An Interesting Dilemma

[Snipes17]

While doing some calculus homework the other night, I found and indefinite integral solver online that did everything I would encounter in the book. Later, I began to think about why TI did not put one into a calc. I thought it would not be too hard so, I started on one in basic. I didn't get far before I began websurfing for an algorithm to help me with me program. Unfortunately, I found out that the process is very complicated and it uses Risch's Theorem as well as Heuristic Style of Algorithm (coding an algorithm that solves a problem without there being a known or optimal process for doing so) coding.

The "best" solver is known as Axiom and the developers have many pages worth of text explaining the process so any dev can pick it up and modify it if possible. Unfortunately, this looks like a hard thing to do in ASM, and an even harder task in basic.

I guess I realize why TI didn't make one now... they didn't even get a perfect algebraic solver implemented and that is simpler. I wish I had some code to show for my rant, but for now you'll have to be content with the back story and a hope for a brighter future. Any help or direction would be greatly appreciated.

[thornahawk]

Risch's algorithm is so terribly big and complicated that you'd be hard-pressed to try and fit the algorithm into a TI calculator, much less the special cases that fall through the cracks. The TI 89 and ilk implement a rather restricted portion of this algorithm, and one shouldn't wonder that it can't do some "simple" indefinite and definite integrals a computer algebra system can spit out in a heartbeat.

As to The Integrator, it uses something more elaborate than Risch's algorithm. See here (scroll down to "Differentiation and Integration") for details.

thornahawk

[DarkerLine]

If you're interested in an easier challenge, try writing a program for symbolic differentiation. Unlike integration, this can be done recursively using the chain rule and such. Simplification can get tricky, depending on how far you go with it.

[Snipes17]

[Snipes17]

With no real time to work on this program, I have only managed to create an equation editor that works from the graphscreen. Anyway, I was wondering if there are any big optimizations that can be made to this:

[Galandros]

Instead of:
If not(F
1→F
Use: F or 1→F

Big optimizations, I had to see more close the program flow.

[Snipes17]

[luby]

No, you should use not(F→F

@ snipes, I think you are confused by the "or" part. That means that you should use the or in the (2nd+math, right) Logic menu. It does an or on it, but I'm not sure it would work.

[calc84maniac]

[Snipes17]

[darkstone knight]

[Weregoose]

The big question is, can F take on a value other than zero or one? If not(F:1→F sets F to one if F is zero, but leaves F alone otherwise. In F or 1→F, it doesn't matter what F is, and isn't what we'd want if F could be something other than zero or one. Looking at it from this angle, the If variety cannot always be substituted for one of the others, but is acceptable in the context of this program. Lastly, the expression F or 1 is always true regardless of F, so we can replace the expression with its inevitable result of one.

Let's try optimizing something more worthwhile.

[Snipes17]

[Weregoose]

Frankly, I would optimize it to the home screen... I know that's not in the spirit of things, but I tend to want to adjust programs in the direction of what'd get the job done in the fastest time or in the least amount of space, and those are rarely graphical. :)

My above comment on finding something more worthwhile to optimize was aimed at the over-attentiveness of something so trivial; posts went by, and it's like no one else had anything to add. I had instead hoped that people would give a good shot at it.

Anyway, since the program is overall pretty decent, I'll only make note of a few things. In parts, the coding is a bit more "safe" than useful, resulting in repeated conditions and extraneous parentheses. One example is the cursor movement...

If B+Ans>93 and C<57
Then
B→[font="arial"]LOL(iPart(C/7
1→B
C+10→C
Else
If B+Ans>93 and C=57
DelVar F
End

...which can be made leaner at a glance. Breaking apart and nesting the conditions (using C≠57→F as a finishing touch):

If B+Ans>93
Then
If C<57
Then
B→[font="arial"]LOL(iPart(C/7
1→B
C+10→C
Else
C≠57→F
End
End

Saved only five bytes, but that's a good five Rollover® bytes, so don't waste it!

Three-valued whitelists like max(Ans={23,45,105}) I rarely use, and this one I'd stay away from; the comparison in question can be replaced by Ans=23 or abs(Ans-75)=30, using the rules explained here.

The logical and has greater precedence than or, so the parentheses around A or (B and C) or D can be dropped, and it will still work the same.

10fPart(.1M)+5(iPart(.1M)-5→E can be replaced by M-25-5int(.1M→E, believe it or not (as long as M remains positive).

Also, tiny things that don't need to be there, like the parenthesis in the last Line( argument, can start packing.

But, nice job with the lookup, I have to say!

[Snipes17]

Thank you for the help Goose. I knew you had some modifications for what I could hardly do any better! As for the text input, it has been a goal of mine to make a graphscreen text input for awhile, so I wanted to do it for this project. I know it takes up a lot more room, but I was doing the graphscreen so I could fit more of the equation on there for the user and use a small amount of prettyprint (not implemented yet, of course) for exponents. I haven't had much time to further this due to basketball every day, but it is moving along, albeit at a snail's pace!