MaplePrimes Posts

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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  • Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on some upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.


    Hollywood Math (with more new examples!)

    Over its storied and intriguing history, Hollywood has entertained us with many mathematical moments in film. John Nash in “A Beautiful Mind,” the brilliant janitor in “Good Will Hunting,” the number theory genius in “Pi,” and even Abbott and Costello are just a few of the Hollywood “mathematicians” that come to mind.

    Although the widespread presentation of mathematics on the silver screen is not always entirely accurate, it does serve as a great introduction to the study of mathematics in general. During this webinar Maplesoft will present a number of examples of mathematics in film. See relevant, exciting examples that you can use to engage your students.At the end of the webinar you’ll be given an opportunity to download an application containing all of the Hollywood examples that we demonstrate.

    To join us for the live presentation, please click here to register.


    Applications of Symbolic Computation in Control Design

    You may already use Maple and/or MapleSim within your organization to solve various problems, but did you know that they have capabilities for control design as well? In one of our upcoming featured webinars for this month, we will explore the Control Design toolbox including the ability to extract symbolic equations of plant models, perform symbolic linearization, design symbolic controllers, and generate very fast code for HIL testing.

    The following examples will be demonstrated:

    • PID Control

    • LQR, Kalman filter design

    • Gain scheduling

    • Feedback linearization

    To join us for the live presentation, please click here to register.

    Updates are now available for both Maple 18 and MapleSim 6.4.

    Maple 18.01 includes a variety of enhancements, including:

    • Significantly enhanced  efficiency for many  numerical linear algebra computations
    • New keyboard shortcuts for “Execute All” ([Ctrl or Cmd]+[Shift]+[Enter]) and for entering slideshow mode ([F11] or [Cmd]+[F11])
    • Improved export of 2-D plots
    • PDF export improvements for documents that include  code edit regions
    • Enhancements to the limit command

     To get this update, you can use Tools>Check for Updates from within Maple, or visit Maple 18.01 Downloads.

    MapleSim 6.4.01 includes:

    • Improvements to the templates for creating custom components using discrete state space and discrete transfer function descriptions
    • Improved handling of variable names that include both symbols and numbers
    • UTF-8 filename support
    • Improved backwards compatibility of the Parameter Inspector with older models


    In MapleSim, use  Help>Check for Updates or visit MapleSim 6.4.01 Update. For best performance, we recommend that you run MapleSim 6.4.01 with Maple 18.01.



    This is the first presentation of updates for the DE and Mathematical Functions programs of Maple 18. It includes several improvements, all in the Mathematical Functions sector, as well as some fixes. The update and instructions for its installation are available on the Maplesoft R&D webpage for DEs and mathematical functions. Some of the items below were mentioned here in Mapleprimes - you are welcome to present suggestions or issues; if possible they will be addressed right away in the next update.

    • Filling gaps in the FunctionAdvisor regarding all the 6 complex components: abs, argument, conjugate, Im, Re, signum, as well as regarding Heaviside (step function), Dirac, min and max.
    • Fix the simplification and differentation rule for doublefactorial
    • Make convert(..., hypergeometric) work the same way as convert(blabla, hypergeom)
    • Implement integral forms for Heaviside(z) and JacobiAM(z, k) via convert(..., Int)
    • Implement appropriate display for the inert %intat function as well as its conversion to the inert Int
    • Make the FunctionAdvisor/DE return not just the PDE system satisfied by f(z, k) = JacobiAM(z, k)and also (new) the ODE satisfied by f(z) = JacobiAM(z, k)
    • Fix conversion rule from Heaviside(z) to Sum
    • Fix unexpected error interruption when differentiating min(...) and max(...) containing more than three arguments
    • Fix issue in simplify/conjugate
    • Improvement in expand/int: factors in disguise are put outside the integration sign
    • Various improvements in the case of multiple integrals involving the Dirac function
    • Make Intat fully inert (before it was evaluating its arguments)
    • Make value of inert indexed objects work

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

    Maple WWW - Maple Worksheets in the World Wide Web

    DigiArea Team is proud to present new modern web technology for Maple Worksheets - Maple WWW. 

