Applications, Examples and Libraries

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For pass argument I use the ssystem command.

So I'm able to pass argument by launching my script like this.

login@hostname:  echo  ARG | ./example.mpl

example.mpl look like this:

-------------example.mpl----------------

#!/usr/bin/maple

with(StringTools):

ResultArray:=ssystem("read MapleArg; echo ${MapleArg}"):

#

The folks at Grand Valley State University have posted a nice set of Maple tutorial videos on YouTube.  The videos have been designed for students taking 200-level math courses, but they are certainly suitable for anyone who is either new to Maple, or looking for a refresher.

Enjoy!

http://www.youtube.com/playlist?list=PL81C1945FA962279F

Bryon

@ThU

Download Quaternion_Fractals_.mw

Not in the same league as the "Mandelbulb" pictures you may be referrng to, but a couple of years ago I messed around with plotting 3D Quaternions in Maple. Pictures in the attached worksheet

Samir

I've submitted an application to the Application Center: Great Expectations.  This is an interactive Maple document, suitable for instructional use in an undergraduate course in Probability.  The mathematical content is related to the Laws of Large Numbers and Central
Limit Theorem.  It requires no knowledge of Maple to use.

Syrup-0.1.8.zip is a rewrite of the Syrup package, an electric circuit solver for Maple.  It reads either a SPICE-like syntax, or a compact ladder notation.This update runs on Maple 15. I've added a few features, such as the ability to export to Modelica, which can be used with the ?MapleSim product.  Also added are two new controls,

No, I'm willing to bet it's about as random as flipping a coin.  You might say, huh?!  I think my theory is interesting but this isn't really a maple question although perhaps we can make it into one, it would be that much more interesting.  I haven't done so yet, but anyone is welcome to.

With practice, I can flip a coin and get 30 heads in a row no problems.  Now say for a roulette wheel operator who uses it constantly, you don't think he's gained...

I have uploaded to the Maplesoft Application Center a worksheet exploring the orbital dynamics of the recently discovered Kepler 16 system, where a planet orbits a double star. 

Your comments and suggestions will be appreciated.

 I would like to pay attention to the article "Exploratory Experimentation and Computation" by David H. Bailey and Jonathan M. Borwein just published in Notices of AMS, 2011, V. 58, N 10, 1410-1419
 ( http://www.ams.org/notices/201110/rtx111001410p.pdf ) . It should be noted that Maple is one of the leading characters of this article.

I was digging through my old worksheets and came across something I created for one of my projects I never finished or well am still intending to work on.  Anyways I had come across a plot created in Matlab and noticed Maple didn't have an option to create gridlines in the axis on a 3d plot like Matlab did (at least I think it was Matlab) in any case I tried to mimic the same thing in Maple as exactly as I could.  The below is the groundwork I came up with and I...

Russian Center of Maple.
02.X.2011
3.000.000 visits in 16 months.

http://webmath.exponenta.ru/

The goal here is to produce plots for inclusion inside Worksheets or Documents of the Standard GUI at specific sizes.

[update: Maple 18 has this as a new feature for 2D plots. See the `size` option described on ?plot,options]

When manually resizing an existing plot, using the mouse pointer, there is no visual cue as to what pixel size has been attained. Hence any worksheet author who wishes to produce a plot of size 600x600 is presented with two barriers. The first is that resizing must be done manually, and the second is that there is no convenient mechanism showing the actual size attained.

The `Resize` package attempts to address these barriers by allowing construction of a plot, inside a worksheet, with programmatically specified width and height in pixels.

The default behaviour of the package is to produce the plot inside a new Worksheet, from whence it may be selected and copied. An optional behaviour is to show the constructed plot inside a Task Template (a form of help-page), where it may be previewed for correctness and inserted into the current Worksheet or Document at the press of a single button.

It appears to function for both 2D and 3D single plots.

It won't work for so-called Array plots, which are collections of multiple plots displayed side-by-side inside a worksheet table.

This first version is a bit rough. The plot is currently being inserted as input, which is why it isn't centered on the page. I suspect that it would be best to insert the first argument (eg. a `plot` call) as input to an execution group, and then have the plot be the output. That would look, and hopefully act, just as usual. And with the plot call inserted as input, the original `Resize` call could be neatly deleted if desired.

To install this thing, use the File->Open from the Standard GUI's menubar. Choose this .mla file as the thing to open. (You may have to slide a scrollbar, and select a view of "All Files", in order to see it in the pop-up File Manager.) Double-clicking on the file, to launch it, should ideally also open it but it looks like that functionality broke for Maple 15.

Resize_installer.mla

Alternatively, you could run the command,

march( 'open', "...full...path...to...Resize_installer.mla");

The attached .mla archive is a (graphically) self-unpacking installer, when opened in this way.

The bundled materials include a pre_built .mla containing the package itself, the source code and a worksheet that rebuilds it from source if desired, a short example worksheet, and a worksheet that rebuilds the whole installer (and re-bundles all those files into it). I used the `InstallerBuilder` to make the self-unpacking .mla installer, as I think it's a handy tool that is under-appreciated (and, alas, under documented!).

It's supposed to work without the usual hassle of having to set `libname`. This is an automatic consequence of the place in which it gets installed.

It seems to work in Maple 12, 14, and 15, on Windows 7. Let me know if you have problems with it.

acer

I saw an image yesterday of some math done similar to how one can write on paper, with each new reformulation shown on the next line, with a down-arrow between each such line. In other words, operations and output moving down the sheet rather than along it to the right.

