Cubic and Quartic Formulae

[parisse]

(08-06-2015 01:42 PM)LCieParagon Wrote:  Additionally, parisse noted that it's more practical to use approximations. I disagree with this. It's in fact a portion of the Ti-nSpire CAS (and the TI-89 for that matter) I prefer to the HP Prime. For instance (if we are talking about degrees), one can find sin(36), sin (18), sin(54), and sin(72) exactly. This angles are incredibly useful for architecture or engineering. One can apply half-angle, addition/subtraction, and double angle formulae to receive every whole number degree divisible by 3.

You misunderstood what I wrote. I did not say it's more practical to use approximations than exact formula. I said that for *both* numerical and symbolic computations, it's very inefficient to use Cardan or Ferrari formula. For numerical, because the expressions are huge and will introduce a lot of rounding errors instead of just one or two with an interative method. For symbolics, it's much much more efficient to work in Q[X]/M[X] where Q[X] is polynomial over the rationals and M is the minimal (irreducible) polynomial of an algebraic number than to work with embedded square roots, cubic roots, etc.