[Axiom-math] relate root representations

[Alejandro Jakubi]

I see that Axiom produces different representations for the roots of
polynomials in the form of lists, but I do not find the operations that
relates the corresponding elements of these lists.

As a concrete example, in a follow-up of the example that I have posted a few 
weeks
ago, consider the lists produced by:

allRootsOf(p^3 - p + 1/10)$RECLOS(FRAC INT)

[%F8,%F9,%F10]

solve((p^3 - p + 1/10=0)::EQ EXPR INT,p)


              +-----------+             +-----------+
              |      2                  |      2
             \|- 3%p0  + 4  - %p0    - \|- 3%p0  + 4  - %p0
  [p= %p0,p= --------------------,p= ----------------------]
                       2                        2
                                 Type: List Equation Expression Integer

radicalSolve(p^3 - p + 1/10=0,p)

                      +------------------+2
                      |    +-+    +-----+
          +---+       |- 3\|3  + \|- 373
     (- 3\|- 3  + 3)  |------------------  - 2
                     3|         +-+
                     \|      60\|3
 [p= -----------------------------------------,
                        +------------------+
                        |    +-+    +-----+
            +---+       |- 3\|3  + \|- 373
         (3\|- 3  + 3)  |------------------
                       3|         +-+
                       \|      60\|3
                      +------------------+2
                      |    +-+    +-----+
          +---+       |- 3\|3  + \|- 373
     (- 3\|- 3  - 3)  |------------------  + 2
                     3|         +-+
                     \|      60\|3
  p= -----------------------------------------,
                        +------------------+
                        |    +-+    +-----+
            +---+       |- 3\|3  + \|- 373
         (3\|- 3  - 3)  |------------------
                       3|         +-+
                       \|      60\|3
        +------------------+2
        |    +-+    +-----+
        |- 3\|3  + \|- 373
     3  |------------------  + 1
       3|         +-+
       \|      60\|3
  p= ---------------------------]
           +------------------+
           |    +-+    +-----+
           |- 3\|3  + \|- 373
        3  |------------------
          3|         +-+
          \|      60\|3
                                     Type: List Equation Expression Integer

So, I mean eg a command that takes %F8 as input and gives as output the
correspondig equation (or rhs) in the second or third list.

Is there such command?

Alejandro Jakubi