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35s Programming (need help) - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: 35s Programming (need help) (/thread-132162.html) |
35s Programming (need help) - Chuck - 02-04-2008 Hi all. I'm covering arc-length in my Calc II class tomorrow, and need some help with the 35s. Consider the problem below:
6 = Int[sqrt(1 + 4t^2),t,0,x) That is, the integral of root(1+4t^2) from 0 to x equals 6: solve for x. This can easily be done on various TI calculators. But on page 15-11 of the 35s manual, it says "SOLVE cannot call a routine that contains an Integral(FN) instruction" and visa-versa (or am I missing something here?) So, is there an elegant way to "solve" an integral equation on the 35s? It pains me to take in a TI. I may have to resort to my HP 50g, but I'd rather do this on a non-graphing machine. I'll work on it later tonight after my rehearsal.
Thanks in advance, Edited: 4 Feb 2008, 9:18 p.m.
Re: 35s Programming (an HP-34C/15C/41 solution) - Karl Schneider - 02-05-2008 Hi, Chuck --
Quote: You're not missing anything. The ability to run SOLVE within INTEG or vice-versa was not provided on the HP-32S in 1988, and that shortcoming has been carried forward on all its successors -- the HP-32SII, the HP-33s, and the HP-35s. From my only HP Forum article: http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/articles.cgi?read=556
Quote:
6 = Int[sqrt(1 + 4t^2),t,0,x) Calculation of the arc length of a function is a standard calculus problem, e.g.: sqrt[(dx)^2 + (dy)^2] = sqrt[1 + (dy/dx)^2].dx This function is apparently parameterized as x = t; y = t2, so sqrt[(dx/dt)^2 + (dy/dt)^2].dt = sqrt[1 + (2t)^2].dt The integrand will be modestly larger than 2t. Integrating 2t.dt from 0 to x such that the integral will be equal to 6.0 yields x = sqrt(6) = 2.449. The actual solution will be lower than that. Here's a program and result returned by my 1982-made LED HP-34C, which is executable without modification on an HP-15C, and as adapted (quite minimally) for the HP-41 with Advantage ROM:
Program: This is a good application of INTEG within SOLVE, the mechanics of which I've done before. However, I've yet to encounter or come up with a realistic and practical application of SOLVE within INTEG. -- KS
Edited: 9 Feb 2008, 1:46 a.m. after one or more responses were posted
Re: 35s Programming (need help) - Antonio Maschio (Italy) - 02-05-2008 K = G
K is a variable that stands for Karl then the above equivalence is true.
-- Antonio
Re: 35s Programming (need help) - Gerson W. Barbosa - 02-05-2008
Quote: Hello Karl, This quite matches what we get when solving 2*X*SQRT(4*SQ(X)+1)-LN(SQRT(4*SQ(X)+1)-2*X)-24 on the HP-33s, that is, 2.30609738256. However the expression was obtained with help of the HP-50G ('sqrt(4*T^2+1)', 'T', RISCH; then the proper substitutions). It's a pity the HP-33s cannot handle INTEG within SOLVE. I was not aware of this. Thanks for the information and explanations! Regards,
Gerson. Edited: 5 Feb 2008, 6:28 a.m.
