Friday, November 10, 2017

[pggkliin] Solvable polynomials

Given a polynomial with integer coefficients, give an algorithm to determine whether it is solvable (in radicals), if only partially (some of the roots).  All polynomials of degree 4 or less are solvable.  Work by Cayley provides the answer to the quintic case.  But beyond that?

Motivation is to avoid collisions between irrational numbers formed with RootOf and irrational numbers formed with radicals.

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