The command root(f(x),x, K) to compute roots of a univariate polynomial f(x),
(let f(x) have integer coefficients), will not return an answer unless *I* do the WORK
FIRST of FINDING THE ROOT to determine over WHICH FIELD (algebraic field, if it's algebraic)
some of the roots of f(x) lie.
The help manual demonstrates this with simple quadratics only. One writes the radical part
of the quadratic solution for K, i.e.
Mathematica had the complete Cardano formulae programmed in for both the cubic and the quartic polynomials with completely indeterminate coefficients.
Does Maple not have the same feature?
How do I denote the field of real numbers for K? Substituting "R" for "K" does not work.
Nor "C" for "K" is I want the field of complex numbers.