Re: 35s Programming (need help) - Valentin Albillo - 02-05-2008 Hi, Chuck: Chuck posted:
What to do ? Well, you'll have to replace one or the other with a user-created program, as simple and efficient as possible. As integration programs tend to be much more complicated and slower than root-finding programs, we'd do well to make use of the built-in Integrate and provide instead our own Solver. To that effect, I suggest you use something like the solver I created and proposed decades ago for its inclusion in the PPC ROM, which you can find in the following thread: Valentin Albillo's Root-finder If you visit that thread (which you should do, for the documentation if nothing else) you'll notice that I wrote the program for the HP-41C which was the rage at the time. For you to be able to use it in your HP35s, I'm providing the following converted (and slightly optimized) version instead
A001 LBL A where the Go at lines A006 and A019 is obtained from the CONSTants menu, defined as the "Conductance quantum", which evaluates to 7.748E-5 approximately. Once you've entered this simple, general, and quite fast root-finding procedure o'mine, you just need to define the equation to solve, which in your case is essentially Integral(0,X) = 6, which gets programmed in the HP35s as:
F001 LBL F I001 LBL I where LBL F is the equation being solved, which uses the built-in Integrate, and LBL I is the function being integrated, which is defined above as an RPN program segment. You can also define it as an ALGebraic equation, like this:
I001 LBL I which is shorter and possibly clearer, but the RPN version above is significantly faster to evaluate. Once you've entered the root-finder program (LBL A), the equation to solve (LBL F), and the function to integrate (LBL I), you can then proceed to specify the precision wanted (FIX 3) and supply a suitable initial guess (3) to get:
FIX 3, 3, XEQ A -> 2.305 in either 17 seconds for the RPN version of the function or 23 seconds for the ALGebraic version, whichever you chose. Hope this is more or less what you wanted. See the thread linked above for documentation on my root finder such as what happens if the computed derivative is zero or if the equation being solved has no real roots or convergence is extremely slow.
For solving equations with complex roots or complex parameters using your HP35s, have a look at my "Boldly Going - Going Back to the Roots" Datafile article published in Datafile September/October 2007 issue (V26N6P28).
Best regards from V.
Re: 35s Programming (need help) - Giancarlo (Italy) - 02-05-2008 Hey, Antonio - how about "V" == "K" in your equation above...? :-) Great job, Valentin! - Gene Wright - 02-05-2008 This is exactly the type of application I wish we'd see more of. Personal note: It appears I will be passing through your country (well, at least the Madrid airport) sometime in May. No, I don't expect we'll see each other :-) but I will think about you when my son and I are spending 4 hours waiting for the next flight.
Cheers!
Re: 35s Programming (need help) - Chuck - 02-05-2008 Valentin and Karl. Thank you so much for the outstanding replies. I will give the programming problem a go during my break today. My attempt was going to involve Newton's method to find the zeros (along with the Fundamential Theorem of Calculus Part 2), but I have a feeling the program length will be quite a bit longer. I would say your method IS as elegant as I was hoping. It looks like I'll have to pull out my 42s from the collection box and try something on that. Much thanks again. You guys are amazing here. :)
CHUCK
Re: 35s Programming (need help) - Valentin Albillo - 02-05-2008 Hi again, Chuck: Chuck posted:
"My attempt was going to involve Newton's method [...] but I have a feeling the program length will be quite a bit longer. I would say your method IS as elegant as I was hoping"
xi+1 = xi - f(xi) / f'(xi)so that's exactly how long it gets on the HP35s ! :-)
Re: Great job, Valentin! - Valentin Albillo - 02-05-2008 Hi, Gene:
Gene posted:
"I will be passing through your country (well, at least the Madrid airport) sometime in May [...] but I will think about you when my son and I are spending 4 hours waiting for the next flight."
At least I hope you'll enjoy a good flight and typical Spanish fair weather, and thanks for thinking about me. In all fairness, we having met would have ruined your mental image of me beyond repair. :-)
Re: 35s Programming (need help) - Karl Schneider - 02-06-2008 Hi, Gerson --
Quote: The somewhat-coarse "FIX 3" diminished the accuracy of the calculation of integrals. I chose it in order to to limit the execution time to a reasonable amount on the HP-34C, which is the slowest of the four RPN models I mentioned. The HP-15C will run the same program without modification, but slightly faster. Using "FIX 4", I got 2.306097460 on an HP-41CV with Advantage Pac, whose "SOLVE" and "INTEG" microcoded programs use the predecessor algorithms. Only slight changes to the program are needed -- alphanumeric external labels for the routines passed to SOLVE and INTEG. I'll post an HP-42S solution when I figure out exactly how to do it. Regards, -- KS
Edited: 6 Feb 2008, 2:29 a.m.