The first thing that came to mind was: can this be done in Maple with context-menus?

Here is an attempt,

    cm_downwards.mw

It would be good I hope to present symbolic-numeric CAE system for framed structures analysis.

It will be available soon as Preview version for enthusiasts

The main features are:

  • One calculation act - all analytical dependencies.
  • Fast designing process for structural systems in industry, consulting and design companies;
  • Fastest parametric analysis of construction. New quality of designing in optimization tasks,...

                      

   This is a promissory Maple package, which is rarely used (I found nothing  in MaplePrimes and in Application Center.). Let us see the ?padic package. It is well known that the field of rational numbers Q is not complete. For example, there does not exist a rational number k/n such that k^2/n^2=2. There are only two ways to complete Q ( http://en.wikipedia.org/wiki/Ostrowski's_theorem ) .  The first way is to create the field of real numbers R including Q. Every real number can be treated as a decimal fraction sum over [k in K] of a[k]*10^(k) with a[k] in {0,1,2,3,4,5,6,7,8,9}, finite or infinite. For example, the numbers 0.3+O(0.1), 0.33+O(0.01), 0.333+O(0.001), 0.3333+O(0.0001), ...  approximate the number  1/3.
   The second way is as follows (see http://en.wikipedia.org/wiki/P-adic_number  for more details). We choose a prime number p and consider the valuation v[p] of a rational number k/m=p^n*a/b <>0 where integers are supposed to be irreducible :v[p](k/m):=p^(-n) , v[p](0):=0. The completion of Q up to this valuation is the field of p-adic numbers Q[p] (also including Q).  Every p-adic number can be treated as a p-adic fraction sum over[k in K]of a[k]* p^(k) with a[k] in {0, 1, 2, 3, p-1}. For example, the numbers 2, 2+O(5),2+3*5+O(5^2),2+3*5+5^2+O(5^3) approximate the number 1/3 in Q[5]. These can be obtained with Maple as follows.
> with(padic);
> evalp(1/3, 5, 1);
                           2
> evalp(1/3, 5, 2);
                        2+O(5)
> evalp(1/3, 5, 3);
                          2+3*5+O(5^2)
> evalp(1/3, 5, 4);
                         2+3*5+5^2+O(5^3)
    The field Q[p] is a very strange object. For example, the set of integers is bounded in Q[p] because v[p](k) <= 1 for every integer k. Another striking statement: the sequence p^n tends to 0 in Q[p] as n approaches infinity. The functions expp(x), logp(x), sqrtp(x) and the others are defined in the usual way as the sums of power series (see ?padic,functions for more details). For example,
> Digitsp := 12;
> logp(2+3*5+5^2, 5);

               5+5^2+4*5^3+5^4+3*5^6+4*5^8+3*5^9+5^10+3*5^11+O(5^12)
> cosp(x, p, 2);

                            padic:-cosp(x, p, 2)
> eval(subs(x = 0, p = 5, padic:-cosp(x, p, 2)));

                             1
> eval(subs(x = 3*5, p = 5, padic:-cosp(x, p, 2)));

                             1                            
    The definition of the limit of a sequence in Q[p] is identical to the one in R (of course,  abs(x[n]-a)<epsilon should be replaced by v[p](x[n]-a)<epsilon for every rational epsilon) and the same with the derivative. But every continuous function is picewise-constant. There also exists a non-injective function on Q[p] having the  derivative 1 at every point of  Q[p] . It should also be noticed that the radius of convergence of the expp(x):=sum(x^n/n!,n=0..infinity) series equals p^(-1) if p >2 and 2^(-2) if p=2. Next, there exists a Haar measure d[p](x)=:dx on Q[p] such that d[p](Z)=1. The definite integral of a real-valued function f(x) over a subset D of Q[p] with respect to  dx is defined in certain cases. For example, the definite integral of 1 over
the ball B(0,p^n):={x in Q[p]: v[p](x)<=p^n} with respect to dx equals p^n, ie. the radius of B(0,p^n). It is clear that there does not exist any analog of the Newton-Leibniz formula in the p-adic case. Because of this reason every calculation of every definite p-adic integral is a hard problem.

        There are a lot of good and diffent books on p-adic analysis. In particular, see http://www.google.com/search?tbm=bks&tbo=1&q=p-adic&btnG= ,  http://books.google.com/books?id=H6sq_x2-DgoC&printsec=frontcover&dq=p-adic&hl=uk&ei=IgFuToupO8SL4gTE-tDOBA&sa=X&oi=book_result&ct=result&resnum=6&ved=
0CEYQ6AEwBQ#v=onepage&q&f=false
, and http://books.google.com/books?id=2gTwcJ55QyMC&printsec=frontcover&dq=p-adic&hl=ru&ei=UAxqTuabD5HGtAamhryxBA&sa=
X&oi=book_result&ct=result&resnum=4&ved=0CDkQ6AEwAw#v=onepage&q&f=false
as a good introduction to the topic.
     Why  is it so important? Which are applications? There are indications that the space  we live in has not  the Archimedean property (see http://en.wikipedia.org/wiki/Archimedean_property) on a very small scale. To verify this hypothesis is  a dozen times more expensive than  the large hadron collider
 (see http://en.wikipedia.org/wiki/Large_Hadron_Collider ). However, the mathematicians already develop the necessary mathematical tools, in particular, p-adic analysis.  Concerning other applications, see the answer by Anatoly Kochubei in
 http://mathoverflow.net/questions/62866/recent-applications-of-mathematics.

Edit. The vanishing text and some typos.

 

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