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I want to simplify (solve) a system of linear + nonlinear symbolic equations as much as possible. the equations are of random orders, without differentiation. is there a general & well-known algorithm for this type of arbitrary systems?

I am writing my solver, complies my solver flow chart. but at this time i am not sure my solver flow chart will really worth working, or perhaps there is a better solution. enter image description here thanks

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  • $\begingroup$ Is there a reason you're not using one of many available computer algebra systems (CAS) for this? You can find a big list here, including Maple, Mathematica, Matlab's Symbolic Math Toolbox, and the free Sage and SymPy. $\endgroup$ – horchler Jun 12 '15 at 13:19
  • $\begingroup$ above systems offer different solvers when facing different types of equations. as an example Mathematica offers NSolve (numerical), Solve (symbolic), FindRoot (numerical), LinearSolve (linear systems). also user have various utilities to work with equations. in my case: 1-user can choose different equations at runtime (by insert different object in model), and software can't predict type of system. 2- performance is a serious matter. $\endgroup$ – Reza Afzalan Jun 13 '15 at 15:10
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    $\begingroup$ Here's an example of a college physics problem solved with Symbolism, a C# computer algebra library. The EliminateVariable method is used to incrementally solve a set of equations. $\endgroup$ – dharmatech Jul 30 '15 at 4:23
  • $\begingroup$ @dharmatech, although symbolic variable elimination could be a solution for systems with explicit linear terms, this approach fails in most cases when terms were implicitly involved in equations. and also could not be the best approach when simple&fast numerical solutions for a sub system or an equation exist. $\endgroup$ – Reza Afzalan Aug 1 '15 at 7:47

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