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Complex factorisation : cFactor

cFactor takes as argument an expression.
cFactor factorizes this expression on the field $ \mathbb {Q}$[i] $ \subset$ $ \mathbb {C}$ (or over the complexified field of the coefficients of the argument) even if you are in real mode.
  1. Factorize x4 - 1 over $ \mathbb {Z}$[i].
    Input :
    Output :
  2. Factorize x4 + 1 over $ \mathbb {Z}$[i].
    Input :
    Output :
  3. For a complete factorization of x4 + 1, check the sqrt box in the Cas configuration or input :
    Output :
    sqrt(2)*1/2*(sqrt(2)*x+1-i)*(sqrt(2)*x-1+i)*sqrt(2)* 1/2*(sqrt(2)*x+1+i)*(sqrt(2)*x-1-i)

giac documentation written by Renée De Graeve and Bernard Parisse