    Maple WWW is a technology that brings Maple Worksheets to the World Wide Web. The technology provides a web application to view and share interactive scientific documents across the web. Maple WWW allows to open Maple worksheets in your browser without any additional plugins or extensions.

    You can read more about the technology here:

    You can see the technology in action right here using the following embedded Maple Worksheet!



    Some years ago member William Fish started a long discussion in part about a numeric integral involving high parameter (high oscillation) Bessel J0. That numeric integration task appeared in a Bitwise Magazine article.

    At that time even obtaining numeric results involved extra effort such as handling real and imaginary components of the integrand separately, and requesting particular methods (sometimes hacked, to bump up the subinterval limit, for very high parameter values).

    That led to a post where I showed that the result could be obtained quickly by using a fast compiled BesselJ (J0) from an external library along with a modified low-level call to a particular evalf/Int solver.

    And sometime after that a numeric result for the real & imaginary split integrand became much more readily (if not quickly) available by using a new `maxintervals` option of evalf/Int to specify the maximal number of subintervals for the particular solver.

    Maple 18 has its own compiled implementations of the Bessel functions for "hardware" (double) precision arguments. So now the numeric evaluations of the integrand are computed much faster.

    Using Maple 18.00 on 64bit Windows 7 the same numeric results obtain in under a second, in a simple, single call to evalf,Int.

      evalf(Int(BesselJ(0, 50001*x)*x*exp(I*(355*x^2*1/2)), x = .35 .. 1))
    memory used=9.28MiB, alloc change=32.00MiB, cpu time=437.00ms, real time=441.00ms, gc time=0ns
                               -8                 -8  
                 3.181753502 10   - 7.798301124 10   I
      evalf(Int(BesselJ(0, 10000*x)*x*exp(I*(355*x^2*1/2)), x = .35 .. 1))
    memory used=6.83MiB, alloc change=32.00MiB, cpu time=218.00ms, real time=211.00ms, gc time=15.60ms
                                -7                 -7  
                 -2.007752340 10   + 4.275388462 10   I


    Of course the ramifications of fast, compiled Bessel functions at double precision extend much farther than just this one example. But I like seeing the speed improvement in terms of a concrete example.


    I think we all know the routine. We walk to a large classroom, we sit down for a test, we receive a large stack of questions stapled together and then we fill in tiny bubbles on a separate sheet that is automatically graded by a scanning machine. We’ve all been there. I was thinking recently about how far the humble multiple choice question has come over the last few years with the advent of systems like Maple T.A., and so I did a little research.

    Multiple choice questions were first widely-distributed during World War I to test the intelligence of recruits in the United States of America. The army desired a more efficient way of testing as using written and oral evaluations was very time consuming. Dr. Robert Yerkes, the psychologist who convinced the army to try a multiple choice test, wanted to convince people that psychiatry could be a scientific study and not just philosophical. A few years later, SATs began including multiple choice questions. Since then, educational institutions have adopted multiple choice questions as a permanent tool for many different types of assessments.

    One of the biggest advances in the use of multiple choice questions was the birth of automatic grading through the use of machine-readable papers. These grew in popularity during the mid-70s as teachers and instructors saved time by not having to grade answer sheets manually.

    Until recently, there has not been much advancement in this area.  It’s true, Maple T.A. can do so much more than just multiple choice questions, so this style of question is less important in large-scale testing than it used to be. But multiple choice questions still have their place in an automated testing system, where uses include leveraging older content, easily detecting patterns of misunderstanding, requiring students to choose from different images, and minimizing student interaction with the system. Luckily, Maple T.A. takes even the humble multiple choice questions to the next level. Now you might be thinking, how is that even possible given the basic structure of multiple choice questions? What could possibly be done to enhance them?

    Well, for starters, in Maple T.A., you can permute the answers. This means you have the option to change the order of the choices for each student. This is also possible with machine-readable papers, but this does require multiple solution sets for a teacher or instructor to keep track of. With Maple T.A., everything is done for you. For example, if you have a multiple choice question in Maple T.A. with 5 answer choices, there are 120 different possible answer orders that students can be presented with. You don’t have to keep track of extra solution sets or note which test version each student is receiving. Maple T.A. takes care of it all.

