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Well,
I picked up (read: tried) an 89Titanium this weekend, and must say that us hp fans have little to complain about.
My 89Ti errata:
There is NO x^2 key (where is it? The "^" key is hardly a workaround! ALL trig functions are shifted (either left or right). That should turn away any practical engineer. The keyboard compares to the first 49g (blue). Finally, why endure all this, when it doesn't even have RPN?
I'll happily take the gold dubloon (49g+) anyday :)
EL
12345
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There are programs that make TIs a RPN calculator. Just google ticalc.org for RPN.
Ciao.....Mike
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From the documentation
"Neither Lars nor I can recommend that you use the HW2PATCH to run RPN. It is truly unfortunate
that RPN will not run on the latest TI hardware and software. Future developments may solve this
problem."
This was written in 2000! It's referring to the old TI89  not even the new titanium edition.
It appears that the TI89 series often break things between ROM versions. Many programs rely on dirty hacks and need to be upgraded.
If you want a reliable, integrated RPN system, you still need to buy a HP. Pity about the hardware quality though.
.
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Yes  the TI tradition goes on with the latest Titanic ROM
HP is more reliable sans the new kb
I still take my 203MHz clocked 49g+ with 1GB SD rather that any TI.
the software simply rocks and the numerical matrix inversion is lightning fast!
(I think that even the HP71B and the HP28 models beat any TI)
[VPN]
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IMHO the discussion about using TI or HP calculators is like the talk about religion: just different ways up the mountain aiming to reach the top. Serendipitously I came across an HP41C  otherwise I would love my old TI.
Ciao.....Mike
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The enduring duel goes on..
Recently, a friend commented that a classmate was almost keeping up w/ my calculations on their Ti. To which I replied, yes, with that furious parenethesis and shifting, it is obvious that they are trying to race.
RPN looks effortless, and yet is so much faster than AOS. I think artsy types would refer to that as "elegance." :)
EL
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Aww yes... calculator racing. In calculus and physics, classmates have just about given up trying to beat my in numeric calculations. On occasion it would be a close race when I didn't know how to directly do numberic integration without first doing an indefinite integral, but since I figured that out, its all good.
RPN really does speed things up. My friends that just use a 32sii realize that RPN is faster for arithmetic, but having never used RPN for entering equations, they have no idea half the joy.
I'm lovin' it!
ben
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The calculated determinants for Hilbert matrices from order 7 through 10 as obtained with various HP and TI machines are listed below in order of increasing accuracy. All results in the table have been rounded to seven significant figures.
7x7 8x8 9x9 10x10
HP41 Math Pac 4.820822E25 2.437673E33 1.605584E42 1.046127E51
HP41 Advantage 4.836648E25 2.704536E33 6.435130E43 1.747106E52
HP49 Nonexact 4.835583E25 2.736296E33 9.802414E43 3.014075E53
HP28S 4.835592E25 2.736365E33 9.819514E43 3.281917E53
TI59 ML02 4.835807E25 2.737082E33 9.687516E43 Note 4
TI95 Math Module 4.835770E25 2.736821E33 9.728025E43 2.338510E53
CC40/TI74 4.835789E25 2.736781E33 9.689026E43 1.898080E53
TI83+ 4.835795E25 2.737004E33 9.721266E43 Note 5
TI85 4.835795E25 2.737004E33 9.721266E43 2.207089E53
HP49 Exact 4.835803E25 2.737050E33 9.720234E43 2.164179E53
Notes:
1. If you find errors in the tables let me know.
2. I do not have access to an HP71 or a TI89. Can someone provide those results?
3. The HP49 Nonexact results were obtained by entering the matrix in the exact mode but pressing NUM before calculating the determinant.
4. The TI59 ML02 program cannot calculate the determinant of a 10x10 matrix due to memory limitations.
5. The TI83 calculates the determinant of a 10x10 Hilbert as zero. It does not calculate the determinant of all 10x10 matrices as zero.
6. The exact determinants from the HP49 are:
7x7: 1 / 2067909047925770649600000
8x8: 1 / 365356847125734485878112256000000
9x9: 1 / 1028781784378569697887052962909388800000000
10x10:. 1 / 46206893947914691316295628839036278726983680000000000
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Hi,
Just some results for an HP86B with matrix module
7x7
4.835591945E25
8x8
2.7363743068E33
9x9
9.82002154449E43
10x10
3.28225800765E53
Edited: 21 Apr 2005, 6:03 a.m.
