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

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This quickly catalogs the solutions, though I'm not fond of the output  
format:

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};
nonNeg = Thread[{k1, k2, k3, k4, k5, k6, k7, Xtot} >= 0];
real = Element[vars = {x1, x2, x3, x4}, Reals];
problem = Flatten@{eqs, nonNeg};
Solve[problem, Reals] // FullSimplify

Bobby

On Tue, 03 May 2011 04:47:36 -0500, dantimatter <google@dantimatter.com>  
wrote:

>
> 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
>


-- 
DrMajorBob@yahoo.com

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Re: anything faster than Solve[] for solving sets of polynomial equations symbolically? DrMajorBob <btreat1@austin.rr.com> - 2011-05-04 10:34 +0000

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