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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