🚀 go-pugleaf

I have to write a program to solve the following
two cubic simultaneous equations in two variables:

a1 u^3 + b1 u^2 v + c1 u v^2 + d1 v^3 + e1 u^2 + 
  f1 u v + g1 v^2 + h1 u + i1 v + j1 = 0,

a2 u^3 + b2 u^2 v + c2 u v^2 + d2 v^3 + e2 u^2 + 
  f2 u v + g2 v^2 + h2 u + i2 v + j2 = 0,

where u, v are variables, ai ... ji, i = 1,2 are 
real constants.

I only care for real roots in [0,1].

I could use some sybolic manipulation tools to combine 
them into a 9-degree polynomial in one variable and 
try to solve the single variable polynomial.  But
I wonder whether there is a better way to do it.
I tried several cases in Mathematica. It seems to
be able to solve it reasonably well.  Any help
will be appreciated.



Jin Chou
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jchou@nas.nasa.gov