A link to real genius... - Karl Schneider - 02-06-2008 Hi, Antonio -- Well! Gosh! :-) I'm certainly pleased that you've appreciated my posts, in particular about the HP-15C. In truth, though, my response to Chuck's integration question was only a straight-ahead presentation of prior knowledge, without exceptional insight. Original work that some very smart people have presented and offered here is far more impressive. True genius is a very rare thing; the term ought to be applied with discretion. Here's one example from science and electrical engineering: http://en.wikipedia.org/wiki/Oliver_Heaviside Best regards, -- KS
Edited: 9 Feb 2008, 1:28 a.m.
HP-71B version - Valentin Albillo - 02-06-2008 Hi, Karl & Chuck: Karl posted:
> FNROOT(2,3,INTEGRAL(0,FVAR,1E-3,SQR(1+4*IVAR^2))-6)(result obtained in negligible time, or you can use 1E-12 instead of 1E-3 above to get full accuracy: 2.30609738256) which is as easy as it gets, as you don't need to write any program code, not even for the function to be integrated or the equation to be solved. Also, you don't need to "figure out exactly how to do it" as is frequently the case with the relatively complicated setup the HP42S needs to solve or integrate your programs. By the way, I'd like to see an RPL version of this. Taking into account that RPL supposedly is "the acme of power and flexibility", I expect the RPL version to be even simpler, shorter, and more immediate to concoct, enter, and execute than even my humble HP-71B solution above, right ? :-)
Best regards from V.
HP 49g / 50g version - Gene Wright - 02-06-2008 Actually, it was pretty easy as well. Here's what I did. I entered the equation writer environment and typed in: (integral from 0 to X of ( 1 + 4 x T^2 ) dT ) - 6 = 0 (Some of those parentheses are to help we humans parse the equation. I stored that into 'EQ' I entered the Num.Slv menu. I pushed down arrow to highlight the X row. I pressed Solve. Returned 2.30609738256
fairly quickly. Not bad and required no programming.
Re: HP-71B version - Egan Ford - 02-06-2008 From the stack: 50/50 ALG/RPL
100% RPL version is much faster. Edited: 6 Feb 2008, 3:53 p.m.
Re: HP 49g / 50g version - Valentin Albillo - 02-06-2008 Hi, Gene: Gene posted:
(integral from 0 to X of ( 1 + 4 x T^2 ) dT ) - 6 = 0 [...] I pressed Solve. Returned 2.30609738256"
Re: HP 49g / 50g version - Gene Wright - 02-06-2008 Yes, that amazing new "GuessUserIntent.lib" file that I installed recently is very helpful. Makes those of us who can't type get correct results more often. :-)
FWIW, I don't know how long the solution would take on a real 49g+/50g. I ran it in a second or so on Power48 on my Palm E2.
Re: (RPL) version - Karl Schneider - 02-06-2008 Good work, Egan!
Quote: Well, of course it is! On the HP-49G at least, the pure-RPL version computes the integral symbolically upon entry of the INTEGRAL symbol, then numerically solves only the antiderivative. The other solutions (including your "50/50 ALG/RPL" method) numerically estimate the integral as part of the function to be root-solved. The difference in speed would be much less for an integrand having no determinable closed-form integral. (This applies to the original HP-48, whose less-capable CAS tries but fails to perform the symbolic integration of this problem.) RPL novices (such as myself) should also note that " 'X' PURGE " is necessary if X exists; else, X will be evaluated upon entry instead of entered into the equation. -- KS
Edited: 6 Feb 2008, 11:58 p.m.
Re: HP 49g / 50g version - Karl Schneider - 02-07-2008 Hi, Gene -- Valentin stated,
Quote: Yours was a very sensible and straightforward approach, but my objection would be that it's not really RPL, which is what Valentin asked for. Egan Ford subsequently provided his solutions using algebraic-equation and pure-RPL approaches. The ability of the particular model of RPL-based calculator to symbolically integrate the equation will have a bearing on computational speed. It's also good that you titled your solution "HP 49G/50g version", because the same input might not work at all, or as well, on different RPL-based models.
