29 Aug
2020
29 Aug
'20
11:23 a.m.
Quoting Henry Baker <hbaker1@pipeline.com>:
Hi Rich, et al: Do any of these radical formulae work for characteristic not zero?
Mostly. The quadratic formula works except in characteristic 2. The cubic & quartic formulas work except in characteristic 2 & 3. [Remember that that the 2-adic & 3-adic fields are characteristic 0.] All of the q/c/q formulas may produce answers in extension fields, and I think the cubic & quartic formulas can require stepping out to an extension field even when the final roots are back in the ground field -- analogous to the case where a three-real-root cubic requires taking cbrts of complex numbers. Another nuisance is that taking square & cube roots needs different algorithms than the real & complex cases. Rich