Senior Developer

I am a Senior Developer in the Mathematical Software Group and have been with Maplesoft since 2007. I am also an Adjunct Assistant Professor in the School of Computer Science at the University of Waterloo.

I have a Ph.D in Mathematics from North Carolina State University as well as Masters and Bachelors degrees from the University of Oregon. I have been working on research in computational mathematics since 1997.

My main research interests in are computational linear and polynomial algebra, especially numerical polynomial algebra. I currently work on the exact algebraic solvers as well as other subsystems of Maple.

Another feature added to Maple 15 partially in response to the MaplePrimes forums is the new/improved ?HTTP package. It provides one-step commands for fetching data from the web: much simpler than using the ?Sockets package directly. In most cases, the command ?HTTP,Get is what you would use:

(s, page, h) := HTTP:-Get("http://en.wikipedia.org/wiki/List_of_Crayola_crayon_colors"):

The above fetches the HTML source of a page from Wikipedia and stores it as a string 'page'. The other two outputs are 's', and integer HTTP status code and 'h' a table of the headers returned in the HTTP response from the server. Compare this to the amount of code needed to fetch data in my Baby Names application for Maple 12, for example.

In part due to a large number of requests on MaplePrimes, the command ?plottools,getdata was added to Maple 15. This new command gives programmers a better way to access the internals of plots and do things with the data they contain.

I was trying to come up with something really fun to do with this command, and another recent obsession came to mind: the game Minecraft. Minecraft is nice, since like Maple it is written in Java and runs on lots of platforms! For the uninitiated, Minecraft is a a sort of mostly unstructured "sandbox" game. The player starts in alone in a procedurally generated landscape consisting of blocks. They player can collect blocks with their hands or with tools and they use them to build new things. The wide array of things that people create in Minecraft is staggering.

So, I thought I would write some commands to export 3D plots in Maple to block structures in Minecraft.

Now that Maple 15 is out, I thought I should share this little application I made: GoalTracker.mw. It is an application partially inspired by the BMI tracker in Nintendo's WiiFit application; you could easily use it to track a weight loss goal. But it could also be used to track other quantifiable goals. I am posting it here mostly because it takes advantage of two new features in Maple 15.

Back when I was working at the University of Waterloo, I found several copies of a VHS tape sitting on a dusty bookshelf full of old Maple boxes and manuals. The tape's cover had a line drawing of Issac Newton on it and the title "Maple V: The Future of Mathematics".

There was...

The Canadian Lotto649 draws are randomized the old fashioned way, the draws are held using a Ryo-Catteau Tulipe ball machine made by a well respected French Company. The draws are video recorded in a secure studio, and broadcast live. There is no reason to suspect that these draws might not be random, but let us look at some ways we might detect it if it were not random.You could look at the Lottery draws as a generator for a binary sequence as I did in my previous post, but as Robert Israel pointed out in the comments, that encoding can hide some non-random behavior (e.g. if the number 25 appeared in every draw, that encoding would not appear less random).

This is not really the next part in my randomness series, but more of an aside. I used Maple's embedded components to use the Lotto649 drawing data from my last post to create a historical lottery simulator. Basically, you fill in your prefered numbers, and it simulates you playing the lottery in every draw since 1982.

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...

In a series of posts now imported to the Maplesoft blog (starting here), I have been talking about pseudo-random number sequences, but since part of what kicked off this series was a paper on true random number generation (with LASERS!) I thought I would share some routines I wrote that alllow you to use the two main true random number sources available on the web (neither using lasers, sadly).

In this post I'll introduce is a nice visual test of randomness from signal processing. The main idea of this test to look at how a random sequence correlates with itself.

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

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');

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 ...

A while back, someone asked me for a good way to plot a Klein Bottle in Maple. I didn't have a good answer at the time, but I recently stumbled upon the following, which does a pretty good job if you don't mind the use of Heaviside in the parameterization.

plot3d( [4*(1-1/2*cos(u))*sin(v), 6*cos(u)*(1+sin(u))+4*(1-1/2*cos(u))*(cos(u)*(1-Heaviside(u-Pi))+Heaviside(u-Pi))*cos(v+Pi*Heaviside(u-Pi)),

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.

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