-- KS
HP-42S solution for INTEG inside SOLVE - Karl Schneider - 02-07-2008 Here are several examples of an HP-42S solution for Chuck's arc-length calculation:
/ X Answer: 2.30609738393 This example shows many of the formalities that must be addressed when performing SOLVE and INTEG on an HP-42S:
And now, the vexing question: So, why can't the HP-32S/32SII/33s/35s run INTEG inside SOLVE and vice-versa? One minor issue is the following: Only one "FN=" statement is provided for use by both SOLVE and INTEG -- unlike the pair "PGMSLV" and "PGMINT" in the HP-42S. This is not a disqualifying limitation, as the information provided within "FN=" at invocation of SOLVE or INTEG could be stored elsewhere. However, this could cause some confusion to the user. More likely, the reason is that the programming effort to maintain this functionality was simply not performed, for reasons of budget or product differentiation. It is noted that integration requires 140 bytes, and SOLVE requires 33.5 bytes, on the HP-32S and HP-32SII, which respectively offer only 190 bytes and 184 bytes of allocatable memory. However, SOLVE and INTEG work together on the HP-34C, HP-15C, and HP-41 Advantage Pac, while requiring no more memory than does INTEG alone. Furthermore, the HP-33s and HP-35s have 31 kB of free memory. -- KS
Edited: 10 Feb 2008, 10:01 p.m. after one or more responses were posted
Re: HP-42S solution for INTEG inside SOLVE - Valentin Albillo - 02-07-2008 Hi, Karl:
That said, I still think that the HP-71B way is by far the easiest, most convenient, most general way of solwing this kind of problem, because:
Re: HP-42S solution for INTEG inside SOLVE - George Bailey (Bedford Falls) - 02-07-2008 Valentin, sorry for hijacking your layout ;-) But it's soooo neat...
Edited: 7 Feb 2008, 6:54 a.m.
Re: HP 49g / 50g version - Damir - 02-07-2008 With standard number format on a real 50g solution would take about 65 seconds and 5 seconds with Fix 3 number format. Damir
Edited: 7 Feb 2008, 7:21 a.m.
Re: HP 49g / 50g version - George Bailey (Bedford Falls) - 02-07-2008 Quote: Measured with the second hand of my watch 49G+ 93s (really, a tad faster) 50G 94s
Edited: 7 Feb 2008, 7:17 a.m.
Re: 35s Programming (need help) - George Bailey (Bedford Falls) - 02-07-2008 Quote:
Me neither in respect to the 35s. But I now found out that the manual tells us so in its 'messages' section.
Re: HP-42S solution for INTEG inside SOLVE - Valentin Albillo - 02-07-2008 Hi, George: George posted:
"I think that the HP 49+/50G way is by far the easiest, most convenient, most general way of solwing this kind of problem"
71B command line vs. 49g+ / 50g apps - Gene Wright - 02-07-2008 I'm pretty sure that Valentin's 71B command line approach would be somewhat / marginally faster than the EquationWriter / Num.Slv approach on the 49g+ / 50g. However, ISTM that there is a bit more syntax knowledge required to use the command line 71B approach than I did with the 49g+ / 50g application approach. The EquationWriter entry of the integral was fairly painless. I really didn't have to know what order to type in arguments - I just keyed in what appeared to be needed to "view" the integral. Num.Slv was a piece of cake too. Don't get me wrong, both the 71B and 49g+ / 50g approaches are MUCH faster/better than probably most other machines could muster. It is my opinion though that the 71B approach would require more knowledge of the command line syntax than any specialized knowledge needed on the 49g+ / 50g. And, yes, there is a :-) scattered throughout.
