Hello all!  It's been a while, hasn't it?

A couple of days ago, one of my professors (I'm in college now) posed the slightly rhetorical question of, "How large of a matrix can your calculators make from the multiplication of two matrices?"  I of course took it literally.  Thus, after talking to her after class and deciding to come up with the best answer I possibly could, I now have what you see below.  So sit back, and enjoy reading about just how big matrices on the TI-83/83+(SE) calcs can get:

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  As discussed on Friday, I think I've figured out the biggest matrix that can be made on a TI-83/84+(SE) series of graphing calculators; it's simply limited by the amount of RAM on the calculator.  These calculators have 24389 bytes of RAM when completely empty; however, anything else, even items in archive take up RAM because of the inner workings of their operating systems.  A single matrix takes up RAM according to the following equation:

RAM = 11 + 9 * (Number of elements) bytes

  Thus, a 3x1 matrix would take up 47 bytes.  Consequently, the largest single matrix that can be made is around a 52x52 matrix (24347 bytes).

  This being said, your question was on how large the product of the multiplication of two matrices could be, which is much smaller.  Not only must all three matrices must be able to fit in RAM at the same time, but due to the inner workings of the calculator, the resulting matrix must be able to fit into RAM twice.  Assuming that we are using two vector matrices to maximize the resulting matrix, the matrices to be multiplied will be in the form 1xN and Nx1.  This allows the following equation to give the size of the largest matrix that can be multiplied on the TI-83/84+(SE) series of calculators:

RAM = (11 + 9 * N) + (11 + 9 * M) + 2*(11 + 9 * N * M) bytes

  For the ease of calculations, I'm going to assume the resulting matrix will be square, leading to this formula:

RAM = 2*(11 + 9 * N) + 2*(11 + 9 * N * N) bytes
RAM = 18N^2 + 18N + 44 bytes

  When solved, this gives a maximum matrix size of 36x36 (totaling to 24020 bytes).  However, this was assuming that the two matrices being multiplied were both vectors.  If the two matrices are both square, then the size drops dramatically:

RAM = 4*(11 + 9 * N^2) bytes

  Here, the largest resultant matrix is 25x25 (totaling to 22544 bytes).  It's worth noting that by the equations given it seems possible to multiply two 26x26 matrices.  However, though by my equations they total to 24380 bytes (9 shy of the RAM limit), there are actually a few more things that go into RAM - such as typing the equation to multiply the two matrices on the homescreen of the calculator - that makes the 26x26s slightly too large to be multiplied.

  Thus, on an empty TI-83/83+(SE) calculator it's possible to multiply matrices as large as 25x25, but the result can be as large as 36x36 if the two initial matrices are vectors.

Congrats on making it on Reddit!  One of my friends was browsing Reddit, found it, and called our attention to it.  What he didn't take into account is that I knew about it already from here.  Awesome job, Deep!

Congrats, cyanophycean314, Adriweb, squidgetx, and Builderboy!  From what I played/saw they were all great games and worthy of victory.

Wow, Hayleia, that looks amazing!  And yeah, double posts for project updates are fine.  Awesome work there!

Here you go!

Haha, really?  How many bytes did they shave off it?

Yeah, me too.  It's a pretty fun thread.

Less than a week to go!  Hopefully we'll all get to see some pretty cool entries; I just finished mine.  (I'm not going to say what it is yet, just remember that it has nothing to do with snake, as detailed above).

Yeah, about that...
Turns out in TI-Basic I can't make it fast enough to be enjoyable while playing, and that's with the simplest AI possible.  So I'm scraping the idea.

I may still enter something; it depends if I get another idea or not.

Yeah, it's been a while.  I generally check once or twice a month, and I rarely post much anymore.

I don't know how we did this, but jsj and I came up with the same idea within about 26 hours of each other completely independently of each other.  I began work on a program as described above thinking that if it's fast enough in TI Basic, I'll enter it in the competition.  Right now it needs optimizations, but if I get some in there I think I can make it fast enough that I'll consider entering it.  It's also worth noting that my AI is super simple right now, as I've only placed the foundation for it.

Am I the only who noticed that the first two pictures both have the orange, Detached Solutions screen covers?  TI made those years ago in such a low quantity that they're probably the rarest thing pictured in the three pictures.  And there are two pictured!

Ah.  Well in that case it'd be you, due to our original conversations on TIBD.

Nah, I met you on TIBD, which I know happened after all the stuff I did on UTI.  It was probably October of 09 or so; I became a UTI member in May of 09; Omnimaga was November 09 for me.

For my it was Graphmastur, off of my first post ever: http://www.unitedti.org/forum/index.php?showtopic=8760

The first person from Omni that I ever messaged with was either nitactu or Builderboy, both of which I remember messaging on UTI as well.

I love the 1984 reference!  Deep, that's awesome!