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## Factorization : factor factoriser

factor takes as argument a polynomial or a list of polynomials and optionnally an algebraic extension, e.g. sqrt(n).
factor factorize the polynomial (or the polynomials of the list) on the field of it's coefficients (the field is complexified in complex mode) or on the smallest extension containing the optionnal second argument. Unlike collect, factor will further factorize each factor of degree 2 if Sqrt is checked in the cas configuration (see also 1.12.9). You can check the current configuration in the status button under Xcas and change the configuration by hitting this status button.
Input :
factor(x^2+2*x+1)
Output :
(x+1)^2
Input :
factor(x^4-2*x^2+1)
Output :
(-x+1)^2*(x+1)^2
Input :
factor(x^ 3-2*x^2+1)
Output if Sqrt is not checked in the cas configuration :
(x-1)*(x^2-x-1)
Output if Sqrt is checked in the cas configuration :
(x-1)*(x+(sqrt(5)-1)/2)*(x+(-sqrt(5)-1)/2)
Input :
factor(x^ 3-2*x^2+1,sqrt(5))
Output :
((2*sqrt(5)-19)*((sqrt(5)+15)*x+7*sqrt(5)-5)*(-x+1)*((sqrt(5)+25)*x-13*sqrt(5)-15))/6820
Input :
factor(x^2+1)
Output in real mode :
x^2+1
Output in complex mode :
((-i)*x+1)*((i)*x+1)

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giac documentation written by Renée De Graeve and Bernard Parisse