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Hi, Palmer:
Palmer wrote:
" I do not have access to an HP71 or a TI89. Can someone provide those results?"
Download the freeware HP71B emulator Emu71 from here at you're all set.
Best regards from V.
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Hi Palmer. I agree with your results for the HP 49G+ and TI83+. By the way, thanks for the post. I learned something from it!
There may be others out there who like myself were not familiar with the Hilbert matrix. A search on google yielded the following description:
http://mathworld.wolfram.com/HilbertMatrix.html
John
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that despite the praise heaped upon the HP15c (and a few other HP's), in a good number of cases, the TI59 continued to run circles around them...these matrix results being but one example.
in fact, until the exact mode on the HP49g and HP49g+, the TI59 outperformed the HP28S and HP48 series. :)
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Hi, Gene:
Gene posted:
"that despite the praise heaped upon the HP15c (and a few other HP's), in a good number of cases, the TI59 continued to run circles around them"
You're joking, right ? Going down to the very, very, very basics, multiplication is neither commutative nor monotonic on the TI 59. Just try
e*Pi  Pi*e
and see what you get. Then try this same rocketscience computation in an HP15C and marvel at the nice "0" you get. I guess it should come as a surprise to any seasoned TI user !
Now, seriously. If the TI59 can't get its basic arithmetic right, can't you really trust all other functions that absolutely depend on it ?
And this is not a case of a contrived example, but one of an incredibly huge multitude of cases where the TI59 basic math algorithms put themselves to shame. I challenge you to produce even one case where an HP15C multiplication fails to be commutative (i.e. a*b # b*a) or monotonic.
Best regards from V.
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There are basic matrix calculations where the HP15c is several orders of magnitude LESS accurate than the builtin ML02 program in the TI59 module.
Take a look at the Hilbert Matrix results, Valentin...the HP41 advantage module matrix code (based on the HP15C) is worse than the old TI59!
If you search through the archives, you'll find several posts by Palmer that will point out how the 15c fares poorly compared to the older TI59 ML02 program.
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http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv014.cgi?read=59485
The HP15c's error is over 400 times larger than the TI59 in this test.
Perhaps we should say that if you can't trust the 15c beyond 5 or 6 decimal places, then perhaps it shouldn't be used? :)
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Hi again, Gene:
I don't want to start a 'religious war', much less against you, but please follow the thread of your own link.
If you do, you'll see the results I gave re this case, in particular the fact that a single step of refinement (available on the HP15C as a microcode function, for superb speed and accuracy, but nowhere to be seen in the TI59) provided the exact result, with zero error.
You're happy with the TI59's crappy math and the slowness of its usercode matrix programs versus the HP15C's microcoded ones ? Good for you.
Best regards from V.
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Valentin, it seems you're displaying the same attitude you criticize regularly in others.
How many times here have you complained about an individual's attachment to RPN when your nice casio's produce better results?
Yet, with the Hilbert problem, it certainly appears that the TI59 gives a better answer than the HP41 math pack, HP41 advantage pack, and the HP28S. And, since the advantage pack was based on the 15c, it seems likely that the TI59 would to beat it too.
My point is the same one you usually make but seem to have taken offense to here...
The best calculator for the solution to a problem often varies depending on the problem.
You point that out when you believe your casio's are better than an RPN machine.
But yet here... :)
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Hi reagain, Gene !
Gene posted:
"Valentin, it seems you're displaying the same attitude you criticize regularly in others."
It's weekend and I'm in a playful mood, Gene ! Take no offence, man, peace !
"How many times here have you complained about an
individual's attachment to RPN when your nice casio's produce better results?"
See ? You're not paying attention ! I've never said a word about "nice casio's", I only do SHARPs (with capitals and all ...)
"My point is the same one you usually make but seem to have taken offense to here..."
Not a chance, I'm only teasing you, out of sympathy. I know you are quite sensitive in all matters TI and I just poke at you from time to time, specially when ...
"You point that out when you believe your casio's are better than an RPN machine."
... when you're not paying attention: I've got *no* casio's, I've got *SHARPs*. Repeat with me: I've got *no* casio's ... :)
You know what ? The "problem" with you guys is that you always take me far too seriously, taking all I say at face value, so you tend to see offence, be it on your part or my part, where in fact there's none, at least as far as I'm concerned. Have a nice weekend and
Best regards from V.
