By nonlinear algebra I mean things relating to multivariate polynomials
Linear modelling of nonlinear systems
The big question: Linear in what? You can always determine a polynomial as a linear algebra problem given sample points. A polynomial can bethought of as linear in it’s coefficients
wiki A matrix designed to have characterstic polynomial
We’re really good at these. Fundamental theorem of algebra
Cylindrical Algebraic Decomposition (CAD)
Linear algebra but wih rings instead of fields. You can’t divide by scalars anymore.
https://github.com/algebraic-solving/msolve msolve. a C library for grobner basis and root calculations. Intresting