Basic operations

 

In Macsyma

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

inputs outputs

• by default, parentheses are not expanded

      pol: (a+b+c)^4;
  

                                          4
                               (c + b + a)

      pol: expand(pol);
  

      4        3        3      2  2           2      2  2      3           2
     c  + 4 b c  + 4 a c  + 6 b  c  + 12 a b c  + 6 a  c  + 4 b  c + 12 a b  c
  
                           2          3      4        3      2  2      3      4
                     + 12 a  b c + 4 a  c + b  + 4 a b  + 6 a  b  + 4 a  b + a

• differentiation

      dpol: diff(pol, a);
  

        3         2         2       2                    2        3         2
     4 c  + 12 b c  + 12 a c  + 12 b  c + 24 a b c + 12 a  c + 4 b  + 12 a b
  
                                                                     2        3
                                                               + 12 a  b + 4 a

      diff(pol, a, 1, b, 2);
  

                            24 c + 24 b + 24 a

• integration

      integrate(dpol, a);
  

          3           2      2  2         2         2          3          3
     4 a c  + 12 a b c  + 6 a  c  + 12 a b  c + 12 a  b c + 4 a  c + 4 a b
  
                                                             2  2      3      4
                                                        + 6 a  b  + 4 a  b + a

• verification

      %-pol;
  

                       4        3      2  2      3      4
                    - c  - 4 b c  - 6 b  c  - 4 b  c - b

• polynomial greatest common divisor

      (a^2-b^2)/(a^2-2*a*b+b^2);
  

                                  2    2
                                 a  - b
                             ---------------
                              2            2
                             b  - 2 a b + a

      ratsimp(%);
  

                                   b + a
                                 - -----
                                   b - a

  
      g : 34*x^19-91*x+70*x^7-25*x^16+20*x^3-86;
  

                   19       16       7       3
               34 x   - 25 x   + 70 x  + 20 x  - 91 x - 86

      f1 : g * (64*x^34-21*x^47-126*x^8-46*x^5-16*x^60-81);
  

          19       16       7       3
     (34 x   - 25 x   + 70 x  + 20 x  - 91 x - 86)
  
                                    60       47       34        8       5
                             (- 16 x   - 21 x   + 64 x   - 126 x  - 46 x  - 81)

      f2 : g * (72*x^60-25*x^25-19*x^23-22*x^39-83*x^52+54*x^10+81);
  

          19       16       7       3
     (34 x   - 25 x   + 70 x  + 20 x  - 91 x - 86)
  
                          60       52       39       25       23       10
                     (72 x   - 83 x   - 22 x   - 25 x   - 19 x   + 54 x   + 81)

      gcd(f1,f2);
  

                   19       16       7       3
               34 x   - 25 x   + 70 x  + 20 x  - 91 x - 86