20 Replies Latest reply: Oct 29, 2010 8:41 AM by lvl107

# TRUE OR FALSE with this calculation ?

Hello all,

I really don't know that TRUE OR FALSE with this calculation ? Attach File below.

Regard,

Loi.

• ###### Re: TRUE OR FALSE with this calculation ?

Alan

• ###### Re: TRUE OR FALSE with this calculation ?

Alan Stevens wrote:

Alan

Viktor

• ###### Re: TRUE OR FALSE with this calculation ?

Mike

• ###### Re: TRUE OR FALSE with this calculation ?

The Maple kernel in MC11 also shows

The numeric calculation is wrong because of roundoff errors.

• ###### Re: TRUE OR FALSE with this calculation ?

The answer is FALSE. Even Mathcad 11's symbolic processor shows: The same result comes from Mathcad 14's symbolic processor, which is from a different source, i.e., MuPad vs. Maple.

So, Mathcad's numeric processor, which is limited in its numerical precision winds up truncating the answer. The symbolic processor's floating point answer is

which, with careful digit counting shows that the numeric processor of almost any calculator and any normal spreadsheet program will truncate the answer to 151, but it's not. You may wish to find some aribtrary precision calculators, some of which can be downloaded from the web, to verify the results. Prime factorization in Mathcad shows the ratio to be composed of products of different primes.

• ###### Re: TRUE OR FALSE with this calculation ?

Excel also says it's true.

151.00000

Mike

• ###### Re: TRUE OR FALSE with this calculation ?

.......................

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• ###### Re: TRUE OR FALSE with this calculation ?

Look at it this way:

Alan

• ###### Re: TRUE OR FALSE with this calculation ?

The question that needs to be asked is what definition of equality is required.

strict mathematical: exactly equal - answer is unproven but probably not (see Alan's post)

Finding a calculator that has higher resolution / precision may give more trailing zeroes but the reality is that at some point there must(?) be some inequality.

scientific:e.g better than1 part in 10^12 - yes, its good enough.

engineering: +/- 1% (usual tolerances that can be expected ...)

Andy

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>engineering: +/- 1% (usual tolerances that can be expected ...)

Or so, for example:

• ###### Re: TRUE OR FALSE with this calculation ?
The FPU (Floating Point Unit) is a separate part of your processor chip, dedicated to floating point (i.e., real number) arithmetics. It has been discovered that some parts of Windows 95/98 (or some drivers used by Windows) may affect the functioning of the FPU, reducing the accuracy of computations from about 19 to about 16 decimal digits.
Most applications will never notice this, as they are usually limited to the 16-digit precision of the C/C++ double type. Kalkulator, however, takes the full advantage of the built-in FPU accuracy, and this advantage is cancelled when your system's FPU performance is degraded.
Problems with the "old" Windows 95 System Agent
Microsoft admitted (in a quite understated way) that the System Agent, included with the Win95 Plus, was affecting the FPU performance. The problem has been fixed in one of the Windows 95 Service Packs, and it should not be present at all in Windows 98. The culprit was identified as one of the Windows' components, sage.dll (version 4.40.310), and the fixed version number is 4.40.311. Turning the System Agent off is also a good workaround.
Problems with other programs
This is not the end of it. Exactly the same problem may sometimes arise without the System Agent (or sage.dll) running. I have so far identified two programs interfering with the FPU and causing exactly the same symptoms:
·xwheel.exe by LCS/Telegraphics. This driver is included by many vendors with their pointing devices, touchpads in particular; probably more commonly seen on notebook computers. Removing xwheel.exe from the startup sequence fixes the FPU problem right away (in my Windows 98 tests I haven't lost any mouse functionality in the process).
·vshield.exe, a memory-resident part of the McAfee antivirus utilities. Again programs of this kind are known to cause problems often. Disabling the Virus Shield fixes the problem.
It is possible that these programs are not the real culprits here, but rather one of the Windows libraries they use; the bottom line remains the same.
Kalkulator work-around
Kalkulator runs a test for the FPU accuracy loss upon startup. If the problem is detected, the display precision setting will be limited to 16 (instead of 18) digits, and so will be the accuracy of some calculations. You will receive an appropriate warning when the FPU problem is detected the first time. If you change your system configuration (for example, by removing the offending program) and the problem goes away, the next time you run Kalkulator, it will detect this fact and give you a notice to this effect.
More on the FPU problem
You can find more details and updates on a Web page I have dedicated to it:
where you will also find a small diagnostics program checking for this condition, together with the (very brief) source code.
____________________________
Well explained by Richard & Eden
The "Machine precision" as explained in Mathematica, is 16 for Pentium IV XP , and there is a test for it it says my box is 16. There was another program causing failure of the floating point [Forge ?]. Ralston [if my recollection is correct] explained that the binary subtraction may eventually fail completely. That particular occurrence of numbers and operators will probably never happen in real engineering work, but nice to know it may cause some headache.
jmG
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Thanks all your help. Attach File below.

Regard.

Loi Le.

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Your question has been answered by Eden, Richard, more extensively by jmG

On my side: no need for more gyzma work sheet.

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jean Giraud wrote:

Your question has been answered by Eden, Richard, more extensively by jmG

More wrongly, you mean. It has nothing to do with other programs interfering with the FPU. It's just a property of numeric math.

On my side: no need for more gyzma work sheet.

No need for rudeness either.

• ###### Re: TRUE OR FALSE with this calculation ?

Your file contains only one of several possible ways that Mathcad can solve and display your particular examples. The particular method you've used is called "dead" symbolics, since any changes to the input equation will not be reflected in the answer.

The attached shows some of the other ways of seeing the answer, all using "live" symbolics.

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>On my side: no need for more gyzma work sheet.<

___________________________________________

You specified "Evaluation in Mathcad 12", thus gyzma version for lower than 12. In fact my Mathcad 11 did open. You can read more in the version 11 attached. Several points of interest [educative]: the fractional representation, PRN, some equivalent forms tough this last point does not apply directly in your examples

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Hi,
My English as Second Language is very little. I do Math just for recreation. I just only had Mathcad 12 and again I am beginner in using. I really still do not know any thing about Mathematica. ( Because I don't have it ). I was trying find the way to solve the Pell's Equation with N = 166, JUST WITH my calculator at home. When I input ( 3204668357^2 - 1 ) / 248730503^2 and the output is a INTEGER ! ( = 166 ). But after being helped from above, and now I do know I was failed with that root. Thanks again.
Regard,
Loi Le.

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"151, outside Pell range"

__________________________________

Often I pass Mathemica as a referee. Your Mathcad "machine precision" is 16 Pentium IV Win XP. For other Win OS: don't know. I agree that Mathcad is missing the error message or warning message "result outside of machine precision". From the Mathcad help, it is however hinted that gross mistake(s) need more attention. Between you and me, calculate the error in microns or diameter of an atom an error of 10e-16 represents at the top of a tower 1 km height !

jmG

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Thanks to all who replied.

Regards,

Loi Le.