Maxima 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 n'th 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.
Example:
(%i1) sqfr (4*x^4 + 4*x^3 - 3*x^2 - 4*x - 1); 2 2 (%o1) (2 x + 1) (x - 1)