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