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The AgsFunction object should give you a front-end to solve linear equation systems. Like functions with one or more variables.
After some research, I have found GNU Scientific Library, which is capable to solve polynomials. Might be there is going to be a dependency to it in later versions.
With some string parsing functions in “ags_math_util.c”, we should be able to bring your provided input into the form of a polynomial. By using Gaussian elimintation we prepare the functions to be processed by GSL.
I am not sure if GSL is able to produce solutions as complex numbers. This might be an obstacle. But I think it is definitely a closer look worthy.
We are going to solve common transformation using matrix processing. A matrix is basically a 2-dimensional array, organizing your polynomials in vectors. A vector is always of the same symbol with matching exponent. So the involved objects are: