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polylib::sqrfree -- square-free factorization of polynomials

Introduction

polylib::sqrfree(f) returns the square-free factorization of f, that is, a factorization of f in the form f = u * p1^e1 * ... * pr^er with primitive and pairwise different square-free divisors pi.

Call(s)

polylib::sqrfree(f <, recollect>)

Parameters

f - a polynomial or an arithmetical expression
recollect - TRUE or FALSE

Returns

a factored object, i.e., an object of the domain type Factored.

Related Functions

content, factor, Factored, irreducible, polylib::primpart

Details

Example 1

The factors in a squarefree factorization are pairwise relatively prime, but they need not be irreducible:

>> polylib::sqrfree(
     2 - 2*x - 6*x^4 + 6*x^5 + 6*x^8 - 6*x^9 -2*x^12 + 2*x^13
   )
                                4       2    3     3
                       2 (x - 1)  (x + x  + x  + 1)

Example 2

Even if a factorization into irreducibles has been found, irreducible factors with the same multiplicity are collected again:

>> polylib::sqrfree( x^6 + x^4*y*6 + x^2*y^2*9 )
                                         2  2
                              (x (3 y + x ))

You can avoid this by giving a second argument:

>> polylib::sqrfree( x^6 + x^4*y*6 + x^2*y^2*9, FALSE)
                               2         2 2
                              x  (3 y + x )

Example 3

polylib::sqrfree works also for polynomials:

>> polylib::sqrfree( poly(2 + 5*x + 4*x^2 + x^3) )
                                    2
                    poly(x + 1, [x])  poly(x + 2, [x])

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