    Maple T.A. allows you to create Algorithmic questions - multiple choice questions in which you can vary different values in your question. And you aren’t limited to selecting values from a specific range, either. For example, you can select a random integer from a pre-defined list, a random number that satisfies a mathematical condition, such as ‘divisible by 3’ or ‘prime’, or even a random polynomial or matrix with specific characteristics. It allows an instructor to create a single question template, but have tens, hundreds, or even thousands of possible question outcomes based on the randomly selected values for the algorithmic variables. The algorithmic variables not only apply to the question being asked by a student, but also the choices they see in a multiple choice question.

    You can even create a question where every student gets the same fixed list of choices, but the question varies to ensure that the correct response changes.  That’s going to confuse some students who are doing a little more “collaboration” than is appropriate!

    Some of the other advantages of using Maple T.A. for multiple choice are also common to all Maple T.A. question types. For example, you can provide instant, customized feedback to your students. If a student gets a multiple choice question correct, you can provide feedback showing the solution (who is to say the student didn’t guess and get this question correct?) If a student gets a multiple choice question incorrect, you can provide targeted feedback that depends on which response they chose. This allows you to customize exactly what a student sees in regards to feedback without having to write it out by hand each time.

    And of course, like in other Maple T.A. questions, multiple choice questions can include mathematical expressions, plots, images, audio clips, videos, and more – in the questions and in the responses.      

    Finally, let’s not forget, in an online testing environment, there is no panic when you realized you accidently skipped line 2 while filling out your card, no risk of paper cuts, and no worrying about what kind of pencil to use!


    Yesterday afternoon, we updated MaplePrimes. The purpose of the update was primarily to squash some bugs and improve user experience.

    Highlights of the update include:

    • The ordering of replies has been corrected, as described in this post by Carl Love.

    • We fixed a problem whereby some members were unable to attach a file to a question or post.

    • Flagging a comment now works correctly.

    • Broken images that were appearing on some of our older posts have been restored. In addition, some older posts had incorrect dates, and these have been restored.

    • Some embedded links to user profiles or messages were resulting in errors, and have been corrected.

    • After receiving a badge, members will now be notified via a pop-up message.

    A number of other small improvements were made as well.

    As always, thank you for letting us know when you encounter a problem, and please continue to do so. We take note of everything that you report, and we try our best to prioritize and take care of the issues.


    Voting is now open for the next individual prize to be awarded as part of the Möbius App Challenge.  The winner will receive an Xbox One Prize Pack! 

    Here are the finalist Apps:

    Note that, if you ever have any problems viewing Apps in your browser, or simply want to work offline, you can always download a Möbius App and view it in Maple or the free Maple Player. To download a Möbius App, follow the link to the App and then click on the Download button near the top left of the page.

    You can vote for your favorite through our Facebook page or, if you’re not on Facebook, send an email with your vote to

    And remember, we are now accepting entries for the next quarterly prize. You could win a Music Prize Pack, including the 64GB 5th Generation Apple iPod Touch, Sennheiser In-Ear Noise Cancelling Headphones and the Bose SoundLink Bluetooth Speaker III!  See the Möbuis App Challenge for details.

    Voting closes April 25th, 2014.


    This is a little more than a new game it potentially uncovers a new class of numbers -- though determining membership might become a hard problem.

    A number that possesses the solitaire property can be written in as ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc,(where the "0" is the first zero in the number), with a radix point anywhere. We are free to pick the base and say it is solitaire with respect to that base. After the initial 0, the subsequent ordinals (the 1,2, etc or the 1,10,11, etc) used to write the solitaire number don't have to be the first ones. For example:

    0 2884
    1 971693993751058
    2 0974944592
    3 078163860
    4 ...



    0 2884197

    1 6939937510582 097494459

    2 3 07816

    3 860
    4 ...
    etc.,are both acceptable. (If the number can be written as  ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc. it is solitaire.)

