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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  • Released today, with over 4500 additions and enhancements, Maple 16 reinforces our track record for consistent innovation and industry leadership in areas like ease of use and symbolic computing performance.

    The*MRB*constant = sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity) and sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity) = sum((-1)^n*(n^(1/n)-1), n = 2 .. infinity)

    But what can we say about

     (∏)(-1)^(n)*(n^(1/(n))-1)?

    ``

    ``

    Maple does not evaluate it:

    evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. infinity))

    product: Cannot show that (-1)^n*(n^(1/n)-1) has no zeros on [2,infinity] product((-1)^n*(n^(1/n)-1), n = 2 .. infinity)

    (1)

    And perhaps it should not because of the alternating sign;

    evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^2))

    -0.3908773173e-101

    (2)

    evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^3))

    -0.7676360791e-1799

    (3)

    evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^3+1))

    0.5316437097e-1801

    (4)

    ``

     

    Download 3232012.mw

    A common example to emphasize that it is not OK to bring absolute values inside the integral compares

    abs( int( cos(n*x), x=0..Pi ) ) asuming n::integer

    and

    int( abs( cos(n*x) ), x=0..Pi ) assuming n::integer

    Maple correctly formulates the first to 0. But the second expression gives it more trouble, returning two messages:

    Warning, unable to determine if (1/2)*Pi*(1+2*_Z7)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option
    Warning, unable to determine if (1/2)*Pi*(1+2*_Z8)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option

    Dr. Gilbert Lai is a mentor for the FIRST Robotics team SWAT 771. He is helping an all girls team from grades 7-12 design a basketball-shooting robot for this year’s annual FIRST Robotics Competition. Dr. Lai is using MapleSim and Maple to help the team understand the principles involved and design their robot. This blog post is part of a series that chronicles the progress of the team.  Posts in the series include:

    • Part 1 - ...

    If you use all the convergents of the simple continued fraction of the MRB constant as the terms of a generalized continued fraction, then likewise use the new convergents in another generalized continued fraction, and so on... you arrive at 0.5557531....  For more on this process see https://oeis.org/wiki/Convergents_constant .

    I was introduced to the geometric interpretation of correlation and linear regression recently.


    Orignially due to the famous statistician R.A.Fisher, the idea is that the correlation between 
    two variables is the cosine of the angle between the 2 vectors in n-dimensional space.
    This can be demonstrated in Maple as follows:

    First, we represent each variable as a vector and transform it so that it is centred at its
    mean and has a length equal...

    This should be a blog post but there is no option for ordinary mapleprimers. 

    If you have a gmail account you can access the data on google insights (what people search for on google and where in the world is that keyword searched the most).  Actually you don't need gmail but you don't get access to the full data and your limited to a few searches.  Using Maples internet connectivity commands I'm sure could prove to create some interesting apps.

    Mechanics of Materials Toolbox Screencasts:

    http://youtu.be/czz_uw0918E

    1dim_roots.mw

    All critics and new ideas would be appreciated.

    Dr. Gilbert Lai is a mentor for the FIRST Robotics team SWAT 771. He is helping an all girls team from grades 7-12 design a basketball-shooting robot for this year’s annual FIRST Robotics Competition. Dr. Lai is using MapleSim and Maple to help the team understand the principles involved and design their robot. This blog post is part of a series that chronicles the progress of the team.  Posts in the series include:

    • Part 1 - 

    N.B. The MaplePrimes site elided everything past the bullet list, which included more description and links for obtaining the package.  It appears as though bullet lists break MaplePrimes, so this is going to be a bit out-of-order.

    This new debugger uses a client/server architecture.  Communication with Maple is via TCP. This permits remote debugging as well as concurrent debugging of multiple Maple processes.  That is useful for comparing different...

    This post is continuing the theme of "animate implicitplot (a heart shape)". I tried to send a reply within this theme, but for some reason, my message is not loaded

    Sometimes it is appealing to have a package export a procedure which does not show up when calling with().

    For example, the procedure might be used elsewhere, but be otherwise so very technically obscure that nobody else would be interested. (The counter-argument is that what is good for the goose is good for the gander! If something else in Maple can make good use of it and need it, then you might too.)

    Now, Maple's modules don't have the concept of "friends",...

    To gain more visibility on the subject I've started a new thread. No solution yet and thanks Acer for trying to look into it. I almost wondered if there was a typo in the code preventing it from working properly since the code for ospd3 exists. We could almost write a loop code to check if something other than the word builtin is possible, using the try catch statement.

    I'll re-iterate the issue

    with(StringTools[PatternDictionary]):
    > bid := Create('ospd3');

    prototypes.zip

    HTML-Navigator of the tasks' prototypes  of the unified state examination in Russia 2012.
    Supplied with the links to the Maple-solutions of 2011.

    Online: http://webmath.exponenta.ru/beg/index.html

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