A better approximation gives more digits of accuracy in the result per digit of precision used in the computation than a good approximation does.  I was wondering if anyone could come up with a better approximation to the MRB constant than 31/165, 

This is an important topic which is why I have labelled it as a post.  Many users would like to know how to implement a minor fix to versions where fixes have not been applied.

I will start with one example.

   pdsolve had an issue where the fourth order term was not evaluated in the pdsolve command.  The issue 
   works Maple 16.  To those users of earlier versions where the code didn't work, it was ...

   showstat(pdsolve)

If anyone was interested Euro 2012 starts tomorrow.  Using the FIFA simulation created by Robert Israel one could enter the new values for the ELO ratings found here http://www.eloratings.net/euro_cup.html to create a similar simlation of Euro 2012.  Just for visual sakes here's the ELO ratings for the teams in the tournament.

Dear Maple Users

I have been testing Maple 16 for some time now, and I am overall very pleased with it. There is however one issue, which is really annoying. In previous version of Maple, images inserted into Maple and plots were printed much bigger than they looked like in the Worksheet. Then me and other users have requested to have the printed output look more like it does in the Worksheet on the computerscreen. Maple has adressed those user complaints in the new...

Way back in Maple 6, the rtable was introduced. You might be more familiar with its three types: Array, Matrix, and Vector. The name rtable is named after "rectangular table", since its entries can be stored contiguously in memory which is important in the case of "hardware" datatypes. This is a key aspect of the external-calling mechanism which allows Maple to use functions from the NAG and CLAPACK external libraries. In essence, the contiguous data portion of a hardware datatype rtable can be passed to a compiled C or Fortran function without any need for copying or preliminary conversion. In such cases, the data structure in Maple is storing its numeric data portion in a format which is also directly accessible within external functions.

You might have noticed that Matrices and Arrays with hardware datatypes (eg. float[8], integer[4], etc) also have an order. The two orders, Fortran_order and C_order, correspond to column-major and row-major storage respectively. The Wikipedia page row-major  explains it nicely.

There is even a help-page which illustrates that the method of accessing entries can affect performance. Since Fortran_order means that the individual entries in any column are contiguous in memory then code which accesses those entries in the same order in which they are stored in memory can perform better. This relates to the fact that computers cache data: blocks of nearby data can be moved from slower main memory (RAM) to very fast cache memory, often as a speculative process which often has very real benefits.

What I'd like to show here is that the relatively small performance improvement (due to matching the entry access to the storage order) when using evalhf can be a more significant improvement when using Maple's Compile command. For procedures which walk all entries of a hardware datatype Matrix or multidimensional Array, to apply a simple operation upon each value, the improvement can involve a significant part of the total computation time.

What makes this more interesting is that in Maple the default order of a float[8] Matrix is Fortran_order, while the default order of a float[8] Array used with the ImageTools package is C_order. It can sometimes pay off, to write your for-do loops appropriately.

If you are walking through all entries of a Fortran_order float[8] Matrix, then it can be beneficial to access entries primarily by walking down each column. By this I mean accessing entries M[i,j] by changing i in ther innermost loop and j in the outermost loop. This means walking the data entries, one at a time as they are stored. Here is a worksheet which illustrates a performance difference of about 30-50% in a Compiled procedure (the precise benefit can vary with platform, size, and what else your machine might be doing that interferes with caching).

Matrixorder.mw

If you are walking through all entries of an m-by-n-by-3 C_order float[8] Array (which is a common structure for a color "image" used by the ImageTools package) then it can be beneficial to access entries A[i,j,k] by changing k in the innermost loop and i in the outermost loop. This means walking the data entries, one at a time as they are stored. Here is a worksheet which illustrates a performance difference of about 30-50% in a Compiled procedure (the precise benefit can vary with platform, size, and what else your machine might be doing that interferes with caching).

