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MathGroup Archive 2005

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Re: Time needed for calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62453] Re: Time needed for calculation
  • From: Peter Pein <petsie at dordos.net>
  • Date: Thu, 24 Nov 2005 06:33:53 -0500 (EST)
  • References: <dm1b2d$ie0$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

JikaiRF at aol.com schrieb:
> Dear Sirs,
> I have some questions about how long a computer can calculate, without 
> damages on hard wear.
> More specifically speaking, I intend to depict trajectories on (k, c) axis, 
> which are derived from programming on Mathematica.
> My program is as follows:
> 
> << Graphics`ImplicitPlot`
> L = 48;
> 
> a = 0.1;
> 
> A = 1;
> 
> r = 0.1;
> 
> t = 0.046296296296296294`;
> 
> ImplicitPlot[A r L (1 - a)((1 -t) c k^a == (a+(1-a)(1- t)) L^2 (1-a)^2 (1- t
> )^3 k^(3a-1)
>                      +L(1-a) c (1- t) (-A(a+(1-a)(1- t))(2- t)-(1-a)(1- t)^2 
> +A a(1- t)) k^(2a-1)
>                      +A c^2 (A(a+(1-a)(1- t))+(1-a)(1- t) -A a(1- t)) k^(a-1) 
> +A^2 r c^2, {k, 0.8, 1.5}]
> 
> This program seems to work well.   However, I cannot obtain the curve which 
> should be derived from the above program, though my computer continues to 
> calculate more than fifteen minutes.   
>  
> I would like to know how   long a computer can calculate without damages on 
> hardware, and additionally how long it takes to obtain the required curve based 
> on my computer.
> Especially, my computer is PowerBook G4 with 1.5 GHz processor. 
> 
>      Sincerely,
>      Fujio Takata. 
> 
> 

Hello,

when you specify only one range in ImplicitPlot, Mathematica tries to 
solve the equation before plotting. When you give the ranges of k _and_ 
c, then another Algorithm will be used. I'm afraid, Mathematica tries to 
solve w.r.t. k. Otherwise the answer should come almost instantly.

In[1]:= L = 48; a = 1/10; A = 1; r = 1/10; t = 5/108;
eqn = FullSimplify[
   A*r*L*(1 - a)*(1 - t)*c*k^a ==
   (a + (1 - a)*(1 - t))*L^2*(1 - a)^2*(1 - t)^3*k^(3*a - 1) +
   L*(1 - a)*c*(1 - t)*((-A)*(a + (1 - a)*(1 - t))*(2 - t) -
   (1 - a)*(1 - t)^2 + A*a*(1 - t))*k^(2*a - 1) +
   A*c^2*(A*(a + (1 - a)*(1 - t)) + (1 - a)*(1 - t) -
   A*a*(1 - t))*k^(a - 1) + A^2*r*c^2,
  k > 0]
Out[2]=
103*c*(16819*k^(1/10) + 648*k) ==
   15*c^2*(1859 + 108*k^(9/10)) + 25132721*k^(1/5)

In[3]:=
First[Timing[ImplicitPlot[eqn, {k, 0.8, 1.2}, {c, 0, 50},
   PlotPoints ->  300, ImageSize -> 500, AspectRatio ->
   GoldenRatio - 1]]]
[plot omitted]
Out[3]= 0.234*Second

And don't be afraid; if you did not overclock your hardware, 
long-lasting calculations will not do any harm to your machine.

Rumors were afloat, some companies use their computers 24 hours/day ;-)

Regards,
   Peter


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