    The Champernowne constant with respect to base 10 has only one representation:













    etc. .


    I know Base 10 Champernowne constant is base 10 solitaire. I can not say the same with certainty for Pi.

    I also propose we can measure the solitude of a number by the average amount of numbers between the 0,1,2,3..., and give a perfect solitude score to Base 10 Champernowne constant. Other constants can be given additional credit, of some kind, if the amounts of numbers between the 1,2,3... follow a specific preset pattern.




    With the package VectorCalculus we can study the speed and acceleration to their respective components. Considering the visualizaccion and algebraic calculations and to check with their respective commands. Both 2D and 3D.


    Velocidad-Aceleració.mw     (in spanish)


    Lenin Araujo Castillo

    Physics Pure

    Computer Science

    The attached presentation is the last one of a sequence of three on Quantum Mechanics using Computer Algebra, covering the field equation for a quantum system of identical particles, its stationary solutions and the equations for small perturbations around them and, in this third presentation, the conditions for superfluidity of such a system of identical particles at low temperature. The novelty is again in how to tackle these problems in a computer algebra worksheet.

    The Landau criterion for Superfluidity

    Pascal Szriftgiser1 and Edgardo S. Cheb-Terrab2 

    (1) Laboratoire PhLAM, UMR CNRS 8523, Université Lille 1, F-59655, France

    (2) Maplesoft, Canada


    A Bose-Einstein Condensate (BEC) is a medium constituted by identical bosonic particles at very low temperature that all share the same quantum wave function. Let's consider an impurity of mass M, moving inside a BEC, its interaction with the condensate being weak. At some point the impurity might create an excitation of energy `&hbar;`*omega[k] and momentum `&hbar;` `#mover(mi("k"),mo("&rarr;"))`. We assume that this excitation is well described by Bogoliubov's equations for small perturbations `&delta;&varphi;` around the stationary solutions `&varphi;```of the field equations for the system. In that case, the Landau criterion for superfluidity states that if the impurity velocityLinearAlgebra[Norm](`#mover(mi("v"),mo("&rarr;"))`) is lower than a critical velocity v[c] (equal to the BEC sound velocity), no excitation can be created (or destroyed) by the impurity. Otherwise, it would violate conservation of energy and momentum. So that, if LinearAlgebra[Norm](`#mover(mi("v"),mo("&rarr;"))`) < v[c] the impurity will move within the condensate without dissipation or momentum exchange, the condensate is superfluid (Phys. Rev. Lett. 85, 483 (2000)). Note: low temperature liquid 4He is a well known example of superfluid that can, for instance, flow through narrow capillaries with no dissipation. However, for superfluid helium, the critical velocity is lower than the sound velocity. This is explained by the fact that liquid 4He is a strongly interacting medium. We are here rather considering the case of weakly interacting cold atomic gases.

    Landau criterion for superfluidity



    Background: For a BEC close to its ground state (at temperature T = 0 K), its excitations are well described by small perturbations around the stationary state of the BEC. The energy of an excitation is then given by the Bogoliubov dispersion relation (derived previously in Mapleprimes "Quantum Mechanics using computer algebra II").


    epsilon[k] = `&hbar;`*omega[k] and `&hbar;`*omega[k] = `&+-`(sqrt(k^4*`&hbar;`^4/(4*m^2)+k^2*`&hbar;`^2*G*n/m))


    where G is the atom-atom interaction constant, n is the density of particles, m is the mass of the condensed particles, k is the wave-vector of the excitations and omega[k] their pulsation (2*Pi time the frequency). Typically, there are two possible types of excitations, depending on the wave-vector k:


    In the limit: proc (k) options operator, arrow; 0 end proc, "epsilon[k]&sim;`&hbar;`*k*"v[c] with v[c] = sqrt(G*n/m), this relation is linear in k and is typical of a massless quasi-particle, i.e. a phonon excitation.


    In the limit: proc (k) options operator, arrow; infinity end proc, `&sim;`(epsilon[k], `&hbar;`^2*k^2/(2*m)) which is the dispersion relation of a free particle of mass "m,"i.e. one single atom of the BEC.