Personally, I wouldn't challenge Valentin to ANY programming contest...command line or NOT!
Re: HP-42S solution for INTEG inside SOLVE - George Bailey (Bedford Falls) - 02-07-2008 Valentin, ;-) 1: real programmers are punch card guys. Well, maybe even spoked metal wheel dials guys ;-) 2: my 50G essentially is master-cleared. And as for this specific problem, I can key in the whole integral in its equation writer with fewer keystrokes as you can type the word "INTEGRAL" on the 71B (actually I need 23, I was just bragging! 32 in total for the result as opposed to your 50 something key strokes. And I don't need an extra Math ROM...). And before we both ride off into the sunset: your 71B is longer than my 50G (just compared it). But my 71B is as long as yours!!! AND my slide rule is even longer!!!!!!!
Edited: 7 Feb 2008, 10:16 a.m.
Re: 71B command line vs. 49g+ / 50g apps - George Bailey (Bedford Falls) - 02-07-2008 Quote:
Yup, I've just hidden behind a tree, taken off my Stetson so he won't find me...
Re: HP-42S solution for INTEG inside SOLVE - Valentin Albillo - 02-07-2008 Hi again, George: George posted:
"I can key in the whole integral in its equation writer with fewer keystrokes as you can type the word "INTEGRAL" on the 71B (actually I need 23, I was just bragging!)."
The natural state of my HP-71B isn't master-cleared, of course, and I actually have a "keys" file in RAM which allows the INTEGRAL and FNROOT statements to be entered (together with their commas and parentheses) at the touch of a few keys in user mode. This also includes FVAR, IVAR, and many other such, so in actual practice I don't really need anywhere near 54 keystrokes to enter that expression, I had to actually count them one by one to get to know just how many were indeed required in a master-clear startup situation.
"AND my slide rule is even longer!!!!!!!"
Re: 71B command line vs. 49g+ / 50g apps - Valentin Albillo - 02-07-2008 ...
Best regards from V.
Re: HP-42S solution for INTEG inside SOLVE - George Bailey (Bedford Falls) - 02-07-2008 Quote:
Why, thank YOU for your 35S solution of Chuck's problem. It made me dive into my 35S more than I had before.
Re: 71B command line vs. 49g+ / 50g apps - George Bailey (Bedford Falls) - 02-07-2008 Quote:
Shit, why did I bring it? Could've left it in the corral with the others...
Re: HP-42S solution for INTEG inside SOLVE - Garth Wilson - 02-07-2008 If you really want to get picky, the 71 has a 2/3-size QWERTY keyboard. When I typed a lot on mine, I was able to do 30+wpm, which is just over half of what I can do on a full-sized keyboard. I quit typing memos and meeting notes on it when the 71 was discontinued and it was kind of sobering to think that I could wear out the keyboard and not have any HP support. By coincidence, I just had this discussion with a friend over the 50g and 71B a few days ago.
Re: HP-42S solution for INTEG inside SOLVE - Thomas Klemm - 02-07-2008 Quote: Re: HP-42S solution for INTEG inside SOLVE - Valentin Albillo - 02-07-2008 Hi, Garth: Garth posted:
over the 50g and 71B a few days ago. "
As for typing on the HP-71B, I remember you could attach an external
Re: HP-42S solution for INTEG inside SOLVE - George Bailey (Bedford Falls) - 02-07-2008 Quote: ;-) And for that there's a set of 71B commands as well
DESTROY ALL @ DIM UNIVERSE[INF] @ EVOLVE NEW CONST @ PRONTO
Re: HP-42S solution for INTEG inside SOLVE - Garth Wilson - 02-07-2008 Quote:There was no conflict about any of it, and he immediately agreed with me concerning the keyboard. He is very pleased with his new 50g though. It's his first HP, and it has gotten him interested in its ancestry-- especially the 41 and 71 which he is also interested in acquiring. But first he wants to expand the use of the serial port on the 50g to interface to lab instrumentation, an area of work we share. Re: 35s Programming (need help) - Marcus von Cube, Germany - 02-07-2008 The TI CAS caluculators manage the task easily: On the Voyage 200 (same for ti-92) you enter: solve(Integ(Sqrt(1+4t^2),t,0,x)=6,x) {Integ and Sqrt are symbols} The result appears after about 95 seconds: x=2.30609738256, accompanied by a warning that more than one solution may exist.