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Yep, was in a casio mood today and that caused the disconnect. Perhaps it was because they were mentioned at the top of this thread:
http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv013.cgi?read=43770
which I was reading just prior to my post. Apologies in labeling you a "casio" user. BIG :)
I do hope you saw the :) in my post...that is my alert to you that I am certainly not mad.
It IS very interesting that in Palmer's post, the TI machines take the top spots in accuracy (other than the exact mode 49g/49g+).
Gene
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Howdy chaps, not that you need a hand with your math expertise and calculator prowess, but just to set the record straight, and to the extent of my necessarily limited knowledge:
The Advantage matrix functions are not based upon on those from the 15C, but rather on the CCD Module.
Maybe this is relevant to your discusion, or maybe not.
Best,
ÁM
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Your are, of course, correct that the TI59 has a non commutative multiply such that e times pi is not equal to pi times e, and that HP products such as the HP41 and HP15 find that the products are the same. The actual results using machines in my collection are
Exact product: 8.53973 42226 73986 ...
TI59 e x pi 8.53973 42226 73
TI59 pi x e 8.53973 42226 45
HP11, HP41 8.53973 4222
I don't have an HP15 but I will take a chance and presume that it gets the same answer as the HP11 and HP41. When you compare the results with the exact answer you find that error in the HP result is substantially larger than either of the TI59 results. The values calculated for determinants of Hilbert matrices show that the TI59 gets substantially better answers than many HP calculators which use ten or twelve digits. That's what the thirteen digits used by the TI59 does even when using a noncommutative multiply.
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Let me add the results for the HP 42S and the TI95 PROCALC:
Exact product: 8.53973 42226 73986 ...
HP 42S: 8.53973 42226 8
TI95 PROCALC: 8.53973 42226 71
The moral: Don't count on the last digit! The relative error on both machines is directly related to the number of digits (12 versus 13).
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Hi, Palmer:
Palmer posted:
"The calculated determinants for Hilbert matrices from order 7 through 10 as obtained
with various HP and TI machines are listed below in order of increasing accuracy. All
results in the table have been rounded to seven significant figures.
[...]
HP49 Exact 4.835803E25 2.737050E33 9.720234E43 2.164179E53
[...]
2. I do not have access to an HP71 or a TI89. Can someone provide those results?"
Why, of course ! Here you are:
>LIST
10 ! ** Determinants for Hilbert matrices from order 7 through 10 **
20 !
30 FOR N=7 TO 10 @ P=1 @ FOR I=1 TO N1 @ P=P*FACT(I) @ NEXT I @ Q=1
40 FOR I=N TO 2*N1 @ Q=Q*FACT(I) @ NEXT I @ DISP N;P^3/Q @ NEXT N
>RUN
7 4.83580262391E25
8 2.73705011379E33
9 9.72023431183E43
10 2.16417922642E53
Pretty accurate, innit ? :) Have a nice weekend !
Best regards from V.
Edited: 22 Apr 2005, 11:30 a.m.
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Thank you for the HP71 results. I had tried to call up the HP71 emulator as you suggested in an earlier transmission. I won't live long enough to figure out how to use that.
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I was surprised at the quality of Valentin's results since I had been told that the HP71B used a twelve digit mantissa. When I looked at his program I concluded that it was a special purpose program which will calculate the determinant of a Hilbert matrix but has no obvious capability to calculate the determinant of a general matrix. I converted his program for use on a TI59 and received the following results:
Order Determinant
7 4.835802623920E25
8 2.737050113787E33
9 9.720234311907E43
10 2.164179226428E53
Pretty accurate I would say, particularly for a machine which is said to be unable to multiply properly.
Clearly, Valentin's results for the HP71B and my results for the TI59 using Valentin's algorithm are not "apples to apples" with the comparative results in my table. Those results were obtained with Hilbert matrices submitted to general purpose determinant solutions which are part of solutions for linear equations. So, I still need some comparative HP71B results.
My 66 step TI59 program is a straightforward translation of Valentin's program with a few exceptions. The Q value overflows the storage range of the data registers of the TI59 for the tenth order Hilbert. To circumvent that problem the calculation sequence was changed as follows:
1. The P value is accumulated in a data register.
2. The cube of P is placed in the data register by recalling P and executing two PRD commands. Experienced TI59 programmers know that this yields more accurate answers than using the y to the x function.