    Problem: An impurity of mass M moves with velocity `#mover(mi("v"),mo("&rarr;"))` within such a condensate and creates an excitation with wave-vector `#mover(mi("k"),mo("&rarr;"))`. After the interaction process, the impurity is scattered with velocity `#mover(mi("w"),mo("&rarr;"))`.


    a) Departing from Bogoliubov's dispersion relation, plus energy and momentum conservation, show that, in order to create an excitation, the impurity must move with an initial velocity


    LinearAlgebra[Norm](`#mover(mi("v"),mo("&rarr;"))`) >= v[c] and v[c] = sqrt(G*n/m)



    When LinearAlgebra[Norm](`#mover(mi("v"),mo("&rarr;"))`) < v[c] , no excitation can be created and the impurity moves through the medium without dissipation, as if the viscosity is 0, characterizing a superfluid. This is the Landau criterion for superfluidity.


    b) Show that when the atom-atom interaction constant G >= 0 (repulsive interactions), this value v[c] is equal to the group velocity of the excitation (speed of sound in a condensate).






    [1] Suppression and enhancement of impurity scattering in a Bose-Einstein condensate

    [2] Superfluidity versus Bose-Einstein condensation
    [3] Bose–Einstein condensate (wiki)

    [4] Dispersion relations (wiki)


    Download   QuantumMechanics3.pdf

    Edgardo S. Cheb-Terrab
    Physics, Maplesoft

    As a reminder, we regularly host live webinars on a variety of topics for our customers, and we wanted to make this information available to the MaplePrimes community as well.

    This featured webinar for this month will outline the Finance Package in Maple 18 including capabilities like the mathematical, statistical, and connectivity tools required to analyse data, calculate forecasts, estimate risks, prototype and develop quantitative algorithms, and leverage parallel programming techniques.

    Other topics include:

    • Data feed connectivity and system integration

    • Price equity and interest rate derivatives

    • Populate reporting tools, deliver documents and share worksheets

    • Optimize portfolios of financial instruments

    • High-Performance Computing (HPC)

    To join us for the live presentation, please click here to register.

    I'll start with a quick positive.  One of the great advantages of upgraded software is the wealth of new features that we all get to play around with.  .. and then I will counter that with a great disadvantage, and that is, we all just about get familiar and comfortable with all the new features then BAM! a new version is released.  Of course we're then mesmorized once again by all the new bells and whistles and maybe even a couple of great celebrations occur with nice small updates throughout the year.  The other downside is that even though a large number of bugs may have been fixed a number of new ones are broght in with those new features. 

    A side effect of a fast release is there are fewer and fewer applications associated with a release, and that is apparent in the application center.  Although mobius apps and the maple cloud may have also had some impact on that as well.

    Now this is pale in comparison to book writers who scramble to keep their books current with new software.  I will quote a section from the introduction in the book Essential Maple 7 which highlights the problems the author had way back then .. I can't imagine how they feel now but here's the passage ...

    "Indeed, one reason that there was so much time between the first and second
    editions of this book is precisely that Maple has been evolving so rapidly in the
    last few years, too rapidly for me to revise this book (much less complete my
    others) while coping with my other duties."

    That just hits the nail on the head, if you think Maple was evolving fast back then, the furious rate that upgrades are released now I would think authors have an almost impossible task to keep up. 

    There are many that would agree with the author, that Maple is advancing so rapidly that we barely have time to gather our thoughts.  Maybe a solution is that we should slow down and create a much more polished piece of software, but again the caveat to that is our competition might just jump out in front.  However the norm today is that each new year represents a new release of software and we all celebrate when that happens.  If life seemed rushed back when Maple 7 was released I can't imagine what it'll be like 10 years from now when Maple 28 rolls around. 

    Addition, subtraction, scalar product, vector, projections and graphs with physics packages and plots. With this you can begin to start the physics course for engineering.   (in spanish)


    Lenin Araujo Castillo

    Physics Pure

    Computer Science

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