My Nspire CAS comes to the same result in about 4 seconds. The entry is with the equation writer and hence more intuitive than the older command line entry method. Edited: 7 Feb 2008, 7:23 p.m.
Re: 35s Programming (need help) - Marcus von Cube, Germany - 02-07-2008 When the function to solve is an integral, can't Newtons method be used "natively" by using the exact derivative instead of an approximation? xn+1 = xn - f(xn) / f'(xn)
In our case:
Am I right?
Re: 35s Programming (TI solution) - Karl Schneider - 02-08-2008 Hi, Marcus --
Quote: I have to admit, that's pretty good -- very straightforward. Several questions:
-- KS
Edited: 9 Feb 2008, 12:54 p.m. after one or more responses were posted
Re: HP 49g / 50g version - Chuck - 02-08-2008 You guys are all great: fun discussion. Since my programming skills aren't what they used to be, and no where near to most here), and since no one has mentioned the ubiquitous HP 200LX, I ran my equation on my 200LX running Derive, and it solved it in 10.1 seconds. Keystrokes: didn't count.
Thanks all for this great discussion, and for everyones insightful programming expertise. Looks like a good weekend coming up. CHUCK
Re: HP 49g / 50g version - George Bailey (Bedford Falls) - 02-08-2008 Quote:
Any photos? ;-)
Re: HP-42S solution for INTEG inside SOLVE - Karl Schneider - 02-08-2008 Hi, Valentin --
Quote: Thank you; it was an exercise I'd never completed, so the structure is more clear to me now. Really, the process for solving this problem and related ones on the HP-42S is fundamentally similar to that for the HP-15C, HP-34C, and HP-41/Advantage. It's just that more formalities must be addressed, due to the greater sophistication of the HP-42S' implementation of SOLVE/INTEG with programming. If one doesn't like RPL and doesn't have an HP-71B with Math ROM, then the HP-42S is the only Saturn-processor tool for the problem posed by "Chuck".
Quote: Not true for Egan Ford's pure-RPL solution, at least. The HP-48G finds the root, but takes a while because it cannot symbolically integrate the function, and must then use numerical integration. The HP-49G's more-capable CAS can do the symbolic integration, and finds the root quickly as a result.
Quote: I've got a well-equipped HP-71B, acquired piecemeal a few years ago through eBay and one benevolent Forum reader. It's got HP-IL, Math ROM, Surveying ROM, HP-41/71 Translator, (32 + 4 =) 36 kB of extra RAM. I have all paper manuals save for one, and all the manuals in electronic form. I've run programs you've posted and have made available, but I'm still not very skilled at the HP-71B. It will take much more time and effort, RTFM and "doing", in order to gain proficiency. While the design is well-engineered as the July 1984 HP Journal articles illustrate, it's still a small computer utilizing a high-level language having its own syntactical requirements.
-- KS
Re: 35s Programming (TI solution) - Marcus von Cube, Germany - 02-08-2008 Karl, it looks as if the CAS is the same in both machines. If I just enter the integral, it is solved symbolically: ln(sqrt(4x^2+1)+2x)/4 + x*sqrt(4x^2+1)/2 I assume that the solver operates on the solution. There is an nSolve command with parameters to direct it to a specific solution. I can't see how the accuracy can be influenced. The display setting doesn't make any difference. I tried the following on my Nspire: nSolve(nInt(sqrt(4*t^2+1),t,0,x)=6,x) It arrives at 2.30609738255 in a mattter of seconds, without any warning. If I set the inital guess to 2, the solution is returned within a second. Numerically solving the symbolic integral with an initial guess of 2 is even quicker.
