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Re: Precision in Mathematica 6

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92286] Re: Precision in Mathematica 6
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 26 Sep 2008 06:25:38 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK

CaveSnow wrote:

*snip*

 > this is the things I written in my notebook
 >
 > FindRoot[\!\(
 > \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(t\)]
 > FractionBox[\(Sin[x]\), \(x\)] \[DifferentialD]x\) == 1, {t, 1}]
 >
 > N[t, 10] /. %

*snip*

 > In other words I used FindRoot to find the t that makes the definite
 > integral from 0 to t of sinx/x be 1.
 > As a result I got a certain rule, that had a small amount of digits
 > (only 6 of them). Then I issued the second command ti get more digits
 > from the result. But the result, even if I asked 10 digits remained
 > the same 1.06484.

*snip*

Here, you are working with machine/hardware-precision numbers (aka 
double-precision floating-point numbers), numbers that usually have up 
to 16 decimal digits.

To control the number of decimal digits that are displayed, you can use 
either *NumberForm* (see below) or goto menu "Preferences" -> 
"Appearance" -> "Numbers" -> "Formating" -> "Displayed precision", there 
change the field called "Number of digits displayed in output" from 6 
(the "factory" default) to whatever you wish.

Note that the above setting does not affect the precision of 
computations and you will not be able to display more that 16 decimal 
digits for machine-precision numbers.


   In[209]:= sol = FindRoot[Integrate[Sin[x]/x, {x, 0, t}] == 1, {t, 1}]
             Precision[t /. sol]
             $MachinePrecision
             Do[Print[NumberForm[t, n] /. sol], {n, 20}]

   Out[209]= {t -> 1.06484}

   Out[210]= MachinePrecision

   Out[211]= 15.9546

   During evaluation of In[209]:= 1.

   During evaluation of In[209]:= 1.1

   During evaluation of In[209]:= 1.06

   During evaluation of In[209]:= 1.065

   During evaluation of In[209]:= 1.0648

   During evaluation of In[209]:= 1.06484

   During evaluation of In[209]:= 1.06484

   During evaluation of In[209]:= 1.0648397

   During evaluation of In[209]:= 1.06483973

   During evaluation of In[209]:= 1.064839726

   During evaluation of In[209]:= 1.0648397255

   During evaluation of In[209]:= 1.06483972554

   During evaluation of In[209]:= 1.064839725537

   During evaluation of In[209]:= 1.0648397255366

   During evaluation of In[209]:= 1.06483972553656

   During evaluation of In[209]:= 1.064839725536558

   During evaluation of In[209]:= 1.064839725536558

   During evaluation of In[209]:= 1.064839725536558

   During evaluation of In[209]:= 1.064839725536558

   During evaluation of In[209]:= 1.064839725536558


Also, the tutorial "Machine-Precision Numbers" might be worth reading:

http://reference.wolfram.com/mathematica/tutorial/MachinePrecisionNumbers.html 


Regards,
-- Jean-Marc


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