Re: Problems when i try to solve a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg89165] Re: [mg89156] Problems when i try to solve a system of equations
• From: DrMajorBob <drmajorbob at att.net>
• Date: Wed, 28 May 2008 04:43:16 -0400 (EDT)
• References: <30940873.1211890046280.JavaMail.root@m08>

```Explicit solution of polynomial equations is limited to order <= 5, so
it's amazing that you expect to Solve with unknown order n and specified
orders up to 8.

Eliminating the FractionBoxes and simplifying the problem in brackets led
to 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 - tau0)^(-1 + n) (1 - tau1)^n (1 - tau2)^n (1 - tau3)^
n == 1, p1 + (1 - tau0)^n (1 - tau1)^(-1 + n) (1 - tau2)^
n (1 - tau3)^n == 1,
p2 + (1 - tau0)^n (1 - tau1)^n (1 - tau2)^(-1 + n) (1 - tau3)^n ==
1, p3 + (1 - tau0)^n (1 - tau1)^n (1 - tau2)^
n (1 - tau3)^(-1 + n) == 1,
tau0 == 2/(163 + 26408 p0 + 4277937 p0^2 + 693025474 p0^3 +
693025476 p0^4 + 693025313 p0^5 + 692999068 p0^6 +
688747539 p0^7 + 2 p0^8),
tau1 == 2/(163 + 26408 p1 + 4277937 p1^2 + 693025474 p1^3 +
693025476 p1^4 + 693025313 p1^5 + 692999068 p1^6 +
688747539 p1^7 + 2 p1^8),
tau2 == 2/(83 + 6808 p2 + 558177 p2^2 + 45770354 p2^3 +
45770356 p2^4 + 45770273 p2^5 + 45763548 p2^6 +
45212179 p2^7 + 2 p2^8),
tau3 == 2/(43 + 1808 p3 + 75897 p3^2 + 3187594 p3^3 +
3187596 p3^4 + 3187553 p3^5 + 3185788 p3^6 + 3111699 p3^7 +
2 p3^8)}, {p0, p1, p2, p3, tau0, tau1, tau2, tau3}]]

\$Aborted

I aborted after a few seconds; there's no chance of a solution.

You didn't list n as a variable OR give it a value, so you're trying for a
closed form solution for ALL values of n. Good luck with that!

Bobby

On Tue, 27 May 2008 06:15:44 -0500, Paco <fmico at uv.es> wrote:

> 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
> paco
>
>

--

DrMajorBob at longhorns.com

```

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