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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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  • Maple 2017 has launched!

    Maple 2017 is the result of hard work by an enthusiastic team of developers and mathematicians.

    As ever, we’re guided by you, our users. Many of the new features are of a result of your feedback, while others are passion projects that we feel you will find value in.

    Here’s a few of my favourite enhancements. There’s far more that’s new - see What’s New in Maple 2017 to learn more.

     

    MapleCloud Package Manager

    Since it was first introduced in Maple 14, the MapleCloud has made thousands of Maple documents and interactive applications available through a web interface.

    Maple 2017 completely refreshes the MapleCloud experience. Allied with a new, crisp, interface, you can now download and install user-created packages.

    Simply open the MapleCloud interface from within Maple, and a mouse click later, you see a list of user-created packages, continuously updated via the Internet. Two clicks later, you’ve downloaded and installed a package.

    This completely bypasses the traditional process of searching for and downloading a package, copying to the right folder, and then modifying libname in Maple. That was a laborious process, and, unless I was motivated, stopped me from installing packages.

    The MapleCloud hosts a growing number of packages.

    Many regular visitors to MaplePrimes are already familiar with Sergey Moiseev’s DirectSearch package for optimization, equation solving and curve fitting.

    My fellow product manager, @DSkoog has written a package for grouping data into similar clusters (called ClusterAnalysis on the Package Manager)

    Here’s a sample from a package I hacked together for downloading maps images using the Google Maps API (it’s called Google Maps and Geocoding on the Package Manager).

    You’ll also find user-developed packages for exploring AES-based encryption, orthogonal series expansions, building Maple shell scripts and more.

    Simply by making the process of finding and installing packages trivially easy, we’ve opened up a new world of functionality to users.

    Maple 2017 also offers a simple method for package authors to upload workbook-based packages to the MapleCloud.

    We’re engaging with many package authors to add to the growing list of packages on the MapleCloud. We’d be interested in seeing your packages, too!

     

    Advanced Math

    We’re committed to continually improving the core symbolic math routines. Here area few examples of what to expect in Maple 2017.

    Resulting from enhancements to the Risch algorithm, Maple 2017 now computes symbolic integrals that were previously intractable

    Groeber:-Basis uses a new implementation of the FGLM algorithm. The example below runs about 200 times faster in Maple 2017.

    gcdex now uses a sparse primitive polynomial remainder sequence together.  For sparse structured problems the new routine is orders of magnitude faster. The example below was previously intractable.

    The asympt and limit commands can now handle asymptotic cases of the incomplete Γ function where both arguments tend to infinity and their quotient remains finite.

    Among several improvements in mathematical functions, you can now calculate and manipulate the four multi-parameter Appell functions.

     

    Appel functions are of increasing importance in quantum mechanics, molecular physics, and general relativity.

    pdsolve has seen many enhancements. For example, you can tell Maple that a dependent variable is bounded. This has the potential of simplifying the form of a solution.

     

    Plot Builder

    Plotting is probably the most common application of Maple, and for many years, you’ve been able to create these plots without using commands, if you want to.  Now, the re-designed interactive Plot Builder makes this process easier and better.

    When invoked by a context menu or command on an expression or function, a panel slides out from the right-hand side of the interface.

     

    Generating and customizing plots takes a single mouse click. You alter plot types, change formatting options on the fly and more.

    To help you better learn Maple syntax, you can also display the actual plot command.

    Password Protected Content

    You can distribute password-protected executable content. This feature uses the workbook file format introduced with Maple 2016.

    You can lock down any worksheet in a Workbook. But from any other worksheet, you can send (author-specified) parameters into the locked worksheet, and extract (author-specified) results.

     

    Plot Annotations

    You can now get information to pop up when you hover over a point or a curve on a plot.

    In this application, you see the location and magnitude of an earthquake when you hover over a point

    Here’s a ternary diagram of the color of gold-silver-copper alloys. If you let your mouse hover over the points, you see the composition of the points

    Plot annotations may seem like a small feature, but they add an extra layer of depth to your visualizations. I’ve started using them all the time!

     

    Engineering Portal

    In my experience, if you ask an engineer how they prefer to learn, the vast majority of them will say “show me an example”. The significantly updated Maple Portal for Engineers does just that, incorporating many more examples and sample applications.  In fact, it has a whole new Application Gallery containing dozens of applications that solve concrete problems from different branches of engineering while illustrating important Maple techniques.