3. The factorials which make up the Q value are divided into the cube of the P value using the INV PRD command.
4. The answer is recalled from the data register at the end of the program.
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These results are for a TI Voyage 200, AMS 2.09, which should be the same as the TI89. The Hilbert matrix entries are floatingpoint, and the determinant is calculated with floatingpoint arithmetic. Exact results for all test cases can of course be obtained with exact elements, and determinant calculation in Exact mode. The numbers in parentheses are the absolute error.
7x7: 4.8357 9853 3552 9 E25 (4.09 E31)
8x8: 2.7370 2158 7761 2 E33 (2.85 E38)
9x9: 9.7211 0716 1519 9 E43 (8.73 E47)
10x10: 2.1916 3783 1282 3 E53 (2.75 E55)
11x11: 0.0
In Exact mode the v200 can find the determinants of matrices sized up to 32x32 before 'Overflow' occurs, if you're willing to wait long enough. The determinant of that matrix is
1/342300937718736341875316480694578784160478532570744843022264
377411818016285649738348396640425838323111117643177083857527
276276421624540790363149391173439489387650276374486251367769
429081436663844014829697166121277156684389942674837249246526
267123532975018955221253356628757271358868395656787942359708
437922987111302598136409090699353808023856084601016357189208
945183452186767000583426895387929067112911767034725732791540
516268984917654473757454636544696668840459248858012619416258
814034046230919546185393229029514072344286649792394690560000
000000000000000000000000000000000000000000000000000
or about 2.92141 E592
(12345 to delete)
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It seems that a somewhat subtle point in all these comparisons using Hilbert matrices is being overlooked. What I'm going to say only applies to calculators *not* in exact mode. Consider what happens when you enter the 2x2 Hilbert matrix manually. You probably enter the matrix editor on a TI or HP machine and type in 1, 1/2, 1/2, 1/3; but the calculator cannot accept exact rational numbers (fractions), so it converts these numbers to floating point numbers. The result is that you have the numbers 1, .5, .5, .33333333333333 on a TI85 and similar recent TI machines that use 14 digits to store numbers, or you have 1, .5, .5, .333333333333 on Saturn based HP calculators.
The same thing happens for the higher order Hilbert matrices; the matrix stored in the calculator is not the exact Hilbert matrix, but an approximation to it. So when you then calculate the determinant of the approximate matrix stored in the calculator, you shouldn't expect to get the exact determinant for that particular Hilbert matrix.
What should you reasonably expect? Use a calculator that can do exact arithmetic such as the TI89 or HP49 and use these values for the Hilbert matrix (2x2 for this example):
To determine what a TI calculator which uses 14 digits to store its numbers *should* get, use
1, 1/2, 1/2, 33333333333333/100000000000000 and calculate the determinant of *this* matrix on the TI89 or HP49 (or use a PC program such as Derive, Maple, or Mathematica which can do exact rational arithmetic).
To determine what an HP Saturn based calculator *should* get, use 1, 1/2, 1/2, 333333333333/1000000000000 and calculate the determinant of *this* matrix with exact rational arithmetic.
Extend this technique for the higher order Hilbert matrices. For example, here are the last three numbers in the last row of the matrix which should be used with exact rational arithmetic to determine what a Saturn based calculator *should* get for the determinant of a 7x7 Hilbert matrix:
......909090909091/1000000000000, 833333333333/1000000000000, 769230769231/1000000000000
It isn't reasonable to expect *any* calculator which uses floating point arithmetic (and not exact rational arithmetic) to get the *exact* determinant of a Hilbert matrix because the input to the determinant calculation *isn't* the Hilbert matrix, but an approximation to it. The best it could possibly do is to get the *exact* determinant of the approximation to the Hilbert matrix which your calculator has stored. So don't compare the result a floating point calculator gets for a Hilbert determinant to the *exact* value for that particular Hilbert Matrix. You can't expect your calculator to get that result. It should in fact get the result from the procedure I described above, and you should use that result to compute the relative error for various calculator's calculated Hilbert determinants. For example, adding to Palmer's table:
7x7 8x8 9x9 10x10
HP41 Math Pac 4.820822E25 2.437673E33 1.605584E42 1.046127E51
HP41 Advantage 4.836648E25 2.704536E33 6.435130E43 1.747106E52
HP49 Nonexact 4.835583E25 2.736296E33 9.802414E43 3.014075E53
HP28S 4.835592E25 2.736365E33 9.819514E43 3.281917E53
TI59 ML02 4.835807E25 2.737082E33 9.687516E43 Note 4
TI95 Math Module 4.835770E25 2.736821E33 9.728025E43 2.338510E53
CC40/TI74 4.835789E25 2.736781E33 9.689026E43 1.898080E53
TI83+ 4.835795E25 2.737004E33 9.721266E43 Note 5
TI85 4.835795E25 2.737004E33 9.721266E43 2.207089E53
HP49 Exact 4.835803E25 2.737050E33 9.720234E43 2.164179E53
HP41 should get 4.835822505E25 2.709988486E33 8.587780880E43
HP Saturn should get 4.83558199919 2.73630981825 9.80342803933
TI85 should get 4.8357998501314 2.7370410057623 9.7218653313429
I left out the exponents of the last two lines to save space.
