# Chapter 20: Calculations
# 
# 
# Maple uses the function RootOf to represent the roots of a polynomial.
# The function allvalues returns the actual symbolic values of the
# roots, where possible, using the function solve. It manages to avoid
# some of the foibles of Cardano's formulas.
# 
> allvalues(RootOf(x^3 - 3*x + 5));

                       2                                1
  - 1/2 %1 - ----------------------, 1/4 %1 + ----------------------
                              (1/3)                            (1/3)
             (20 + 4 sqrt(21))                (20 + 4 sqrt(21))

                         /                     2           \
         + 1/2 I sqrt(3) |- 1/2 %1 + ----------------------|, 1/4 %1
                         |                            (1/3)|
                         \           (20 + 4 sqrt(21))     /

                     1
         + ----------------------
                            (1/3)
           (20 + 4 sqrt(21))

                         /                     2           \
         - 1/2 I sqrt(3) |- 1/2 %1 + ----------------------|
                         |                            (1/3)|
                         \           (20 + 4 sqrt(21))     /

                         (1/3)
  %1 := (20 + 4 sqrt(21))

> allvalues(RootOf(x^4 - 3*x + 3));

  1/2 I sqrt(3) + 1/2 sqrt(3 - 2 I sqrt(3)),

        1/2 I sqrt(3) - 1/2 sqrt(3 - 2 I sqrt(3)),

        -1/2 I sqrt(3) + 1/2 sqrt(3 + 2 I sqrt(3)),

        -1/2 I sqrt(3) - 1/2 sqrt(3 + 2 I sqrt(3))