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D.8.5.3 roots

Procedure from library zeroset.lib (see zeroset_lib).

Usage:
roots(f); where f is a polynomial

Purpose:
compute all roots of f in a finite extension of the ground field without multiplicities.

Return:
ring, a polynomial ring over an extension field of the ground field, containing a list 'theRoots' and polynomials 'newA' and 'f':
 
  - 'theRoots' is the list of roots of the polynomial f (no multiplicities)
  - if the ground field is Q(a') and the extension field is Q(a), then
    'newA' is the representation of a' in Q(a).
    If the basering contains a parameter 'a' and the minpoly remains unchanged
    then 'newA' = 'a'.
    If the basering does not contain a parameter then 'newA' = 'a' (default).
  - 'f' is the polynomial f in Q(a) (a' being substituted by 'newA')

Assume:
ground field to be Q or a simple extension of Q given by a minpoly

Example:
 


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