Basic operations

 

In Derive

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

inputs outputs

• by default parantheses are not expanded

      p := (a+b+c)^4
  

                      4
      P := (a + b + c)

  expand

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

• derivation

      d := dif(p,a)
  

           d     
      D := --  P 
           da    
  
  
         3       2                  2            2       3       2           2
      4 a  + 12 a  (b + c) + 12 a (b  + 2 b c + c ) + 4 b  + 12 b  c + 12 b c
  
  
            3
       + 4 c
  
  
     d   d   d    4      3        3        2  2       2          2  2        3
     --  --  --  a  + 4 a  b + 4 a  c + 6 a  b  + 12 a  b c + 6 a  c  + 4 a b
     db  db  da  
  
  
               2             2        3    4      3        2  2        3    4 
       + 12 a b  c + 12 a b c  + 4 a c  + b  + 4 b  c + 6 b  c  + 4 b c  + c  
                                                                              
  
         
         
         
  
  
     24 a + 24 b + 24 c

• integration

      i := int(d,a)
  

            
      I :=   D da
  
  
       4      3              2   2            2          3       2           2
      a  + 4 a  (b + c) + 6 a  (b  + 2 b c + c ) + a (4 b  + 12 b  c + 12 b c
  
  
            3
       + 4 c )

• verification

      i - p
  

      I - P
  
  
          4      3        2  2        3    4
      - (b  + 4 b  c + 6 b  c  + 4 b c  + c )

• greatest common divisor of polynomials

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

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

      g := 34 x^19-91 x+70 x^7-25 x^16+20 x^3-86
  
      f := g  (64 x^34-21 x^47-126 x^8-46 x^5-16 x^60-81)
  
      h := g  (72 x^60-25 x^25-19 x^23-22 x^39-83 x^52+54 x^10+81)
  
      f/h
   

  insufficient memory