The following is incomplete. I'll finish it later when I'm not so busy. This was posted so that I wouldn't lose the entire thing midway through due to a freak accident
Spoiler For Spoiler:
Welcome to what I hope to be the first of several tutorials on Algorithms for Computer Algebra. I've seen several people express an interest in the subject for the purposes of learning how to write a CAS, so I thought I'd share one of the most commonly desired algorithms: Symbolic Differentiation. As we all learn in Calculus, Differentiation is the operation of finding the function describing the slope of a curve at any point along that curve. There are many different ways of doing this, all of which are equivalent. Some involve heuristic rules, such as those taught in standard Calculus, while others might involve insane projections onto new spaces, simplifying the differentiation operation dramatically. However, Diffferentiation is almost always done in what is called the Euclidean plane (the XY plane we all hate know and love), so that's where this tutorial will focus.
Symbolic math in Computer Programming often relies quite heavily on String manipulations. Differentiation is no different. Keep in mind while reading this that familiar operations such as Addition may not be as simple as using the available CPU addition instructions.
Differentiation is an excellent example of a difficult problem to implement in software. When one first tackles it, the immediate problem one encounters is how to represent functions so that the operation can be written and tested. This is precisely the wrong way to go about solving it. Let us first go back to class and see how we learned how to differentiate on paper.
If you took the same classes I did, then you learned to differentiate through the use of limits. The derivation probably went something like this:
Let the derivative be the slope of the curve at a point (X,Y). We will denote the change in x at (X,Y) as Δx and the change in y at (X,Y) as Δy. If the curve is linear, then the slope at (X,Y) is
Next, let us observe that many functions are approximately linear in the neighborhood near a point. If we substitute h for Δx and g for Δy, then for a curve f(x)=y, the slope at a point is approximately
As we make h and g smaller and smaller, the approximation becomes closer and closer to the true tangent. To do this, we take the limit as h goes to 0 (meaning g also goes to 0).
Thus, we have arrived at the geometric definition of a derivative. However, it's completely useless for computers. Finding limits is hard; harder than finding a derivative in fact (particularly for multivariate functions, where limits become extremely difficult to determine). We need a new method to try.
Another method is more algorithmic and algebraic in nature. It's typically taught in the middle of the first semester of Calculus and involves the use of rules. Rules such as the Product rule (d/dx f(x)g(x) = f(x)g'(x)+f'(x)g(x) ) as used to break functions down into simpler components. These methods were the basis of the original Symbolic Differentiation programs and remain important today. For our algorithm, we'll be using several rules: the Product Rule, the Chain Rule, the Power Rule, the Logarithmic Differentiation method, the Constant Rule, and the Addition Rule. These will be used to break the function down into simpler parts.
Rules table:
d/dx h(x) = ?
Case 1: h(x) = C*f(x) d/dx h(x) = C * d/dx f(x)
Case 2: h(x) = xn d/dx h(x) = nxn-1except when n=0
My school has gotten the idea that an ideas competition would do something beneficial for the school and I'm required to participate in it. Unfortunately, several of the most popular ideas not only don't work, but would violate the laws of physics. Let's get some artificial vote inflation going and support my [made-up] project.
I'm not sure there's any reward for winning, but on the off chance there is and I win, then the money would be donated to the next legitimate project or to charity. Also, I'm not responsible for any legal implications or bodily injury/maiming that may occur as a result of voting.
A classmate of mine with whom I am working on a project has decided to learn Android programming. Unfortunately, he's in over his head and didn't really know where to begin, to he asked me for help. Does anyone know of any good resources for an absolute beginner to programming for Android devices?
It's high time I made a post on one of my favorite subjects, Chemistry.
As most people know, Chemistry is one of the three main branches of Science and explains much of the macroscopic world. Fewer people know that it's actually one of the easiest fields to get into and one of the most complex once you get too far in to back out. Even simple things like Benzene or Carbon nanotubes have incredibly complex behavior under many conditions.
