Factorization

 

In Reduce

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

inputs outputs

• factorization is the transformation of a polynomial into a product of polynomials

      factorize(a^2-b^2);
  

      {a - b,a + b}

      on complex;
  
      factorize(a^2+b^2);
  

      {a - i*b,a + i*b}

      off complex;
  
      fa:=(x**2*z+y**4*z**2+5)*
          (x*y**3+z**2)*
          (-x**3*y+z**2+3)*
          (x**3*y**4+z**2);
  

                9  8      8  5  3    7  12  2      7  8    6  9  4
      fa :=  - x *y *z - x *y *z  - x *y  *z  - 5*x *y  - x *y *z
  
                6  7  3      6  7        6  5  2    6  4  3    5  4  5
             + x *y *z  + 3*x *y *z - 5*x *y *z  - x *y *z  + x *y *z
  
                  5  4  3    5    5    4  11  4      4  11  2    4  8  4
             + 3*x *y *z  - x *y*z  + x *y  *z  + 3*x *y  *z  - x *y *z
  
                  4  7  2       4  7      4  4  2    3  8  6      3  8  4
             + 5*x *y *z  + 15*x *y  - 5*x *y *z  + x *y *z  + 3*x *y *z
  
                3  5  6      3  4  4       3  4  2    3  3  5      3  3  3
             - x *y *z  + 5*x *y *z  + 15*x *y *z  + x *y *z  + 3*x *y *z
  
                  3    4    2  7      2  5      7  6        7  4
             - 5*x *y*z  + x *z  + 3*x *z  + x*y *z  + 3*x*y *z
  
                    3  4         3  2    4  8      4  6      6       4
             + 5*x*y *z  + 15*x*y *z  + y *z  + 3*y *z  + 5*z  + 15*z

      factorize fa;
  

          3    2
      {x*y  + z ,
  
        2      4  2
       x *z + y *z  + 5,
  
           3      2
        - x *y + z  + 3,
  
        3  4    2
       x *y  + z }