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

*To*: mathgroup at smc.vnet.net*Subject*: [mg67058] Re: Two questions (1) Sollve and (2) Precision*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 8 Jun 2006 04:53:43 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <e666j8$nbj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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