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D.8.5.5 zeroSet

Procedure from library zeroset.lib (see zeroset_lib).

Usage:
zeroSet(I [,opt] ); I=ideal, opt=integer

Purpose:
compute the zero-set of the zero-dim. ideal I, in a finite extension of the ground field.

Return:
ring, a polynomial ring over an extension field of the ground field, containing a list 'theZeroset', a polynomial 'newA', and an ideal 'id':
 
  - 'theZeroset' is the list of the zeros of the ideal I, each zero is an ideal.
  - if the ground field is Q(b) and the extension field is Q(a), then
    'newA' is the representation of b 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).
  - 'id' is the ideal I in Q(a)[x_1,...] (a' substituted by 'newA')

Assume:
dim(I) = 0, and ground field to be Q or a simple extension of Q given by a minpoly.

Options:
opt = 0: no primary decomposition (default)
opt > 0: primary decomposition

Note:
If I contains an algebraic number (parameter) then I must be transformed w.r.t. 'newA' in the new ring.

Example:
 


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