HP Saturn includes the HP28, HP48S, HP48G, etc., but the HP48G and HP49 (approximate mode) will give better results than the earlier Saturn machines because the matrix arithmetic was reworked to use 15 digits for all internal matrix calculations.
According to these numbers, the relative error the TI85 gets for the 7x7 Hilbert matrix is 1.0029e6. The relative error for the HP49 nonexact is 2.068E7. This value is not quite right because Palmer reported an insufficient number of digits to accurately calculate the relative error. (There may be a similar problem with the reported results for the TI85.) More digits would allow an improved result for relative error. The HP48G gets 4.83558259986E25 for the determinant for a relative error of 1.24E7 which is also what the HP49 (nonexact) gets.
Another way around the problem is to multiply a Hilbert matrix by the least common multiple (LCM) of all the denominators in the original Hilbert matrix, and find the determinant of *this* matrix. This replaces the Hilbert matrix with another which contains only integers, which can be represented *exactly* on a floating point calculator. For a Hilbert matrix of order n, divide the determinant of this "integerized" matrix by the LCM of the denominators of the original Hilbert matrix, raised to the power n, and that will be the determinant of the original Hilbert matrix. Or, just calculate the determinant of the "integerized" matrix exactly on a TI89 or HP49 (or Derive, etc.) and compare that to the result gotten from the floating point calculator.
As an example, the LCM of the denominators of the 7th order Hilbert matrix is 360360. The exact determinant of the 7x7 Hilbert matrix which has been multiplied by 360360, is 381614277072600. The HP48G gets 3.81614292044E14, for a relative error of 3.92E8. Readers could try this on their own calculators and report the results. And beware, you can't just take the 7th order Hilbert matrix already stored in your floating point calculator and multiply it by 360360 to get the "integerized" version. In the process where you created the Hilbert matrix by inputting 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, etc., instead input 360360/1, 360360/2, 360360/3, 360360/4, 360360/5, 360360/6, 360360/7, etc. This guarantees that you get integers.
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My first exposure to the use of Hilbert and subHilbert matrices to test the capability of matrix processing calculator mechanizations dates back to the HP vs TI competitions in the late 1970's and early 1980's as docmented in the PPC Calculator Journal and in 52 Notes (later TI PPC Notes). The idea was not that we needed the answers for the various Hilbert problems. In general, the answers were already well known. Rather, the idea was that the Hilberts provided challenging problems which could be used to assess the relative capabilities of machines and software.
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You say: "...the Hilberts provided challenging
problems which could be used to assess the relative capabilities of machines and software."
I'm not disputing that at all. I'm simply pointing out that when testing a calculator that doesn't do exact rational arithmetic with a Hilbert matrix, one shouldn't compare its results with the exact solution to that Hilbert matrix. The calculator couldn't get that result even if it could do *perfect* floating point arithmetic, because the matrix it's starting with *isn't* the Hilbert matrix.
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I am still working on your transmmission of April 24. In the process I will try to publish a table with more digits. I had done the exact work on an HP49 loaned to me by Gene. Unfortunately I have returned it to him so I have to get the exact answers elsewhere. I may have an old multiprecision divide program which I will use if I can find it. Meanwhile I will offer comments based on my preliminary interpretation.
You seem to be saying that it doesn't make sense to compare a result from a nonexact machine with an exact result because the nonexact machine can't be expected to get the exact result. I see things another way.
