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MathGroup Archive 2007

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Re: Trouble with a system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77512] Re: Trouble with a system of equations
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Mon, 11 Jun 2007 04:23:51 -0400 (EDT)
  • References: <f4gn49$htt$1@smc.vnet.net>

$VersionNumber
5.2

In[21]:=
eqns = {a + b + c + d == 4*m0, b + d == 4*m1, c + d == 4*m2, d ==
4*m3} /. {a -> t0/(1 + t0), b -> (t0*t1)/(1 + t0*t1),
    c -> (t0*t2)/(1 + t0*t2), d -> (t0*t1*t2*t3)/(1 + t0*t1*t2*t3)}
Reduce[eqns, {t0, t1, t2, t3}]

Out[21]=
{t0/(1 + t0) + (t0*t1)/(1 + t0*t1) + (t0*t2)/(1 + t0*t2) +
(t0*t1*t2*t3)/(1 + t0*t1*t2*t3) == 4*m0,
  (t0*t1)/(1 + t0*t1) + (t0*t1*t2*t3)/(1 + t0*t1*t2*t3) == 4*m1,
(t0*t2)/(1 + t0*t2) + (t0*t1*t2*t3)/(1 + t0*t1*t2*t3) == 4*m2,
  (t0*t1*t2*t3)/(1 + t0*t1*t2*t3) == 4*m3}

Out[22]=
(m3 == 0 && m2 == 0 && m1 == 0 && m0 == 0 && t0 == 0) || (m3 == 0 &&
m1 == 0 && -1 + 4*m0 - 4*m2 != 0 &&
   t0 == -((4*(m0 - m2))/(-1 + 4*m0 - 4*m2)) && t1 == 0 && (m0 -
m2)*(-1 + 4*m2) != 0 &&
   t2 == (-m2 + 4*m0*m2 - 4*m2^2)/((m0 - m2)*(-1 + 4*m2)) && m2 != 0)
|| (m3 == 0 && m2 == 0 && -1 + 4*m0 - 4*m1 != 0 &&
   t0 == -((4*(m0 - m1))/(-1 + 4*m0 - 4*m1)) && (m0 - m1)*(-1 + 4*m1) !
= 0 &&
   t1 == (-m1 + 4*m0*m1 - 4*m1^2)/((m0 - m1)*(-1 + 4*m1)) && t2 == 0
&& m0 != 0) ||
  (-1 + 4*m0 - 4*m1 - 4*m2 + 4*m3 != 0 && t0 == -((4*(m0 - m1 - m2 +
m3))/(-1 + 4*m0 - 4*m1 - 4*m2 + 4*m3)) &&
   (-1 + 4*m1 - 4*m3)*(m0 - m1 - m2 + m3) != 0 &&
   t1 == (m1 - 4*m0*m1 + 4*m1^2 + 4*m1*m2 - m3 + 4*m0*m3 - 8*m1*m3 -
4*m2*m3 + 4*m3^2)/
     ((-1 + 4*m1 - 4*m3)*(-m0 + m1 + m2 - m3)) && (m0 - m2)*(-1 + 4*m2
- 4*m3) != 0 &&
   t2 == (-m2 + 4*m0*m2 - 4*m1*m2 - 4*m2^2 + m3 - 4*m0*m3 + 4*m1*m3 +
8*m2*m3 - 4*m3^2 - m2*t1 + 4*m1*m2*t1 + m3*t1 -
      4*m1*m3*t1 - 4*m2*m3*t1 + 4*m3^2*t1)/((m0 - m2)*(-1 + 4*m2 -
4*m3)) && (m1 - m3)*(m2 - m3)*(-1 + 4*m3) != 0 &&
   t3 == ((-m3)*t0 + 4*m1*m3*t0 + 4*m2*m3*t0 - 16*m1*m2*m3*t0 -
8*m3^2*t0 + 16*m1*m3^2*t0 + 16*m2*m3^2*t0 - 16*m3^3*t0)/
     (4*(m1 - m3)*(m2 - m3)*(-1 + 4*m3))) || (m0 == m2 && 1 + 4*m1 -
4*m3 != 0 && t0 == -((4*(m1 - m3))/(1 + 4*m1 - 4*m3)) &&
   -1 + 4*m1 - 4*m3 != 0 && t1 == (1 + 4*m1 - 4*m3)/(-1 + 4*m1 - 4*m3)
&& (-1 + 4*m2 - 4*m3)*(m1 - m3) != 0 &&
   t2 == (m2 + 4*m1*m2 - m3 - 4*m1*m3 - 4*m2*m3 + 4*m3^2)/((-1 + 4*m2
- 4*m3)*(m1 - m3)) && (m2 - m3)*(-1 + 4*m3) != 0 &&
   t3 == (m3 - 4*m2*m3 + 4*m3^2 + 2*m3*t0 - 8*m2*m3*t0 + 8*m3^2*t0)/
((m2 - m3)*(-1 + 4*m3))) ||
  (m3 == 0 && m2 == 0 && m0 == 0 && 1 + 4*m1 != 0 && t0 == -((4*m1)/(1
+ 4*m1)) && -1 + 4*m1 != 0 &&
   t1 == (1 + 4*m1)/(-1 + 4*m1) && t2 == 0 && m1 != 0)

Dimitris



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