:#    n:=64: m:=7:

a[0], b[0] := exp(-Pi*I/n), exp(Pi*I/n):
c[0]:=b[0]+(a[0]-b[0])/sqrt(2)*exp(I*Pi/4):  
for k to m+1 do  
  c[k]:=a[k-1]+b[k-1]-c[k-1];
  b[k]:=c[k]*(1+exp(2*Pi*I/n))-b[k-1];
  a[k]:=conjugate(b[k])  od:
b[-1]:=c[0]*(1+exp(2*Pi*I/n))-b[0]:
a[-1]:=conjugate(b[-1]):
c[-1]:=a[-1]+b[-1]-c[0]:
seq( map[inplace](evalf@[Re,Im], w), w=[a,b,c] ):
Q:=polygonplot([seq([a[k],c[k],b[k],c[k+1]],k=0..m-1), [c[m],a[m],b[m]], [a[-1],b[-1],c[0]]]):
display(seq(rotate(Q, 2*k*Pi/n, [0,0]),k=0..n-1), disk([0,0],c[m][1]/3), axes=none, size=[800,800], color=black);