I do think that comparing the result from a nonexact machine with the best results that can be expected from that machine is useful in evaluating software. I refer you to the entries in my table for the HP41 with two different sets of matrix software; namely, the Math Pac and the Advantage packages. The entries for the 7th and 8th order determinants clearly show the superiority of the Advantage software. Other testing with Hilbert and subHilbert matrices not published here shows the superiority of the Advantage software for other matrix functions as well.
But what if a potential user is deciding between machine/software combinations? Does he really much care if a machine and its software does nearly as well as it can do; that is, that the designers of the software got nearly as much out of the machine as it can deliver? I submit that he should care if the machine and its software are capable doing as much as his application requires. To make that kind of comparison the potential user needs to compare the results of the various machine/software combinations with the exact result.
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You said: "I do think that comparing the result from a nonexact machine with the best results that can be expected from that machine is useful in evaluating software."
I totally agree with this statement because that is exactly what I am saying. In using the Hilbert matrices to evaluate calculators, it is good to know what is the *best* a 12 digit (or 10 digit, or 14 digit) floating point machine could possibly do. What I showed in my earlier long post is just how to find the best that can be expected from an Ndigit floating point calculator, keeping in mind that the best that can be done is *not* the exact result. That is an unrealistic goal for a nonexact, floating point calculator.
You said: "I refer you to the entries in my table for the HP41 with two different sets of matrix software; namely, the Math Pac and the Advantage packages. The entries for the 7th and 8th order determinants clearly show the superiority of the Advantage software. Other testing with Hilbert and subHilbert matrices not published here shows the superiority of the Advantage software for other matrix functions as well."
This is all quite true and making your comparisons with the *best* that Ndigit floating point software can do rather than with the *exact* results with Hilbert matrices doesn't change any of your conclusions.
Just to give further examples, here's a table showing the relative error made by the HP48G, the HP48S and the TI86 (which I own. It gets the same result you got for the 7x7 with the TI83+ and TI85). I show the relative error for the determinant of a 7x7 Hilbert matrix compared with the exact result and compared with the *best* you could expect from each of these machines. Notice that the relative error computed with the exact Hilbert determinant would indicate that the HP48G and HP48S are very similar in their results.
But the relative errors computed with the *best possible* result shows that the HP48G is substantially more accurate (that is to say, its arithmetic is better) than the HP48S for matrix determinants. In fact, the matrix arithmetic for the HP48G was reworked by Paul McClellan to use 15 digit numbers for all internal computations and is improved by more than an order of magnitude over the 48S. Even the TI is better than you would have thought by computing the relative error in comparison with the exact Hilbert determinant.
HP48G HP48S TI86
Rel err using exact det 4.55e5 4.358e5 1.577e6
Rel err using *best possible* 1.24e7 2.04e6 1.0027e6
This table would seem to indicate that the HP48G is *better* than the TI86. As an unqualified statement that would be false. What we *can* conclude is that the HP48G lives up to it *potential* better than the TI. In other words, the HP48G does a better job with its 12digit arithmetic than the TI does with its 14digit arithmetic. Neither the HP nor the TI gets what it *should* get using the arithmetic it has. I am much more familiar with the internal workings of the HP than the TI and I know that part of the reason the HP doesn't do somewhat better is that HP didn't do proper "round to even" for 15 form numbers.
All other things being equal (ceteris parabus, as the Romans would say), it is better to have more digits. The Saturn series of 12digit calculators is *better* than the HP41's 10digits, and the TI's 14digit arithmetic is *better* is some ways than the HP48. It certainly returns 2 more digits for simple functions like sin, sqrt, +, , *, /, etc. But they still don't do their basic arithmetic as well as the HP machines, and these examples of the Hilbert determinants show it, if you compare relative errors using the *best* an Ndigit machine could do as your reference. So that if you work a problem that has a *lot* of number crunching, the HP48 with its 12digit arithmetic may give a more accurate result than the TI with its 14digit arithmetic.
In the case of the Hilbert determinant, TI has improved their arithmetic enough that the 14 digit TI85 gets a result closer to the *exact* result than the HP48G. Since they compute the determinant with 14digit arithmetic, we would expect that they would get a less accurate result than the HP48G which calculates the determinant with 15digit arithmetic.
**The reason they don't is due to the fact that the 7x7 Hilbert matrix stored in the TI has 14 digits per element, so they are computing the determinant from a more accurate starting point.**
If you were to store the 7x7 Hilbert matrix in a HP48G in 15 form and then compute the determinant, you would probably get a much better result than the TI. Maybe somebody will try this.
