A 4th order polynomial equation, with non-constant coefficients is solvable. They can do anything, right? But look at what happens when you try to solve simultaneous polynomial equations like this.įor example, two quadratic equations in two unknowns will reduce to a 4th order equation when you eliminate one of the unknowns. Yes, I know that computers are big, fast, powerful. But for general real alpha, this is too much to do. Unless alpha and beta are 1 or zero (or apparently 1/2), the equations will be equivalent to something that is too high of an order for analytical solution, though I cannot be certain of that without looking more carefully. If Matlab is not capable enough to solve it, are there other tools that can solve nonlinear equation system?Īlmost certainly, no, these are not analytically solvable. If it can solved, am I using Matlab Symbolic Toolbox in the wrong way? Matlab can actually solve it. However, if I try to substitute both alpha and beta to 0.5. Warning: Explicit solution could not be found. Here is the Matlab code: syms x1 x2 y1 y2 alpha beta delta1 delta2 The equations are described in the following image:

I am using Matlab Symbolic Toolbox with its solve function and attempting to solve a nonlinear system of 4 equations,Īnd 4 parameters delta1 delta2 alpha beta

Matlab symbolic toolbox solve functions