A Deterministic PTAS for the Algebraic Rank of Bounded Degree Polynomials

@inproceedings{Bhargava2019ADP,
  title={A Deterministic PTAS for the Algebraic Rank of Bounded Degree Polynomials},
  author={Vishwas Bhargava and Markus Bl{\"a}ser and Gorav Jindal and Anurag Pandey},
  booktitle={SODA},
  year={2019}
}
We present a deterministic polynomial time approximation scheme (PTAS) for computing the algebraic rank of a set of bounded degree polynomials. The notion of algebraic rank naturally generalizes the notion of rank in linear algebra, i.e., instead of considering only the linear dependencies, we also consider higher degree algebraic dependencies among the input polynomials. More specifically, we give an algorithm that takes as input a set f := {f1, . . . , fn} ⊂ F[x1, . . . , xm] of polynomials… 
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Basics of Invariant theory Invariant Theory and Computational Complexity 1
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