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MathGroup Archive 2006

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Re: Two questions (1) Sollve and (2) Precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67065] Re: Two questions (1) Sollve and (2) Precision
  • From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 8 Jun 2006 04:54:05 -0400 (EDT)
  • References: <e666j8$nbj$1@smc.vnet.net> <4486B0CA.3060002@gmail.com> <a3224ef10606070653u22303b57g87c303547b8913ab@mail.gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

On 6/7/06, Bharat Bhole <bbhole at gmail.com> wrote:
>
> Thanks for your help Jean-Marc. I really appreciate it. I have two comments
> about your response, and it would be very helpful if things work on your
> computer after taking these into account.
>
> (1)  As I replied to all, somehow my equations were posted with an error.
> The right hand sides in the two equations were 1 and 0 respectively and not
> 8A1 and 8A0. Also, I had used two equal signs (== and not just = when
> writing the equations).

OK! I spotted the single equal sign but not the additional 8A. Now,
I've got the same result as yours, that is an empty list. Also, I have
tried Reduce and FindInstance with no more success.

In[1]:=
Solve[{64919121*x - 159018721*y == 1,
   4.18695205*^7*x - 102558961*y == 0}, {x, y}]

Out[1]=
{}

In[2]:=
$Version

Out[2]=
5.2 for Microsoft Windows (June 20, 2005)
In[3]:=
Reduce[{64919121*x - 159018721*y == 1,
   4.18695205*^7*x - 102558961*y == 0}, {x, y}]

Out[3]=
False

In[4]:=
Reduce[{64919121*x - 159018721*y == 1.,
   4.18695205*^7*x - 102558961*y == 0.}, {x, y}]

Out[4]=
False

In[5]:=
FindInstance[{64919121 x-159018721 y\[Equal]1.,4.18695205*^7 x-102558961
      y\[Equal]0.},{x,y}]

Out[5]=
{}

In[6]:=
{64919121*x - 159018721*y == 1,
   4.18695205*^7*x - 102558961*y == 0} /.
  {x -> 205117922, y -> 83739041}

Out[6]=
{True,True}

> (2) For the second problem you have calculated %%%-%. So basically you are
> calculating Out[5]-Out[7] in your solution below. However, I was talking
> about Out[4]-Out[7], which is not zero even in your case.

Sorry about that, I miscounted the number of outputs! Again, I got the
same rsult as yours:

In[8]:=
123456789123*123456789123-SetPrecision[123456789123*123456789123.0,50]

Out[8]=
-729335.000000000000000000000000000


Best regards,
Jean-Marc

> Thanks very much.
>
>
>  Bharat.
>
>
> On 6/7/06, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
> > Bharat Bhole wrote:
> > > Would appreciate if someone can point out why Mathematica is not giving
> the
> > > expected output in the followng two cases.
> >
> > Here is what I get with Mathematica
> >
> > In[3]:=
> > $Version
> >
> > Out[3]=
> > 5.2 for Microsoft Windows (June 20, 2005)
> >
> > > (1) I was trying to solve the follwing two linear equations using
> 'Solve'.
> > >
> > >
> > > *In:
> Solve[{64919121*x-159018721*y=8A1,41869520.5*x-102558961*y=8A0},{x,y}]*
> > >
> > > *Out: {}*
> > >
> > In[1]:=
> > Solve[{64919121*x - 159018721*y == 8*A1,
> >    4.18695205*^7*x - 102558961*y == 8*A0}, {x, y}]
> >
> > Out[1]=
> >                   9                8
> > {{x -> -1.27215 10  A0 + 8.20472 10  A1,
> >
> >                    8                8
> >    y -> -5.19353 10  A0 + 3.34956 10  A1}}
> >
> >
> > > However, the solution exists and is given by  x = 205117922, y =
> 83739041
> >
> > It is meaningless to speak about "The" solution if you do not tell what
> > values A0 and A1 have been assigned:
> >
> > In[2]:=
> > Solve[{64919121*x - 159018721*y == 8*A1,
> >     4.18695205*^7*x - 102558961*y == 8*A0} /.
> >    {x -> 205117922, y -> 83739041}, {A0, A1}]
> >
> > Out[2]=
> > {{A1 -> 0.125, A0 -> 0.}}
> >
> > > Why is Mathematica unable to solve this simple linear equation? Am I
> doing
> > > something wrong?
> > >
> > >
> > >
> > > (2) I suppose that the default precision for numerical calculations is
> > > MachinePrecision which is less than 16. If I increase the precision,
> should
> > > I not get more accurate results? The example below seems to contradict
> that.
> > >
> > > (i) Exact Calculation
> > >
> > > *In[1]: 123456789123 * 123456789123*
> > >
> > > *Out[1]: 15241578780560891109129*
> > >
> > > (ii) Numerical Calculation with Default Precision
> > >
> > > *In[2]: 123456789123 * 123456789123.0*
> > >
> > > *Out[2]: 1.52416 =D7 10^22*
> > >
> > > (iii) Numerical Calcuation with a higher precision.
> > >
> > > *In[3]:SetPrecision[ 123456789123 * 123456789123.0 , 50 ]*
> > >
> > > *Out[3]:
> 1.5241578780560891838464000000000000000000000000000 x
> 10^22*
> > >
> > > Now if I calculate Out[1]-Out[2], I get zero.
> > >
> > > But if I calculate Out[1]-Out[3], I get
> -729335.000000000000000000000000000
> > > .
> > >
> > > This seems to suggest that calculation 2 is more accurate even though it
> has
> > > smaller precision. Where am I making a mistake?
> > >
> > > Thanks very much for your help.
> > >
> > >
> >
> > What version of Mathematica do you use? Work fine for me:
> >
> > In[4]:=
> > 123456789123*123456789123
> >
> > Out[4]=
> > 15241578780560891109129
> >
> > In[5]:=
> > 123456789123*123456789123.0
> >
> > Out[5]=
> >           22
> > 1.52416 10
> >
> > In[6]:=
> > %%-%
> >
> > Out[6]=
> > 0.
> >
> > In[7]:=
> > SetPrecision[123456789123*123456789123.0,50]
> >
> > Out[7]=
> > 1.5241578780560891838464000000000000000000000000000
> >
> >     22
> >   10
> >
> > In[8]:=
> > %%%-%
> >
> > Out[8]=
> > 0.
> >
> > In[9]:=
> > $Version
> >
> > Out[9]=
> > 5.2 for Microsoft Windows (June 20, 2005)
> >
> > Regards,
> > Jean-Marc
> >
>
>


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