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2.12.10  Complex factorisation : cFactor

cFactor takes as argument an expression.
cFactor factorizes this expression on the field ℚ[i] ⊂ ℂ (or over the complexified field of the coefficients of the argument) even if you are in real mode.
Examples

  1. Factorize x4−1 over ℤ[i].
    Input :
    cFactor(x^4-1)
    Output :
    -((x+-i)*((-i)*x+1)*((-i)*x+i)*(x+1))
  2. Factorize x4+1 over ℤ[i].
    Input :
    cFactor(x^4+1)
    Output :
    (x^2+i)*(x^2+-i)
  3. For a complete factorization of x4+1, check the sqrt box in the Cas configuration or input :
    cFactor(x^4+1,sqrt(2))
    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)

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