To say that a problem is illconditioned is to say that it is extremely sensitive to initial conditions. That is the case with the Hilbert matrices, and that is why *starting* with more digits is more important than doing the arithmetic with one more digit.
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You write
"... All other things being equal (ceteris parabus, as the Romans would say), it is better to have more digits. ..."
I couldn't agree more. My first exposure to the idea came back in 1961 while working on an inertial navigation system. We observed that there was a tendency for longitude errors to go in one direction. One member of our team showed that truncation effects in our stateoftheart 20 bit M252 machine was the cause.
I have managed to generate the full length results (as opposed to the rounded seven digit values in my original table) for the HP41 with the Math Pac, the HP28, the TI59, TI85 and TI95. I note that Valentin has started a new thread. I will stop entering data in this thread and move there.
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To the 89Titanium's defense, it is more straightforward (though much slower) to do simple things like integrate and take a derivative or solve an equation. I rarely use mine (lent to me by the school) because it just takes so long to input equations... plus it is slow.
Of course, my 49g+ is annoying me more and more as my ON button has become unsocketed... it now moves about rather than staying put. Makes little difference, but i feel bad pressing it.
I am tempted to try and get HP to replace it, even though it is a premarket model. Is the newer keyboard worth it, with respect to the original 49g+ keyboard?
Ben Salinas
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Ben,
Sorry to hear about the kbd deterioration. Here are my takes on the models I've had: The *snap* of the older ones feel better. The newer one requires less force to depress keys. The older keys are glossier, while the new keys have a rougher texture.
Are you experiencing the "other" issues, such as missed presses? I've seen much less trouble after installing the clockspeed tools (I use 124) found on hpcalc.org.
Since you've used the Ti89, how DO you square numbers in routine use? Do you have to hit the "^" key and then 2?
On the replacement issue, you could forward hp an email or call to this effect: I am grateful for the 49g+ preprd example. However, I have begun to experience this and that..any advice on what to do?
Best regards,
BTW, I glanced at Olin's site, sounds interesting!
Eric
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I don't miss too many keystrokes now that I am used to using it. At first I missed a fair amount, but it is nothing a quick undo can't correct. Frankly, the 49g+ took me from hating all graphing calculators (something I mentioned just before Tony Jones, worldwide director of product development for HP, gave me the prerelease 49g+... oops), to being able to tolerate, and even enjoy using one. I definitely don't use the 49g+ to its full potential, but the features it has are wonderful (totally beat the TI89 anyday).
When I do use the 89 (which is very seldom), I spend 34 times as long entering an equation because I cannot think in algebraic mode. I can't figure out, "I need to put 5 open parentheses here to make this equation work", so I always go back and put parentheses as I need them. (Plus closing parentheses is crazy). I use the ^ and 2 buttons for squaring a function.
I probably will send my 49g+ back, but probably not till after the AP exams (which start in just under 2 weeks). I will need my 49g+ for the calculus AP (no scientific calculators allowed), and for my Calc semester exam (next week). After that I won't use it again till next school year, so there will be plenty of time to mail it back.
Ben
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I have also had the problem of a disconnected key on my 48gii. For me it was the 2 key that acted like a tooth about to fall out.
I could rant about the other 3 hps I have gone through in the past few months, or the one that is overdue for arrival, but suffice it to say the keyboards have not changed much since the first one (it had rom 1.22)
If you ask, you could probably get a replacement pretty quickly, by the end of this week. All except the one I am waiting for (it may not have been sent) were FedExed with a two day shipment.
Billy
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Hi Billy. Have you noted the serial numbers associated with all of your 49G+'s? That information would be useful is helping to determine whether or not the keyboards are getting any better with subsequent production lots. I've got a 428... and it seems to work fine.
Regards,
John
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>Is the newer keyboard worth it, with respect to the original 49g+ keyboard?
Yes. The old keyboard is garbage in comparison. There are sill some missed keypressed.
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By all means ask. Hp knows about their early model problems and should do something. If it is beyond warrenty and you do not want to fight to hard, you can just pay the replair fee (you send in old calc and payment). They don't bother to repair, but replace with a new unit. Hp's repair fee is 2550% the cost of a new calculator.
I think you should be able to get a free replacement if you whine enough, but if not, $3060 would probably get you a new Hp49G+ which is worth it also.
