• Corpus ID: 244488139

Explicitly solvable algebraic equations of degree 8 and 9

@inproceedings{Calogero2021ExplicitlySA,
  title={Explicitly solvable algebraic equations of degree 8 and 9},
  author={Francesco Calogero and F. Payandeh},
  year={2021}
}
The generic monic polynomial of degree N features N a priori arbitrary coefficients cm and N zeros zn . In this paper we limit consideration to N = 8 and N = 9 . We show that if the N —a priori arbitrary—coefficients cm of these polynomials are appropriately defined—as it were, a posteriori—in terms of 6 arbitrary parameters, then the N roots of these polynomials can be explicitly computed in terms of radicals of these 6 parameters. We also report the constraints on the N coefficients cm… 
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References

Two classes of explicitly solvable sextic equations

The generic monic polynomial of sixth degree features 6 a priori arbitrary coefficients. We show that if these 6 coefficients are appropriately defined—in two different ways—in terms of 5 arbitrary