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math.RA2026
Root of the generic cubic as a power series in the discriminant
Jason Bland, Skip Garibaldi, Joel Rosenberg
An observation of J-P. Serre implies that the generic monic cubic polynomial, unique among generic monic polynomials of degree at least two, has a root that is a power series in th…
math.CA2026
The longest and shortest roots of a real cubic
Jason Bland, Skip Garibaldi, Joel Rosenberg
There are many formulas in the literature providing roots of a real cubic that avoid some of the well-known pathologies of Cardano's formulas. Among these, we identify two that con…