5.13.11 Complex factorization: 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
-
Factorize x4−1 over ℤ[i].
Input:
cFactor(x^
4-1)
Output:
-((x+-i)*((-i)*x+1)*((-i)*x+i)*(x+1))
- Factorize x4+1 over ℤ[i].
Input:
cFactor(x^
4+1)
Output:
(x^
2+i)*(x^
2+-i)
- 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)