    Designed as a starting point for engineers using Maple, the Portal also includes information on math and programming, interface features for managing your projects, data analysis and visualization tools, working with physical and scientific data, and a variety of specialized topics.

     

    Geographic Data

    You can now generate and customize world maps. This for example, is a choropleth of European fertility rates (lighter colors indicate lower fertility rates)

    You can plot great circles that show the shortest path between two locations, show varying levels of detail on the map, and even experiment with map projections.

    A new geographic database contains over one million locations, cross-referenced with their longitude, latitude, political designation and population.

    The database is tightly linked to the mapping tools. Here, we ask Maple to plot the location of country capitals with a population of greater than 8 million and a longitude lower than 30.

     

    There’s much more to Maple 2017. It’s a deep, rich release that has something for everyone.

    Visit What’s New in Maple 2017 to learn more.

    Meta Keijzer-de Ruijter is a Project Manager for Digital Testing at TU Delft, an institution that is at the forefront of the digital revolution in academic institutions. Meta has been using Maple T.A. for years, and offered to provide her insight on the role that automated testing & assessment played in improving student pass rates at TU Delft.

     

    Modern technology is transforming many aspects of the world we live in, including education. At TU Delft in the Netherlands, we have taken a leadership role in transforming learning through the use of technology. Our ambition is to get to a point where we are offering fully digitalized degree programs and we believe digital testing and assessment can play an important role in this process.

     

    A few years ago we launched a project with the goal of using digital testing to drastically improve the pass rates in our programs. Digital testing helps organize testing more efficiently for a larger number of students, addressing issues of overcrowded classrooms, and high teaching workloads. To better facilitate this transformation, we decided to adopt Maple T.A., the online testing and assessment suite from Maplesoft. Maple T.A. also provides anytime/anywhere testing, allowing students to take tests digitally, even from remote locations.

     

    Regular and repeated testing produces the best learning results because progressive monitoring offers instructors the possibility of making adjustments throughout the course. The randomization feature in Maple T.A. provides each student with an individual set of problems, reducing the likelihood that answers will be copied. Though Maple T.A. is specialized in mathematics, it also supports more common question types like multiple choice, multiple selection, fill-in-the-blanks and hot spot. Maple T.A.’s question randomization, possibilities for multiple response fields per question and question workflow (adaptive questions) are superior to other options. By offering regular homework assignments and analyzing the results, we gain better insight into the progress of students and the topics that students perceive as difficult. Our lecturers can use this insight to decide whether to repeat particular material or to offer it in another manner. In many courses, preparing and reviewing practice tests comprise an important, yet time-consuming task for lecturers, and Maple T.A. alleviates that burden.

     

    At TU Delft, we require all first-year students to take a math entry test using Maple T.A in order to assess the required level of math. Since the assessment of the student’s ability is so heavily dependent upon qualifying tests, it is extremely important for the test to be completed under controlled conditions. In Maple T.A., it is easy to generate multiple versions of the test questions without increasing the burden of review, as the tests are graded immediately. Students that fail the entry test are offered a remedial course in which they receive explanations and complete exercises, under the supervision of student assistants. The use of Maple T.A. facilitates this process without placing additional burden on the teacher. When the practice tests and the associated feedback are placed in a shared item bank in Maple T.A., teachers are able to offer additional practice materials to students with little effort. It makes it considerably easier on us as teachers to be able to use a variety of question types, thus creating a varied test.

     

    Each semester, TU Delft offers an English placement test that is taken by approximately 200 students and 50 PhD candidates, in which students are required to formulate their reasons for their program choices or research topics. It used to take four lecturers working full-time for two days to mark the tests and report the results to participants in a timely manner. The digitization of this test has saved us considerable time. The hundred fill-in-the-blank questions are now marked automatically, and we no longer have to decipher handwriting for the open questions!

     

    TU Delft is not alone in its emphasis on digital testing; it has a prominent position on the agendas of many institutions in Europe and elsewhere. These institutions are intensively involved in improving, expanding and advocating the positive results from digital testing and digital learning experiences. Online education solutions like Maple T.A. are playing a key role in improving the quality of digital offerings at institutions.

