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polylib::divisors -- divisors of a polynomial, polynomial expression, or Factored element

Introduction

polylib::divisors(p) computes the set of all monic divisors of the polynomial or polynomial expression p.

Call(s)

polylib::divisors(p)
polylib::divisors(f)
polylib::divisors(e)

Parameters

p - a polynomial or polynomial expression
f - Factored (return value of factor)
e - element of a domain of category Cat::Polynomial

Returns

polylib::divisors returns a set of polynomials. The polynomials are from the same type as the polynomials in the argument.

Related Functions

Cat::Polynomial, DOM_POLY, Dom::Polynomial, Dom::MultivariatePolynomial, Dom::UnivariatePolynomial, factor, irreducible, numlib::divisors, polylib::sqrfree

Details

Example 1

If the argument is a polynomial, a set of polynomials is returned:

>> polylib::divisors(poly(x^2 - 2*x + 1))
                                                2
         {poly(1, [x]), poly(x - 1, [x]), poly(x  - 2 x + 1, [x])}

Example 2

If the argument is a polynomial expression, a set of polynomial expressions is returned:

>> polylib::divisors(x^2 - 1)
                                            2
                         {1, x - 1, x + 1, x  - 1}

Example 3

If the argument is of type Factored (a factor return value) a set of polynomials is returned:

>> p := factor(poly(x^2 - 1));
   polylib::divisors(p)
                     poly(x - 1, [x]) poly(x + 1, [x])
      
      {poly(1, [x]), poly(x - 1, [x]), poly(x + 1, [x]),
      
               2
         poly(x  - 1, [x])}

The polynomials in the resulting set have the same type as the polynomials in the Factored element:

>> p := factor(x^2 - 1);
   polylib::divisors(p)
                              (x - 1) (x + 1)
      
                                            2
                         {1, x - 1, x + 1, x  - 1}

Example 4

polylib::divisors works on polynomials from category Cat::Polynomial as well:

>> P := Dom::Polynomial(Dom::IntegerMod(7)):
   polylib::divisors(P(x^3 + 2*x^2 + 1))
                                 3              2
            {1 mod 7, (1 mod 7) x  + (2 mod 7) x  + (1 mod 7)}

Changes




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