Algebraic numbers

 

In Reduce

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Mathematica

inputs outputs

• module arnum dealing with algebraic numbers

      load_package arnum;
  
      defpoly sqrt2**2-2;
  
      1/(sqrt2+1);
  

      sqrt2 - 1

      (x**2+2*sqrt2*x+2)/(x+sqrt2);
  

      x + sqrt2

      on gcd;
  
      (x**3+(sqrt2-2)*x**2-(2*sqrt2+3)*x-3*sqrt2)/(x**2-2);
  

        2
       x  - 2*x - 3
      --------------
        x - sqrt2

  
      off gcd;
  
      sqrt(x**2-2*sqrt2*x*y+2*y**2);
  

      x - sqrt2*y

• multiple algebraic extensions

      off arnum;
  
      defpoly sqrt5**2-5,cbrt3**3-3;
  

      *** Defining the polynomial for a primitive element:
  
        6        4       3        2
      a1  - 15*a1  - 6*a1  + 75*a1  - 90*a1 - 116

      cbrt3**3;
  

      3

      sqrt5**2;
  

      5

  
      cbrt3;
  

           120     5     27     4    2000    3    1170    2    6676
       - (------*a1  + ------*a1  - ------*a1  - ------*a1  + ------*a1
           8243         8243         8243         8243         8243
  
              6825
           - ------)
              8243

  
      sqrt(x**2+2*(sqrt5-cbrt3)*x+5-2*sqrt5*cbrt3+cbrt3**2);
  

            240     5     54     4    4000    3    2340    2    21595
      x + (------*a1  + ------*a1  - ------*a1  - ------*a1  + -------*a1
            8243         8243         8243         8243         8243
  
               13650
            - -------)
               8243