Maplesoft Blogger Profile: John May

Guru

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.

Posts by John May

This is Maple:

These are some primes:

22424170499, 106507053661, 193139816479, 210936428939, 329844591829, 386408307611,
395718860549, 396412723027, 412286285849, 427552056871, 454744396991, 694607189303,
730616292977, 736602622363, 750072072203, 773012980121, 800187484471, 842622684461

This is a Maple prime:


In plain text (so you can check it in Maple!) that number is:

111111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111116000808880608061111111111111111111111111111111
111111111111111111111111111866880886008008088868888011111111111111111111111111
111111111111111111111116838888888801111111188006080011111111111111111111111111
111111111111111111110808080811111111111111111111111118860111111111111111111111
111111111111111110086688511111111111111111111111116688888108881111111111111111
111111111111111868338111111111111111111111111111880806086100808811111111111111
111111111111183880811111111111111111100111111888580808086111008881111111111111
111111111111888081111111111111111111885811188805860686088111118338011111111111
111111111188008111111111111111111111888888538888800806506111111158500111111111
111111111883061111111111111111111116580088863600880868583111111118588811111111
111111118688111111111001111111111116880850888608086855358611111111100381111111
111111160831111111110880111111111118080883885568063880505511111111118088111111
111111588811111111110668811111111180806800386888336868380511108011111006811111
111111111088600008888688861111111108888088058008068608083888386111111108301111
111116088088368860808880860311111885308508868888580808088088681111111118008111
111111388068066883685808808331111808088883060606800883665806811111111116800111
111581108058668300008500368880158086883888883888033038660608111111111111088811
111838110833680088080888568608808808555608388853680880658501111111111111108011
118008111186885080806603868808888008000008838085003008868011111111111111186801
110881111110686850800888888886883863508088688508088886800111111111111111118881
183081111111665080050688886656806600886800600858086008831111111111111111118881
186581111111868888655008680368006880363850808888880088811111111111111111110831
168881111118880838688806888806880885088808085888808086111111111111111111118831
188011111008888800380808588808068083868005888800368806111111111111111111118081
185311111111380883883650808658388860008086088088000868866808811111111111118881
168511111111111180088888686580088855665668308888880588888508880800888111118001
188081111111111111508888083688033588663803303686860808866088856886811111115061
180801111111111111006880868608688080668888380580080880880668850088611111110801
188301111111111110000608808088360888888308685380808868388008006088111111116851
118001111111111188080580686868000800008680805008830088080808868008011111105001
116800111111118888803380800830868365880080868666808680088685660038801111180881
111808111111100888880808808660883885083083688883808008888888386880005011168511
111688811111111188858888088808008608880856000805800838080080886088388801188811
111138031111111111111110006500656686688085088088088850860088888530008888811111
111106001111111111111111110606880688086888880306088008088806568000808508611111
111118000111111111111111111133888000508586680858883868000008801111111111111111
111111860311111111111111111108088888588688088036081111860803011111111863311111
111111188881111111111111111100881111160386085000611111111888811111108833111111
111111118888811111111111111608811111111188680866311111111111811111888861111111
111111111688031111111111118808111111111111188860111111111111111118868811111111
111111111118850811111111115861111111111111111888111111111111111080861111111111
111111111111880881111111108051111111111111111136111111111111188608811111111111
111111111111116830581111008011111111111111111118111111111116880601111111111111
111111111111111183508811088111111111111111111111111111111088880111111111111111
111111111111111111600010301111111111111111111111111111688685811111111111111111
111111111111111111111110811801111111111111111111158808806881111111111111111111
111111111111111111111181110888886886338888850880683580011111111111111111111111
111111111111111111111111111008000856888888600886680111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111111

This is a 3900 digit prime number. It took me about 400 seconds of computation to find using Maple.

It turns out be be really easy to do because prime numbers are realy quite common.  If you have a piece of ascii art where all the characters are numerals, you could just call on it and get a prime number that is still ascii art with a couple digits in the corner messed up (for a number this size, I expect fewer than 10 of the least significant digits would be altered).  You may notice, however, that my Maple Prime has beautiful corners!  This is possible because I found the prime in a slightly different way.

To get the ascii art in Maple, I started out by using to import ( )  and process the original image.  First then and to get a nice 78 pixel wide image.  Then to make it a pure 1-bit black or white image.

Then, from the image, I create a new Array of the decimal digits of the ascii art and my prime number.  For each of the black pixels I randomly use one of the digits or and for the white pixels (the background) I use 's.  Now I convert the Array to a large integer and test if it is prime using (it probably isn't) so, I just randomly change one of the black pixels to a different digit (there are 4 other choices) and call again. For the Maple Prime I had to do this about 1000 times before I landed on a prime number. That was surprisingly fast to me! It is a great object lesson in how dense the prime numbers really are.

So that you can join the fun without having to replicate my work, here is a small interactive Maple document that you can use to find prime numbers that draw ascii art of your source images. It has a tool that lets you preview both the pixelated image and the initial ascii art before you launch the search for the prime version.

Prime_from_Picture.mw

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)),
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