### The Maxima on-line user's manual

Algebra Calculator

#### Sqfr

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.

Example:

```          (%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) ```

### Related Examples

##### sqfr

explain(sqfr(3/(x+y)^...

Calculate

##### sqfr-true-verbose

verbose:true;

sqfr(3/(x+y)^2 - 4/(x...

Calculate

sqfr(156);

Calculate

sqfr(x^2+4*x+2);

Calculate

sqfr(16);

Calculate

? sqfr;

Calculate

##### sqfr

sqfr (4*x^3 - 3*x^2 -...

Calculate

##### sqfr

sqfr(3/(x+y)^2 - 4/(x...

Calculate

##### sqfr

sqfr (4*x^4 + 4*x^3 -...

Calculate

sqfr: 14=x-4;

Calculate