Here's a nice electronic density plot of beneze, which clearly reveals the delocalized Pi bonding underlying much of its unusual behavior:
/* Khavi context switcher (to be located in RAM and accessed from */ /* Uses Round robin for simplicity */
/* Table bitfields: * First node: [Address of current linked list][Address of next linked list][registers] * All secondary nodes: [Address of next linked list][registers] */
/* Should also store/reload the table if planning to implement process/thread distinction */
Start_switcher: mov.l r2,@-r15/* Store registers for use */ mov.l r1,@-r15 mov.l r0,@-r15 mov.l first_table,r0 mov.l @r0,r0/* move address of current table into r0 */ add #0x7F,r0/* Offset r0 to end of table. Needs to be tuned properly. */
mov.l @r15+,r2/* Store r0 to table */ mov.l r2,@-r0 mov.l @r15+,r2/* Store r1 to table */ mov.l r2,@-r0 mov.l @r15+,r2/* Store r2 to table */ mov.l r2,@-r0
Apparently Microsoft decided to get the jump on the inevitable leaks for their upcoming OS, Windows 8. Windows 8 has been a source of significant controversy in the past few months as a result of its use as both a Tablet and PC operating system. If you've been concerned, now's your chance to try it out!
Be warned that this is a pre-beta version of Windows 8 and will likely have some remaining bugs.
One thing I've noticed from a lot of people is the assumption that the tools they use are at fault for the errors they observe. While this can indeed be the case (one only has to look at the bugs list of any major project for evidence), the first, second, and third rules of debugging are to assume that the tools are perfect until all other possibilities are disproven as the source(s) of the error(s). One example relevant to the TI is that of OS v. 2.5x, an OS often cited as the cause of many inexplicable errors. However, it is well known that the vast majority of errors are user errors, not code errors, especially in any prominent piece of code. As comfortable as it is to blame the tools, those same tools are debugged very thoroughly for the simple reason that bugs are often far more important in a tool than in a random program. In general, important programs such as Operating Systems, Compilers and Interpreters1 are among the least buggy programs available by sheer necessity. Before claiming an error is caused by any of the above, please stop and consider whether the errors are valid bugs. Spend time looking at the documentation. Check previous bug reports and your own code carefully. Major bugs in tools are extremely rare, highly publicized, and almost always well documented.
1: There is almost never a good reason to assume a hardware bug in commercial hardware. Don't do it without extremely strong evidence to back that claim (such as integer addition of 1 and 1 producing 3, in which case you should still be checking your display and register loading routines first).
Introducing the future of text editors, the Tidal editor. Hand-written in raw, optimized Brainf*ck (after being ported from both the TI-84+ and Casio FX-CG families of calculators) and released under a GPL license for this exclusive beta download, Tidal is the fastest and most powerful Brainf*ck text editor around.
Spoiler For Screenshots:
Spoiler For Usage:
Tidal is a standard text editor designed to work with the Brainf*ck Developer. Normal usage is very simple: Just type in the text you want to edit on the input line. Backspace is used by entering the "~" character as input. Also, please comment about features you'd like to see added to Tidal, such as a native brainf*ck interpreter or dynamic refresh.
While I was taking a small Java programming test (I don't know even Java ), I came across an interesting problem called the equilibrium index. Basically, given a list such as {-7, 1, 5, 2, -4, 3, 0}, there is an index into the list for which the sum of the elements up to that index is equal to the sum of the elements after. For this particular data set, it happens to be at the indices 6 and 7.
Your challenge is to write a program in TI-BASIC (or Axe if you wish) that will compute the equilibrium index of any list. If it doesn't exist, then the program must return -1. You are allowed to assume that the list is in L1 and that the dimension of the list is in N.
NOTE: Don't use Google. As it turns out, a lot of people have unwittingly made a mistake in declaring the problem such that the example list has indices at 3 and 6. The index of 3 is actually only true when L1(4) is eliminated from the list.
Timing: It took me about three minutes to write the program and a further five minutes to notice the error everyone had made wasn't actually a bug in my program, but their mistake. It shouldn't take longer than half an hour max to do.
In response to the recent downtime on #omnimaga, several people have asked questions and voiced concerns about the security of the channel from takeover.
