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Maple uses the LGPL licensed GMP as a support library for doing large integer and high precision float computations. There exists is a later version of GMP than was bundled and shipped in Maple 14.x. A natural question is whether it would improve Maple's performance. Another question is whether it can be used within Maple 14.

(This is a reply to PatrickT, who asked about a certain ArrayTools:-Copy example.)

Suppose that you need to do a computation which requires, in part, a certain subportion of a Vector V. Let's call the routine which does the work as `f`. Let's suppose that `f` is a system command and not something that we write ourselves. One natural way to call `f` and supply the subvector is to call `f` like so:

   f( V[a..b] );

Here the inner range a..b denotes...

Perhaps you have heard the terms "ordering difference" or "session dependent" applied to results of some Maple computation. It used to get heard more often back before Maple 12, when elements of sets in Maple were ordered according to address.

In this series of blog posts, I have picked on Baseball win-loss records already.  Looking for other sources of things that might or might not be random, I decided to look at lottery draws.  Since I live in Canada, the obvious lottery to look at is the national Lotto 6/49.

A lotto 6/49 draw consists of drawing 6 numbered balls from...

I've been making some use of the Maple Cloud for a while now, and thought that I'd share some comments.

So far, it's been quite useful to me, and I like it. This surprised me a bit. I expected not to find it useful, and to dismiss it with an old-timer's "Bah, humbug... as useless as Maple+twitter!" But, to the contrary, I've found a use for it; a need that isn't otherwise...

Quite often, when plotting an expression in involving trigonometric functions applied to (a rational polynomial of) the main variable, it is desirable to have the major ticks along the x-axis be labeled by multiples of Pi. In particular, it can be much more appealing to have those tickmarks be labeled with short rationals multiplied by the 2D Math symbol π.

It's been a while since I wrote one of these random posts, but I still have a couple more I wanted to write.  In this post, I want to describe one of the tests used in the paper that initially inspired this series of posts: the Wald-Wolfowitz runs test.  This test is interesting in that it does not test for uniformity

Let's compare the performance of two methods of computing the inverse of a large datatype=float[8] Matrix.

The two methods are that of calling `MatrixInverse`,...

I used to have a blog entry which contained an except from an Isaac Asimov story entitled "The Feeling of Power".

I had removed that blog entry, but here is a link to the full text.

I was recently reminded of it by two things. The first was that I was reading a blog entry at Walking Randomly which mentioned Maple 14. And I remembered noticing a page on that site before. And the second was ISSAC 2010.

As alluded to in my previous post in this series, one of the most straight forward ways to test if a PRNG is generating good random sequences is by examining the frequency of 0's and 1's.  This is just a couple lines in Maple using Statistics:

(**) r1 := rand(0..1):L := [seq(r1(), i=1..10000)]:
(**) n := nops(L); tally := `+`(op(L));
(**) Statistics:-ChiSquareGoodnessOfFitTest(
      [n-tally, tally], [n/2, n/2], ':-output'=':-hypothesis');

This describes in more detail (with permission and citation) the method posted here of solving problem 2 in the XKCD comic Substitute.

Download RaptorMath.mw

Today is my birthday, and in fact it is also the birthday of at least one other Maplesoft employee (not surprising since more than 23 people work here - considering the generalized birthday problem, I even know of 3 people here who share the same birthday).  Of course, it turns out that birthdays are not evenly distributed through out the year and so I wanted to know if someone with an August birthday is more likely to share than someone with an April birthday. 

Continuing on in this series of posts, here is a way to test the randomness of a sequence of bits from a PRNG that is the appropriate to the first morning back after the August long weekend.  It is a very fast, and not very formal test done by checking how well a sequence compresses. This is really easy in Maple 14, with the new commands ?StringTools:-Compress and StringTools:-Uncompress which use ...

In a previous post, I promised to write about testing the quality of pseudo-random number sequences.  I'll post later about some of the statistical tests often used, but I first wanted to mention a sort of practical test one can do. One of the many things you might want to do with pseudorandomly generated numbers is Monte Carlo integration/simulatation/etc.  As mentioned by acer in this comment, Monte Carlo integration can be shown to work better with some of the pseudorandom number generators (PRNGs) which are considered inferior in a statistical sense.  In this post, we will play with a simple Monte Carlo approximation of π.

There are two pieces of extended functionality that I quite often want from the Maple Compiler. The first (task A) is to be able to link in and use an arbitrary function from some other external ("3rd party") shared library, within my Compile'd Maple procedure. The second (task B) is to directly call the compiled Maple procedure from within some computational routine in a 3rd party shared library (which I would then access using define_external). This post is about the first of those, task A.