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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  • I was thinking about the area problem, yet again, and found myself asking the question: why must we go through such elaborate means to get Maple to generate a plot of the region between two (or more curves)? I use the word elaborate to describe any process that would might become overwhelming, for, say a student, to go through to accomplish a task. Anyone with the most basic of backgrounds can understand the area problem, but yet, such an individual might not find it a trivial...

    If there is a regression in an update it should be fixed within the same version and not left as an open bug in current versions.

    Since 16.01 update is no longer available and 16.02 is the only option.  It would be very much appreciated by the mapleprimes community and maple users to see a 16.03 update.

    The following (downsized) images of Lyapunov fractals were each generated in a few seconds, in Maple 16.

     

    I may make an interface for this with embedded components, or submit it in some form on the Application Center. But I thought that I'd share this version here first.

    I'm just re-using the techniques in the code behind an earlier Post on Mandelbrot and Julia fractals. But I've only used one simple coloring scheme here, so far. I'll probably try the so-called burning ship escape-time fractal next.

     

     

     

     

    Here below is the contents of the worksheet attached at the end of this Post.

     

     

    The procedures are defined in the Startup code region of this worksheet.

     

    It should run in Maple 15 and 16, but may not work in earlier versions since it relies on a properly functioning Threads:-Task.

     

    The procedure `Lyapunov` can be called as

     

              Lyapunov(W, xa, xb, ya, yb, xresolution)

              Lyapunov(W, xa, xb, ya, yb, xresolution, numterms=N)

     

    where those parameters are,

     

     - W, a Vector or list whose entries should be only 0 or 1

     - xa, the leftmost x-point (a float, usually greater than 2.0)

     - xb, the rightmost x-point (a float, usually less than or equal to 4.0)

     - ya, the lowest y-point (a float, usually greater than 2.0)

     - yb, the highest y-point (a float, usually less than or equal to 4.0)

     - xresolution, the width in pixels of the returned image (Array)

     - numterms=N, (optional) where positive integer N is the number of terms added for the approx. Lyapunov exponent

     

     

    The speed of calculation depends on whether the Compiler  is functional and how many cores are detected. On a 4-core Intel i7 under Windows 7 the first example below had approximately the following performce in 64bit Maple 16.

     

     

    Compiled

    evalhf

    serial (1 core)

    20 seconds

    240 seconds

    parallel (4 cores)

    5 seconds

    60 seconds

     

     

     

    with(ImageTools):


    W:=[0,0,1,0,1]:
    res1:=CodeTools:-Usage( Lyapunov(W, 2.01, 4.0, 2.01, 4.0, 500) ):

    memory used=46.36MiB, alloc change=65.73MiB, cpu time=33.87s, real time=5.17s


    View(res1);


    W:=[1,1,1,1,1,1,0,0,0,0,0,0]:
    res2:=CodeTools:-Usage( Lyapunov(W, 2.5, 3.4, 3.4, 4.0, 500) ):

    memory used=30.94MiB, alloc change=0 bytes, cpu time=21.32s, real time=3.54s


    View(res2);


    W:=[1,0,1,0,1,1,0,1]:
    res3:=CodeTools:-Usage( Lyapunov(W, 2.1, 3.7, 3.1, 4.0, 500) ):

    memory used=26.18MiB, alloc change=15.09MiB, cpu time=18.44s, real time=2.95s


    View(res3);


    W:=[0,1]:
    res4:=CodeTools:-Usage( Lyapunov(W, 2.01, 4.0, 2.01, 4.0, 500) ):

    memory used=46.25MiB, alloc change=15.09MiB, cpu time=33.52s, real time=5.18s


    View(res4);

     

     

    Download lyapfractpost.mw

    Dear friends,

    every once in a while I come across an integral that Maple does not readily compute and post it here, so that your programmers may perhaps include it in the integration engine.

    I am writing today concerning the integral int(x^q/(exp(x)-1), x=0..infinity); for q a real number. Maple can do this integral for rational q but not for irrational ones, e.g. try q=14/10 vs. q=sqrt(2). I hope you can make good use of this hint. The original computation...

    Today's SMBC strip by Zach Weinersmith is a silly math joke but it was pretty much begging for implementation.

    So, here is a simple brute force Maple program to compute the Fouriest transform of an integer.

    fouriest := proc(n::posint, ob::posint:=10)
    local b,f,cap,i,rdx,fc;
    ...

    We assume that the length of a match is 1, then the perimeter of a polygon is equal to the number of matches N. If a match can be located at arbitrary angles to each other, then at a given perimeter of the area can take on any value between zero and the area of a regular polygon (for even number of matches) . For an odd number of matches the lower bound equals to the area of an equilateral triangle of side 1. For any given area within these boundaries will be infinitely many solutions.



    A set of three taped video interviews with famous physicist and mathematician Cornelius Lanczos (1893-1974) has been made available online by the University of Manchester.

    webmath.exponenta.ru

    Maple Russian site: 7.000.000 visits, 12,000 visitors per day.

    In February, I will place a new package - DeMapler.

    Several thousands of solutions of standard problems. Step by Step.

    From first order differential equations to systems of DEs.

    For reference this question was posted exactly 9:05

    Well, it’s been more than 17 years since First Leaves: A Tutorial Introduction to Maple V was first published as a hardcover book, and since that time, Maple, the Maple documentation, and the world have undergone huge changes.   We are now in a state where all our documentation is available electronically, including both in-product and online; where the vast majority of our customers receive our products electronically and never even see the printed...

    Although unfinished, this project I had left idle for a while and just thought to share with the community.  Not fancy by any means, no graphs or anything, was just having fun creating a worksheet on mortgages but then ran out of free time to work on things as usual, anywyas.  I skipped the derivation for the formula after n payments at the end and just provided the formula and dove right into an example.  For interest, my applications usually have numbers after...

    Dear friends, I recently answered a query concerning the action of the automorphism group of the Petersen graph on its edges at math.stackexchange.com. The algorithm that I present is quite naive, but it does produce the desired result. I thought I would share it here because it makes a nice Maple programming exercise e.g. for a talented student at high school level. (I have always thought that Polya counting and permutation groups belong into the high school curriculum.) It makes extensive use of Maple's internal hash function for compound objects to efficiently compare them during the computation. It is quite interesting to observe how Maple does work hard for several minutes to do this computation and then comes up with the correct answer. (Obviously the core computation needs to be done only once.) Enjoy!

    Best regards, Marko Riedel

    If you come up with a better algorithm then please do share it at the stackexchange link.

    Important update Mar 24 2016. The algorithm at the above post is middling to say the least, but can perhaps serve as an example of Maple computational techniques. There is an efficient algorithm including Maple code here at math.stackexchange.com.

    Maple T.A. 9 is here!

    The new release includes a large selection of useful new features and enhancements, including:

    - Content. Maple T.A. 9 includes an easy mechanism to share questions with the community and access questions created by others, through the Maple T.A. Cloud. The Maple T.A. Cloud already contains thousands of questions that you can use and modify.

    - Adaptive Testing. Expanding on the adaptive question...

    Dear friends,

    I have recently been calculating a sum from this link.

    The problem here is to calculate the sum sum_{n>=1} (-1)^(n+1)/(n^2+a) with a some positive real number. You probably all agree that it is preferable to express it using elementary functions from basic calculus as opposed to the Gamma, Zeta and Digamma...

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