Some years ago, before the advent of the Statistics package, a colleague asked for a fast way to generate thousands of normally distributed random numbers in Maple. The suggestion that worked quickest and most easily (using existing, simple Maple Library routines) was to generate random deviates using the usual formula associated with the distribution. But the key was to replace the scalar values (representing the uniformly distributed input) with a whole Matrix of input values....

I wanted to see how difficult it would be to use the OpenMaple API from a C# program.  It turns out that it is pretty easy to access C .dlls from C#.  I was able to reproduce a commandline equivalent (minus the command history and editing features). 

The source code can be found here: openmaple.cs

  restart; Digits:=14;     # using Maple 12.02
  J:=Int(arctan(z)^2/(1+4*z^2),z=0..infinity);


  evalf(J);
                           0.40325004753375

  value(J); evalf(%); Re(%);

                ...

Following the midi crash course written by Daniel White, and using a table of midi note numbers, it is rather easy to write a Maple procedure producing midi files. Here is an example that I posted in Simple Sounds thread, slightly modified by adding an instrument as a 3rd parameter:

An annoying feature of Maple is that if it crashes (all too often) & you have not given your worksheet a name, the file is lost despite having activated Auto-Save.

1)   Is the previous statement correct for Maple 9.5?

2)   If so, has this bug been corrected in later versions?

Alla

The Maplesoft office is currently in the process of being burried in snow and many of us are getting ready to head off for the holidays.  Before leaving, I wanted to share this great animated GIF created using 3d plots.  It was sent to me by Bruce Char at Drexel University. The greeting and the Maple script to generate it are after the break.

In my previous post, I was parsing data out of HTML tables so that I could glean some trivia from it.  My true goal was to compile data out of dozens of such tables and so I needed a way to do the whole process in Maple.   So, now, here is how I used Sockets and StringTools to automate the whole process.

Recently there was some discussion in the Maplesoft office about unisex baby names (that is, names that nearly as likely to belong to males as females). Whenever discussing names, I usually head to the US Social Security Administration's wonderful baby names site. They have data on the top 1000 male and female names for children born in the US each year for more than the last century (that includes about 80% of names). They slice the data a little by US state, and popular names for twins and such, but they do not include data on unisex names. So, I applied Maple to the task.

Recently, I was reading about random.org again.  It is an online random number generating service that uses atmospheric noise gathered from radios tuned between stations as a source of randomness.  It has been running more or less continuously for about ten years.   On their analysis page there is a nice pair of bitmaps (scroll down past the Dilbert comic) that contrast their random bits with those from one version of the PHP rand() function. Basically this demonstrates how easy it is to create a pseudo-random number generator that is periodic with too small of a period.

I decided to take a look at Maple's random number generator in comparison.

Consider this problem in differentiation:

d/dx [ sqrt(u^2) ],  where u is a differentiable function of x and u < > 0.

The answer is:

u'  (u/|u|),  where u' is the derivative of u with respect to x.

This problem involves implicit differentiation & the chain rule.

What Maple input will produce the answer above?

Alla

I have used Maples' least squares capability to fit quadratic & cubic models without any problems.  However, the documentation includes this curious statement: "One can also specify nonlinear curves -- as long as the unknown parameters appear linearly."  What does this mean?  What would nonlinear parameters look like?
 

Alla

Does Maple support Ternary diagrams that can be used for exploring parameters like thee phase relative permeabilities

Hello everybody, I'd like to write from a procedure results in a table as output. Something like this, that I show at the end.

In the volume Advanced Programming Guide of the Maple manual, the "clasical" picture of the Maple system architecture is depicted:

 A1: Internal Organization

Components

Maple consists of three main components: a kernel, a library, and a user interface. The kernel and library together are known as the math engine.

Kernel The kernel is written in the C language and is responsible for low-level operations such as arbitrary precision arithmetic, file I/O, execution of the Maple language, and the performance of simple mathematical operations such as differentiation of polynomials.

Library Most of the Maple mathematical functionality is in the Maple library, which is written in the Maple language. The library is stored in an archive, and pieces of it are loaded and interpreted by the kernel on demand.

User Interface The user interface is the part of Maple that the user sees, and is conceptually separate from the math engine. The same math engine can be used with different user interfaces.

However, the architecture of the system has been moving away from this picture for several years already. Eg:

A second parser has been implemented in the Standard GUI, instead of the kernel.

Some time ago, I had a blog post about a compendium of inequalities,  Some people took a look and found problems in that paper.  So I took the time to track down the author and point him to the mapleprimes page.

He got back to me some time later, thanking me for pointing out the errors.  But in the same email, he pointed me to 2 other papers, http://xxx.lanl.gov/abs/0707.2098 and http://xxx.lanl.gov/abs/0707.2584 which contain (interesting?) conjectures which seem amenable to Maple exploration. I meant to look at these myself, but it has now become clear that I won't for quite some time yet. Perhaps these will pique the curiosity of some MaplePrimes member.