    In the recent years much software has undergone a change towards allowing for better sharing of documents. As is the case with other software as well, the users are no longer mainly single persons sitting in a dark corner doing their own stuff. Luckily Maplesoft has taken an important step in that direction too by introducing MapleCloud some years ago. This means that it is now possible quite easily to discuss calculations done in Maple in the classroom. One student uploads and the Teacher can find the document seconds later on his own computer connected to a Projector and show the student's solutions for the other  students in the classroom. That's indeed great! Maple is however lacking in one important aspect: It's Graphics User Interface (GUI) is not completely ready to for that challenge! I noticed that quite recently when the entire teaching staff received new netbooks: 14 inch Lenovo Yoga X1 with a resolution of 2560 x 1440 pixels. From factory defaults text zoom was set to 200%. Without it, text would be too small in all applications used on the computer. The Microsoft Office package and most other software has adapted to this new situation dealing with high variation in the users screen resolutions, but not Maplesoft:

    1. Plots and Images inserted become very small
    2. Open File dialogs and the like contain shortened text for folder names ... (you actually have to guess what the folders are)
    3. Help menus are cluttered up and difficult to read.

    I show screen images of all three types below.

    I know it is possible to make plots larger by using the option size, but since it relies on pixels it doesn't work when documents are shared between students and teachers. You cannot expect the receiving student/teacher to make a lot of changes in the document just to be able to read it. It will completely destroy the workflow!

    Why doesn't Maplesoft allow for letting documents display proportionally on the users computer like so many other programs do? Why do it need to be in pixels? If it is possible to make it proportional, it would also solve another issue: Making prints (to a printer or to pdf) look more like they do on the screen than is the case at present.

    I really hope Maplesoft will address this GUI challenge, because I am sure the issue will pile up quite rapidly. Due to higher costs, most laptops/netbooks among students don't have that high resolution compared to computer dimensions at the moment, but we already have received a few remarks from students owning such computers. Very soon those highend solution computers will dive into the consumer market and become very common.

    I have mentioned this important GUI issue in the beta-testing group, but I don't think those groups really are adapted to discussions, more bug fixes. Therefore I have made this Post in the hope that some Maple users and some chief developers will comment on it!
         

    Now I have criticized the Maple GUI, I also feel urged to tell in what departments I think Maple really excels:

    1. The Document-structure is great. One can produce good looking documents containing 'written math' (inactive math) and/or 'calculated math'. All-in-one! Other competting software does need one to handle things separatly.
    2. Sections and subsections. We have actually started using Maple to create documents containing entire chapters or surveys of mathematics or physics subjects, helping students to get a better overview. I am pretty sure the Workbook tool also will help here.
    3. Calculations are all connected. One can recalculate the document or parts of it, eventually using new parameters. Using Maple for performing matematical experiments. Mathematical experiments is a method entering more into the different mathematics curriculums.
    4. MapleCloud. Easy sharing of documents among students and teachers.
    5. Interactive possibilities through the Explore command and other commands. Math Apps as well.
    6. Besides that mathematical symbols can be accessed from the keyboard, they can also be accessed from palettes by less experinced users.  
    7. Good choice by Maple to let the user globally decide the size text and math is displayed in Maple - set globally in the menu Tools < Options.
    8. Maple can handle units in Physics
    9. Maple has World-Class capabilities. If you have a mathematical problem, Maple can probably handle it. You just need to figure out how.
    10. etc.

     

    Small plots:

     

    Shortened dialog text:

     

    Cluttered help menus:

     

    Regards,

    Erik

     

    Earlier today, we published an update that improves the way MaplePrimes handles tags.

    New features include: 

    • There are now tags for Maple Commands and Maple Packages. These tags are denoted with special icons, and cannot be edited. The hope is that these special tags will be useful to anyone looking for assistance with a particular command or package, and will provide another centralized location to find support. For example, a command tag for the plot command will look as follows:.  A package tag looks like:
    • The tags page has been completely updated to show tag use over time, and also provides information about specific tags. Users with moderator privileges can also edit tags directly from this page.
       
    • Hundreds of inappropriate or 'garbage' tags have been removed.

     

    In addition to the changes to our tagging, we made a few other improvements and updates, including:

    • New academically- and techically-focused social networks have been added to user profiles
    • Updates to the message editor to improve WYSIWYG consistency
    • A variety of smaller fixes and improvements

    I hope you find these improvements valuable, and look forward to your comments and suggestions for future improvements.

     

    I noticed Mapleprime have entries of users who clearly create an account just to put a bad website URL in there and they are just spam.