After a small debacle last night between Manager Eeems and CoT SirCmpwn ([email protected]) got out of hand, SirCmpwn shut down the channel and kicked all Operators. This resulted in approximately 37 minutes of downtime, during which the channel was relocated to irc.omnimaga.org (port 6667, #omnimaga for future reference). This was fixed by our kindly forest squirrel, Cooliojazz and the channel is back to normal. SirCmpwn also attempted to delete the Axe Parser releases thread, but Juju easily undeleted it. SirCmpwn has been banned, security measures are being discussed and implemented that will hopefully prevent this terrible occurrence in the future. We apologize for the discrepancies in the logs and any inconvenience this downtime may have caused.
We might make irc.omnimaga.org, also known as OmniNet, our main IRC server for more security. Unlike EFNet, OmniNet have services, which can protect your nickname from impersonation, much more features and the servers are ran by Omnimaga staff, which is obviously not the case of EFNet. Please give us your feedback in the comments EFNet and OmniNet are already linked together with OmnomIRC.
(12:37:37 AM) OmnomIRC: (O)<DJ_O> yeah (12:42:33 AM) Eeems: SirCmpwn, don't try to pm me I wont get it. (12:42:44 AM) SirCmpwn: good for you (12:43:20 AM) Eeems: Don't test me (12:45:06 AM) SirCmpwn: oh, of course not (12:45:14 AM) SirCmpwn: you're pretty testy tonight, I wouldn't want to push it (12:45:56 AM) Eeems: No I was fine until you started being an ass (12:46:17 AM) SirCmpwn: yeah, I thought we were pretty good until it got mutual (12:46:38 AM) SirCmpwn left the room (Kicked by Eeems (SirCmpwn)). (12:46:41 AM) SirCmpwn [[email protected]] entered the room. (12:46:42 AM) mode (+v SirCmpwn) by Netbot45 (12:46:42 AM) mode (+o SirCmpwn) by Netbot45 (12:46:42 AM) Netbot45: [SirCmpwn] A Coding Knight has arrived (12:46:46 AM) SirCmpwn: ooh, fancy op powers (12:46:49 AM) SirCmpwn: !deop Eeems (12:46:55 AM) mode (-o Eeems) by SirCmpwn (12:46:57 AM) Eeems: you can't deop me (12:46:58 AM) Eeems left the room (Kicked by SirCmpwn (Eeems)). (12:47:05 AM) mode (+b Eeems!*@*) by SirCmpwn (12:47:07 AM) OmnomIRC: (#)<Eeems> because I'm still here (12:47:14 AM) SirCmpwn: oooh, cool, you can use OmniNET (12:47:22 AM) ***New post by calc84maniac in TI-Nspire GB Emulator http://omniurl.tk/1243/182248 (12:47:30 AM) ***New post by NecroBumpist in Lua Q&A http://omniurl.tk/9120/182249 (12:47:35 AM) OmnomIRC: (#)<Eeems> and if you don't unban me I will ban you for abuse of your powers (12:47:47 AM) SirCmpwn: good for ya (12:47:50 AM) SirCmpwn: I look forward to it (12:48:03 AM) geekbozu: wtf is going on >.< (12:48:24 AM) OmnomIRC: (#)<Eeems> geek ban Sir (12:48:28 AM) OmnomIRC: (#)<Eeems> unban me (12:48:32 AM) OmnomIRC: (#)<Eeems> one hour (12:48:33 AM) geekbozu: wtf is going on first (12:48:41 AM) OmnomIRC: (#)<Eeems> he's being an ass (12:48:43 AM) geekbozu: while i try to remember how to ban from weechar >.< (12:48:45 AM) OmnomIRC: (#)<Eeems> and insulting me via pm (12:48:57 AM) CoolioJaz [[email protected]] entered the room. 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), I came across an interesting problem called the equilibrium index. Basically, given a list such as {-7, 1, 5, 2, -4, 3, 0}, there is an index into the list for which the sum of the elements up to that index is equal to the sum of the elements after. For this particular data set, it happens to be at the indices 6 and 7.
EFNet and OmniNet are already linked together with OmnomIRC.