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Solve can't solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89185] Solve can't solve
  • From: Paco <fmico at uv.es>
  • Date: Wed, 28 May 2008 04:47:00 -0400 (EDT)

Hi all

(Mathematica 6.0.0 Windows XP)

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[], I get this message:
"No more memory available.
Mathematica kernel has shut down.
Try quitting other applications and then retry."

I tried with NSolve[] and the result was the same.

I discovered that if I give a value to n, I get something with FindRoot[] but results are false (I tried several init values for p0,p1,etc - results are different and all are wrong).

Does anybody know what I'm doing wrong?
Thanks
paco


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