Racionální funkce

In Axiom

Pro srovnani s jinymi CAS zvolte Derive Macsyma Maple Mathematica Reduce

rf:= (3*a*b**2-5*a**2*b)/(a**4-2)

        2     2
    3a b  - 5a b
    ------------
        4
       a  - 2
                                            Type: Fraction Polynomial Integer

• integrování

  integrate(rf, a)

             +--------------------------------------+
             |        2                      2     4
           (\|- 12%%G1  - 8%%G0 %%G1 - 12%%G0  + 9b   - 2%%G1 - 2%%G0)
        *
           log
                  (24a %%G1 + 24a %%G0 - 60b - 50a)
               *
                   +--------------------------------------+
                   |        2                      2     4
                  \|- 12%%G1  - 8%%G0 %%G1 - 12%%G0  + 9b
              +
                        2                               2
                48a %%G1  + (120b + 100a)%%G1 + 48a %%G0  + (120b + 100a)%%G0
              +
                       4
                - 27a b  - 250b
       +
               +--------------------------------------+
               |        2                      2     4
           (- \|- 12%%G1  - 8%%G0 %%G1 - 12%%G0  + 9b   - 2%%G1 - 2%%G0)
        *
           log
                  (24a %%G1 + 24a %%G0 - 60b - 50a)
               *
                   +--------------------------------------+
                   |        2                      2     4
                  \|- 12%%G1  - 8%%G0 %%G1 - 12%%G0  + 9b
              +
                          2                                 2
                - 48a %%G1  + (- 120b - 100a)%%G1 - 48a %%G0
              +
                                           4
                (- 120b - 100a)%%G0 + 27a b  + 250b
       +
                           2                            4
         4%%G1 log(96a %%G1  + (240b + 200a)%%G1 - 27a b  + 250b)
       +
                           2                            4
         4%%G0 log(96a %%G0  + (240b + 200a)%%G0 - 27a b  + 250b)
    /
       4
                                            Type: Union(Expression Integer,...)
  

• rozklad na částečné zlomky

  (10*x**2-11*x-6)/(x**3-x**2-2*x)

         2
      10x  - 11x - 6
      --------------
        3    2
       x  - x  - 2x
                                              Type: Fraction Polynomial Integer
  

  padicFraction( _

  partialFraction(numerator(

  factor(denominator(

  Factored UnivariatePolynomial(x, Fraction Integer)))

      3     2       5
      - + ----- + -----
      x   x - 2   x + 1
                 Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)