Function: sqfr (<expr>) is similar to
factor except that the polynomial factors are "square-free." That is, they have factors only of degree one. This algorithm, which is also used by the first stage of
factor, utilizes the fact that a polynomial has in common with its nth derivative all its factors of degree greater than n. Thus by taking greatest common divisors with the polynomial of the derivatives with respect to each variable in the polynomial, all factors of degree greater than 1 can be found.
(%i1) sqfr (4*x^4 + 4*x^3 - 3*x^2 - 4*x - 1); 2 2 (%o1) (2 x + 1) (x - 1)
(%o1) true (%i2)