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Re: Solve can't solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89311] Re: Solve can't solve
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 5 Jun 2008 00:43:23 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g1j6ib$qok$1@smc.vnet.net>

Paco wrote:

> (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?

The code you posted contains some low-level display-only expressions 
such as FractionBox[1, 1 - (1 - p0)] rather than the 
algebraically-evaluable expression 1/(1 - (1 - p0)). You should correct 
that first.

Hope this helps,
-- Jean-Marc



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