    Why do not the moderators of Mapleprime purge these out? Mapleprime is full of these spam marketing users.   Here are just few I found in few clicks

    http://www.mapleprimes.com/users/Frenettees8d
    http://www.mapleprimes.com/users/Ingegneriaq7r
    http://www.mapleprimes.com/users/Inabinetaq6s
    http://www.mapleprimes.com/users/Bruggemanse5l
    http://www.mapleprimes.com/users/vito5854
    http://www.mapleprimes.com/users/deblogepa
    http://www.mapleprimes.com/users/organicjunk80

    There are hundereds of these spam URLS in there. They make an account, only to add their infected web site URL there so if someone clicks on it they get virus.

    Moderators of mapleprime should do better job and remove these cleary spam entries from Mapleprime.

    The is and coulditbe commands of Maple are known to be buggy.
    Here are some math inventions done by these commands in Maple 2016.2.

    restart; assume(x::real, y::real);
    is(exp(x+I*y) <> 0);
                                 false
    coulditbe(exp(x+I*y) = 0);
                                  true
    coulditbe(exp(x+I*y) = infinity);
                                  true
    coulditbe((x+I*y)^2 = infinity);
                                  true
    

    It should be noticed that

    is((-infinity)::real);
                                 false

    though

    exp(-infinity+0*I);
                                   0

    The latter means

    limit(exp(x),x=-infinity);
                                       0

    , no more and no less.

    This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. I hope you use something that is fully developed with embedded components.

    In Spanish

    Vector_Force.mw

    Vector_Force_updated.mw

    Lenin Araujo Castillo

    Ambassador Of Maple

     

     

    I am very pleased to announce a new user community centered around Maplesoft's online testing and assessment and courseware products. The new site is specifically for instructors and administrators currently using Maple T.A. or Möbius. This community of users are a small, specialised group who we want to bring together so they can share ideas and best practices. To find the community, go to either mapletacommunity.com or mobiuscommunity.com.

    "The Maple T.A. Community has grown organically to support new developers as they pool their knowledge and queries. This has resulted in a fluid searchable structure, with answers available for all levels of question - from beginner to pushing the frontiers of what Maple T.A. has been designed to do. Our summer student interns rely on the Community as they become proficient in their question writing skills - and many have become contributors as they realise that they are in a position to teach others. Opening it out more broadly will be great in sharing good practice on a 'need to know now' basis.”

    ----Professor Nicola Wilkin, University of Birmingham

     

    What content is in the community?

    The community has many posts from active Maple T.A. and Möbius users from beginners to advanced users. The site is broken down into categories like 'Best Practices' - longer form posts that cover a broader concept in more detail and 'Quick Code snippets' that are small piece of code that you can drop straight into your question algorithms.

    Much of the content is openly available and can be found by google, however there is additional content that can only be accessed by members of the community, such as the Maple T.A. school material which teaches you how to author content in Maple T.A. and Möbius.

     

    Who runs the community

    The community is jointly run by users based at the University of Birmingham, TU Wien, The University of Turin and TU Delft.

     

    How does this fit into Mapleprimes?

    It began as an offshoot of a private, internal customer forum. As this community grows, the ultimate goal is to eventually roll it into MaplePrimes proper. But this alternative site gave us the quickest way to get up and running. Maple T.A. and Möbius questions and posts are still welcome on MaplePrimes, and will continue to be monitored by Maplesoft.

     

    How do I access the community?

    You can find the community by going to either mapletacommunity.com or mobiuscommunity.com.

     

    Where else can I get support for Maple T.A. and Mobiüs?

    Official support for Maple T.A. and Möbius is provided by the wonderful Customer Success Team at Maplesoft. You can contact them at help@maplesoft.com. For other contact methods see www.maplesoft.com/support/.

     

     

    I am pleased to announce the public release of Möbius, the online courseware environment that focuses on science, technology, engineering, and mathematics education. After months of extensive pilot testing at select leading academic institutions around the world, Möbius is now available to everyone for your online learning needs.

    We are very excited about Möbius. As you can imagine, many of us here at Maplesoft have backgrounds in STEM fields, and we are truly excited to be working on a project that gives students a hands-on approach to learning math-based content.  You can’t learn math (or science, or engineering, or …) just by reading about it or listening to someone talk about it. You have to do it, and that’s what Möbius lets students do, online, with instant feedback.  Not only can students explore concepts interactively, but they can find out immediately what they’ve understood and what they haven’t - not a few hours after the lecture as they are reviewing their notes, not two weeks later when they get their assignments back, but while they are in the middle of learning the lesson.

