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anything faster than Solve[] for solving sets of polynomial equations symbolically?

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  anything faster than Solve[] for solving sets of polynomial equations symbolically? dantimatter <google@dantimatter.com> - 2011-05-03 09:47 +0000

#2059 — anything faster than Solve[] for solving sets of polynomial equations symbolically?

Hi Everyone,

I've got a set of equations and I'd really like to determine the number of real solutions in terms of the unspecified parameters.   The equations are: 

eqs = {-k5 x1 x3+k6 x4==0, k1 x1-k4 x2-2 k2 x2^2+2 k3 x3+k7 x4==0, k2 x2^2-k3 x3-k5 x1 x3+k6 x4==0,x1+x4-Xtot==0};

where x1, x2, x3, and x4 are the variables I'd like to solve for and k1, k2, k3, k4, k5, k6, k7, and Xtot are real numbers that are greater than or equal to zero.   I've tried doing 

Solve[eqs, {x1, x2, x3, x4}, Reals]

but after days and days I still have no solution.  Perhaps there's a faster or better way to do this?  

Thanks,
Dan

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