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EL says:
"My 89Ti errata:
There is NO x^2 key (where is it? The "^" key is hardly a workaround! ALL trig functions are shifted (either left or right). "

1) What's the big deal about a x^2 key? That is a SHIFTED function on my HP41CX, 48SX, 48G and 49G. I don't have my 49G+ or 33S handy, so I'm not sure of the situation with them.
So it takes TWO keystrokes to square a number on my HPs and it takes the SAME number of keystrokes to square a number on the TI89/92/92+/Voyage200. So what?
2) Granted trig functions are shifted on the TI89. However, the big advantage of the Voyage200 (and older 92 & 92+) over the TI89 is UNSHIFTED trig functions.
3) My biggest objection to the TI92/92+/Voyage200 keyboard is that EE is a shifted function (just as it is on the lesser models of TI, such as the 83, 84, 85 & 86).
Oh well...........
Mark
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I wondered about all the fuss over shifted trig functions. I looked at my TI collection and found that the great majority of TI calculators have trig functions which are not shifted. That includes the TI30, SR40, SR52, SR56, TI68, and TI80 through 85. The exceptions are the TI57, TI58, TI59, TI66 and TI89. I never had noticed the difference.
I looked at my HP collection and found that the trig functions were not shifted on the HP35, HP45, HP41, HP11, etc. The trig functions are shifted on the HP27, HP33C, and notably the HP67. Again, I never had noticed the difference. Does anyone really think that the shifted trig functions on the HP67 turned practical engineers away from that device?
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I would guess that it depends.
If someone uses SIN or COS constantly, then it might.
But then, someone might use Y^X constantly and if it were shifted, that might make someone disappointed.
I personally think it is just one way to put an "X" against the TI89. :)
don't get me wrong, the keyboard layout of the TI89 is not one that I particularly like, but I'm not sure shifted trig is a big problem, unless the above applies!
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Mark,
You stated:
So it takes TWO keystrokes to square a number on my HPs and it takes the SAME number of keystrokes to square a number on the TI89/92/92+/Voyage200. So what?
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HP's traditionally (bar the 33s) feature x^2 and x^0.5 that are assigned to the same key. Typically the square is primary and then the root is LS of the same key.
Now, you mentioned the # of keystrokes to do square a number. to square 3 on a TI requires, [3 ^ 2 ENTER], that's four strokes. Remember, you want the result, right? You must therefore count the ENTER key stroke.
On an HP, it would be [3 LS SQR], only 3 keys.
Now, if you take the root of 3 on a TI, you'd key in [3 ^ . 5 ENTER], that's five strokes versus only TWO on an HP. Plus, as the number of keystrokes increases, one is tempted to do a brain calc approx instead.
The voyager is just too large to carry around, for me. Plus I'd feel pretty childish pulling that out in an engineering class. They're (ti's) are considered high school gaming machines around my circles. But, enjoy the calc you like.
That's two cents I can afford to lose :)
EL
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I was at WALMART today and saw an HP33S in their calculator display. The first thing that I noted was that the keyboard in not laid out in a rectangular grid but the old horizontal rows have been changed into arcs. Then I noticed that the TI84 Plus also has the old horizontal rows changed into arcs. What is that all about? My best guess is that it has something to do with the younger calculator users. I have heard that they no longer hold their calculators in the palm of one hand and press the keys with the index finger of the other hand, but rather hold the calculator between their hands and press the keys with their thumbs as they learned to do when playing games. Is that really what they do? Is the keyboard layout of the HP33S and TI84 Plus the wave of the future?
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"... Is the keyboard layout of the HP33S and TI84 Plus the wave of the future?
Oh, boy! I hope not. I got used to the 33S, but hope later models will reincorporate the more traditional layouts.
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I think the typical calculator usage scenario for the younger users (= high school students) has the calculator lying on a table, surrounded by other clutter like paper and pens etc., and being used without being held in the hand.
Speaking personally, when I use a calculator while holding it in my hand, I usually hold it in my right hand and press the keys with my right thumb. On the Woodstocks and 41 that works fine; for the Voyagers and 42S, I do what you described: I hold the calc with both hands and use both thumbs (unless I'm just doing basic arithmetic: then all the keys I need are within reach of my right thumb).
This has nothing to do with playing games  I do own a Game Boy, but I was using calculators long before that (I'm 40). I think the "chevron" key layout is just a gimmick to make the 33S look "cool". I'm sure it's successful  this is what you do when targeting a demographic that buys colored face plates for their cell phones!
 Thomas