Edited: 14 Feb 2008, 11:58 a.m. after one or more responses were posted
Particularized version - Valentin Albillo - 02-08-2008 Hi, Marcus: Marcus posted:
For the particular case of solving integral equations such as Chuck's, you can indeed make use of the fact that the exact derivative is available and further it's already needed and thus stored in program memory for the purpose of computing its integral, so it can be called at no extra cost. The resulting particularized program for the HP35s looks as this:
A001 LBL A A014 X=0?
which is three steps shorter, and much faster, taking just 9 seconds to compute the 2.305 root at FIX 3. This is almost twice as fast, but the price you pay for it is, of course, that this particularized version will only work for equations involving integrals in a similar way as the original Chuck's problem. By the way, I find it quite curious that my original message, which was #3 at the time I originally posted it, just after Karl Schneider's #2, is now at #36 and going down all the time as other much more recent posts are inserted before it. Come to think of it, this seems a good way to effectively get rid of someone else's posts: just post a large number of messages in reply to an earlier post than the one you want to get rid of, and it will simply go down into oblivion as no one will care to scroll down that long.
See what happened to my original listing: it's now so far from the beginning of the thread that anyone casually reading the thread will obviously think my reply was made much, much after the original request for help and after seeing tons of other people's messages and solutions when in fact it's exactly the opposite ! :-) Re: 35s Programming (an HP-34C/15C/41 solution) - Valentin Albillo - 02-08-2008 Hi, Karl: Karl posted:
LBL Bexecution: [...]
LBL Bwhich saves 3 full steps (50%). Looks smart as well, doesn't it ? :-) Best regards from V.
Re: 35s Programming (an HP-34C/15C/41 solution) - Karl Schneider - 02-08-2008 Hi, Valentin -- Hmm, I dunno. Your alternative is a clever optimization for fewest instructions, but it kind of "defeats the purpose" two ways:
Best regards,
-- KS Edited: 8 Feb 2008, 3:28 p.m.
Re: HP 49g / 50g version - Chuck - 02-08-2008 Here's the one in the garage: Dietzgen Here's the 7-footer in my office: Pickett
CHUCK
Re: Particularized version - Thomas Klemm - 02-08-2008 Hi Valentin,
Quote:
With 8 posts in this thread you're part of the problem.
Thomas Edited: 8 Feb 2008, 12:49 p.m.
Re: HP 49g / 50g version - George Bailey (Bedford Falls) - 02-08-2008 Chuck, And now I go hide where you won't find me. I'm scared! Your's are sooo much bigger than mine ;-)
But speaking of Dietzgen, I might take this one which can easily be attached to the belt "for a quick draw"... Edited: 8 Feb 2008, 2:19 p.m.
Re: 35s Programming (TI-82 solution) - Karl Schneider - 02-14-2008 Marcus -- OK, using your solution template, the TI-82 manual, and some experimentation, I got a solution on my 1993 TI-82. (Good thing it wasn't a "pressure situation"...) solve(fnInt(sqrt(1+4*T2),T,0,X)-6,X,{2,3}) yields 2.306093783 For "solve" in this problem, one or two guesses are required, even though the manual suggests that they are optional. (I used 2 and 3.) Also, a pair of guesses cannot be entered in descending order, for no justifiable reason. The value for the "tolerance" parameter for integration -- undefined in the manual -- is omitted in my expression, so the TI-82 uses a default value of 1E-5. The TI-82's Gauss-Kronrod numerical-integration method is very fast and accurate for routine, well-behaved integrals. I'm also sure that its microprocessor is no slouch, as the calc's 4 x "AAA" cells would suggest. However, the quadrature lacks the real-world sophistication of HP's implementation, such as evaluability at limits for which the integrand is undefined. -- KS
Edited: 16 Feb 2008, 1:44 p.m.
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