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Problems when i try to solve a system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89156] Problems when i try to solve a system of equations
  • From: Paco <fmico at uv.es>
  • Date: Tue, 27 May 2008 07:15:44 -0400 (EDT)

Hi all,
I'm trying to solve this:

Assuming[0 < p0 < 1 && 0 < p1 < 1 && 0 < p2 < 1 && 0 < p3 < 1 && 
  0 < tau0 < 1 && 0 < tau1 < 1 && 0 < tau2 < 1 && 0 < tau3 < 1, 
 Solve[{p0 == 
    1 - (1 - tau0)^(n - 1) (1 - tau1)^n (1 - tau2)^n (1 - tau3)^n, 
   p1 == 1 - (1 - tau0)^n (1 - tau1)^(n - 1) (1 - tau2)^n (1 - tau3)^
      n , p2 == 
    1 - (1 - tau0)^n (1 - tau1)^n (1 - tau2)^(n - 1) (1 - tau3)^n, 
   p3 == 1 - (1 - tau0)^n (1 - tau1)^n (1 - tau2)^n (1 - tau3)^(
      n - 1), tau0 == 1/\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 0\), \(4\)]\((\((1 + 
FractionBox[\(1\), \(1 - \((1 - p0)\)\)] \(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(16\ 
\*SuperscriptBox[\(2\), \(j\)]\)]
\*FractionBox[\(16\ 
\*SuperscriptBox[\(2\), \(j\)]\ \  - \ k\), \(16\ 
\*SuperscriptBox[\(2\), \(j\)]\)]\))\)\ 
\*SuperscriptBox[\(p0\), \(j\)])\)\) (1 - p0^5)/(1 - p0), 
   tau1 == 1/\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 0\), \(4\)]\((\((1 + 
FractionBox[\(1\), \(1 - \((1 - p1)\)\)] \(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(16\ 
\*SuperscriptBox[\(2\), \(j\)]\)]
\*FractionBox[\(16\ 
\*SuperscriptBox[\(2\), \(j\)]\ \  - \ k\), \(16\ 
\*SuperscriptBox[\(2\), \(j\)]\)]\))\)\ 
\*SuperscriptBox[\(p1\), \(j\)])\)\) (1 - p1^5)/(1 - p1), 
   tau2 == 1/\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 0\), \(4\)]\((\((1 + 
FractionBox[\(1\), \(1 - \((1 - p2)\)\)] \(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(8\ 
\*SuperscriptBox[\(2\), \(j\)]\)]
\*FractionBox[\(8\ 
\*SuperscriptBox[\(2\), \(j\)]\ \  - \ k\), \(8\ 
\*SuperscriptBox[\(2\), \(j\)]\)]\))\)\ 
\*SuperscriptBox[\(p2\), \(j\)])\)\) (1 - p2^5)/(1 - p2), 
   tau3 == 1/\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(j = 0\), \(4\)]\((\((1 + 
FractionBox[\(1\), \(1 - \((1 - p3)\)\)] \(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(4\ 
\*SuperscriptBox[\(2\), \(j\)]\)]
\*FractionBox[\(4\ 
\*SuperscriptBox[\(2\), \(j\)]\ \  - \ k\), \(4\ 
\*SuperscriptBox[\(2\), \(j\)]\)]\))\)\ 
\*SuperscriptBox[\(p3\), \(j\)])\)\) (1 - p3^5)/(1 - p3)}, {p0, p1, 
   p2, p3, tau0, tau1, tau2, tau3}]]

With Solve[] (like here) and NSolve[] I get "No more memory available.Mathematica kernel has shut down.Try quitting other applications and then retry." message.

With FindRoot[] results are false.

I'm sure the problem is that I don't know how to use efficiently Mathematica but if somebody knows how to do it better, please help me.
Thanks in advance
paco


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