Arrayorder.mw

Maple 16 introduced dramatic changes to the postscript export facility of 3d plots. This is great news, but some bugs remain. Let me report here about my experience. (Note: Maple 15's 3d ps export was something like an encapsulated bmp, while Maple 16 is a genuine level3 postscript export tool)

The initial release in Maple 16.00 was buggy. In my experience, the export would hang most of the time. An improved release came with Maple 16.01. I have not experienced any...

Maplesoft has these interesting bits of Math on their website.  For example this one here

http://www.maplesoft.com/mathmatters/airplanes.aspx

It is all nice and all but I would like to see some reference examples to maple for each one, a cool application worksheet that portrays each one nicely. 

Using the example link above I searched maplesoft application center for navier stokes...

Not really a review but I think Maple has so much cool stuff one can do with it, that we get sidetracked from one project to the next.   Before you know it, a new release is out and you've put your project on hold to try out and play with the new features - and not really forging ahead on any projects.  One year between new releases isn't enough time to have customers really, and I mean really, dive into Maple.

Here is what a reviewer at computing world said about Maple16

This does not make any sense to me :-)

restart:
A := Matrix([[seq(i, i = 1 .. 10)], [seq(i, i = 11 .. 20)], [seq(i, i = 21 .. 30)]]):
A[.. -1,..] ;
A[.. -2,..] ;



You would assume that A[..-1,..] would remove the last row but that is not the case!
Instead you have to do A[..-2,..] he he it seems a bit odd!

This is a problem I've had with the new mapleprimes. Contributions listed as "answers" to a question are listed according to the number of votes they receive. This is a system used on forums like mathoverflow, for instance, websites designed to provide answers to specific questions, websites where "discussions" are discouraged. But, in my opinion, mapleprimes is both a discussion and question/answer forum and the "rank by vote" is not suited to it.

In the example I...

The MRB constant Z will probably have several parts.

The following example is from the Maple help pages
> with(GraphTheory);
> with(SpecialGraphs);
> H := HypercubeGraph(3);

DrawGraph(H)

Download May262012.mw

Just wanted to let everyone know that there is a Maple 16 update available. Maple 16.01 includes improvements to the mathematics, interface, and plotting capabilities of Maple, including:

• Enhancements to the Physics package in the area of general relativity
• Translations of tutors and assistants into French and Brazilian Portuguese
• A correction to the problem in plotting multiple plots at once in non-Cartesian coordinates, as

Using techniques previously used for generating color images of logistic maps and complex argument, attached is a first draft of a new Mandelbrot set fractal image applet.

A key motive behind this is the need for a faster fractal generator than is currently available on the Application Center as the older Fractal Fun! and Mandelbrot Mania with Maple entries. Those older apps warn against being run with too high a resolution for the final image, as it would take too long. In fact, even at a modest size such as 800x800 the plain black and white images can take up to 40 seconds to generate on a fast Intel i7 machine when running those older applications.

The attached worksheet can produce the basic 800x800 black and white image in approximately 0.5 seconds on the same machine. I used 64bit Maple 15.01 on Windows 7 for the timings. The attached implementration uses the Maple Compiler to attain that speed, but should fall back to Maple's quick evalhf mode in the case that the Compiler is not properly configured or enabled.

The other main difference is that this new version is more interactive: using sliders and other Components. It also inlines the image directly (using a Label), instead of as a (slow and resource intensive) density plot.

Run the Code Edit region, to begin. Make sure your GUI window is shown large enough for you to see the sides of the GUI Table conveniently.

The update image appearing in the worksheet is stored in a file, the name of which is currently set to whatever the following evaluates to in your Maple,

cat(kernelopts('homedir'),"/mandelbrot.jpg"):

You can copy the current image file aside in your OS while experimenting with the applet, if you want to save it at any step. See the start of the Code Edit region, to change this filename setting.

Here's the attachment. Comments are welcome, as I'd like to make corrections before submitting to the Application Center. Some examples of images (reduced in size for inclusion here) created with the applet are below.

This post can be downloaded here:  Download May202012.mw

Below we have approximations involving the MRB constant. The MRB constant plus a fraction is saved as P while a combination of another constant is saved as Q. We then subtract Q from P and always have a very small result!