# Solve polynomial system

I am trying to solve

Solve[t23*(n12 - x123 - x124 + x1234)*(n13 - x123 - x134 +
x1234) == (x123 - x1234)*(n1 - n12 - n13 - n14 + x134 + x123 +
x124 - x1234) &&
t24*(n12 - x123 - x124 + x1234)*(n14 - x124 - x134 +
x1234) == (x124 - x1234)*(n1 - n12 - n13 - n14 + x134 + x123 +
x124 - x1234) &&
t34*(n13 - x123 - x134 + x1234)*(n14 - x124 - x134 +
x1234) == (x134 - x1234)*(n1 - n12 - n13 - n14 + x134 + x123 +
x124 - x1234) &&
t234*(n1 - n12 - n13 - n14 + x134 + x123 + x124 - x1234)*(x134 -
x1234)*(x124 - x1234)*(x123 - x1234) == (n12 - x123 - x124 +
x1234)*(n13 - x123 - x134 + x1234)*(n14 - x124 - x134 +
x1234), {x123, x124, x134, x1234}]


where all 4 variables should be reals 0<=x<=1, all the n parameters are also 0<=n<=1, and t parameters are 0<=t<Infinity. It says running but no output is returned :-(

• It is most likely bogged in computational complexity since it is dealing with parameters. If it helps, might instead use NSolve when parameters are given actual values. – Daniel Lichtblau Jul 26 '18 at 20:30
• I assume you have tried Reduce and similar commands instead? My real question is where did these equations come from? How did they arise? (There's really no guarantee that arbitrary systems of polynomials can be solved, reduced, simplified in a helpful way.) – Kellen Myers Jul 27 '18 at 1:55
• After several hours of processing, my 16GB computer ran out of memory. Perhaps, this is your situation as well. – bbgodfrey Jul 27 '18 at 12:56