30 Aug
2013
30 Aug
'13
7:45 p.m.
OK, so now I'm curious: Consider the space of all monic polynomials of degree n >= 5 over the reals or complexes. They are in bijective correspondence with R^n (resp. C^n), so let's give them that topology. What does the set of solvable monic polynomials look like within the space of all of them? Even more basic: What is the *dimension* of the space of solvable monic polynomials in the space of all of them (over R or C) ? --Dan On 2013-08-30, at 11:59 AM, Bill Gosper wrote: . . . . . .
a (rational) continuum of irreducible, supposedly solvable sextics: (125 - u)*x^6 + 12*u*(u + 3)^2*x + u*(u - 5)*(u + 3)^2 . . . . . .