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Oct 23, 2018 at 22:10 comment added Jonathan Frink I'm also a little bit confused by this argument - is it possible to make it a little bit more rigorous?
Oct 23, 2018 at 18:25 comment added Alexandre Eremenko @Avi Steiner: rational operation is what you obtain by performing the 4 arithmetic operations on numbers and variables. 4 arithmetic operations are addition, subtraction, multiplication and division. Solving systems of linear equations involves only these operations.
Oct 23, 2018 at 15:31 comment added Avi Steiner Also, although the $n=1$ case (with $f=(2,1)$) isn’t algebraic in the sense of an algebraic subset, it is a real algebraic variety as it is exactly the set of $\Bbb R$-valued points of the (quasiaffine) complex algebraic variety $\Bbb C^2 \setminus V(x-y)$.
Oct 23, 2018 at 15:15 comment added Avi Steiner What is a rational operation in this context? I am not very familiar with real algebraic geometry.
Oct 23, 2018 at 13:22 history answered Alexandre Eremenko CC BY-SA 4.0