Organization of this Repository
Solving a System of Polynomial Equations
Groebner bases can be used to find solutions to a system of polynomial equations. Unfortunately, computing Groebner bases is known to be unstable due to floating point error propagation. Polynomials in the power basis can be represented by a summation of Chebyshev polynomials, which are good for stable computation. Converting the polynomials to Chebyshev polynomials reduces the error significantly. Here's an example using the code from this repository:
Example
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