    During its pilot phase, Möbius was used by multiple institutions around the world for a variety of projects, such as preparing students in advance for their first year math and engineering courses, and for complete online courses.  Over one hundred thousand students have already used Möbius, and the experiences of these students and their instructors has fed back into the development process, resulting in this public release.  You can read about the experiences of the University of Waterloo, the University of Birmingham, and the Perimeter Institute for Theoretical Physics on our web site.

    We are also happy to announce that Maplesoft has partnered with the University of Waterloo, one of the largest institutions in the world for STEM education, to provide institutions and professors with rich online courses and materials that enable students to learn by doing.  These Möbius courses are created by experts at the University of Waterloo for use by their own students and for their outreach programs, and will be made available to other Möbius users.  Course materials range from late high school to the graduate level, with initial offerings available soon and many more to follow.

    Visit the Möbius section of our web site for lots more information, including videos, whitepapers, case studies, and upcoming user summits.

    Let us consider 

    sol := pdsolve({diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) = (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t}, {u(0, t) = 0, u(x, 0) = 0, v(0, t) = 0, v(x, 0) = 0}, time = t, numeric, timestep = 0.1e-1, spacestep = 0.1e-1, range = 0 .. 1); 
    sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 .. 1);

    A nice plot similar to the one produced by Mma (see the  attached pdf file pdesystem.pdf) is expected. 
    The exact solutions u(x,t)=x*t,v(x,t)=x*t^2 are known

    pdetest({u(x, t) = x*t, v(x, t) = x*t^2}, {diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) =
    (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t});
                                  {0}

    But the wrong result

                   module() ... end module         
    Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.26000000000000006):
    solution becomes undefined, problem may be ill posed or method may be ill suited to solution

    is obtained. Also 

    sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 ..0.1);


     

    The plot 

    sol:-plot3d(v(x, t), x = 0 .. .5, t = 0 .. .1);

    is not better.

    Hi everybody,

    The Collatz conjecture can be used to give students a taste of a topic in Number Theory.  See the Wikipedia article for a good explaination.

    https://en.wikipedia.org/wiki/Collatz_conjecture

    Also, a conjecture is something that is probrably true.  Enjoy my little Maple procedure.  (in .mw and .pdf forms)

    Collatz_third_time.mw

    Collatz_third_time.pdf

    Comments are appreciated.

    Matt

     

    Here is a problem from SEEMOUS 2017 (South Eastern European Mathematical Olympiad for University Students)
    which Maple can solve (with a little help).

    For k a fixed nonnegative integer, compute:

    Sum( binomial(i,k) * ( exp(1) - Sum(1/j!, j=0..i) ), i=k..infinity );

    (It is the last one, theoretically the most difficult.)

    Application that allows us to measure the reliability of a group of data through a row and columns called cronbach alpha at the same time to measure the correlation of items through the pearson correlation of even and odd items. It can run on maple 18 to maple 2017. This will be useful when we are developing a thesis in the statistical part.

    In Spanish

    StatisticsSocialCronbachPearson.zip

    Lenin Araujo Castillo

    Ambassador of Maple

     

     

    Let us consider the help to RectangleWindow SignalProcessing-RectangleWindow.pdf SignalProcessing-RectangleWindow.mw.
    Let us execute the example, taking N:=4 (in order to display the outputs).

    with(SignalProcessing):
    N := 4;
    a := GenerateUniform(N, -1, 1);
             Matrix(1, 4, [[.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156]])         
    RectangleWindow(a);
             Vector[row](4, [.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156])      
    c := Array(1 .. N, 'datatype' = 'float'[8], 'order' = 'C_order'):
    RectangleWindow(Array(1 .. N, 'fill' = 1, 'datatype' = 'float'[8], 'order' = 'C_order'), 'container' = c);
                  Vector[row](4, [1., 1., 1., 1.])
    u := `~`[log](FFT(c)):
    plots:-display(Array([plots:-listplot(Re(u)), plots:-listplot(Im(u))]));
    



    We see an uncommented code which (intentionally or unintentionally) produces two empty plots.
    The questions arise:

    • What is the aim of the RectangleWindow command which does nothing 
      but the conversion of a Matrix(1,N,...) /Array(1..N,...) to a Vector[row](N,...)? 
    • Could such help be called friendly to Maple users?

    There are many questions to Maplesoft and there are no answers from them: strategic silence.
    RectangleWindow.mw

     

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