I am unable to create a differential operator to generate Legendre Polynomials using the Axiom Book prescription or using HyoerDoc?. I have tried on both Windows and Mandrake Linux versions and the result is the same.

Gerald Farmer

(1) -> L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)

dx := operator("D") :: OP(POLY FRAC INT)

(1)

Dp(p) == D(p, 'x)

-- use an explicit function instead of anonymous
evaluate(dx, Dp)

Compiling function Dp with type Polynomial(Fraction(Integer)) -> 
      Polynomial(Fraction(Integer))

(2)

E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)

L 15

Compiling function L with type Integer -> Polynomial(Fraction(
      Integer))

Compiling function L as a recurrence relation.

(3)

E 15

   There are no library operations named ** 
      Use HyperDoc Browse or issue
                                 )what op **
      to learn if there is any operation containing " ** " in its name.
   Cannot find a definition or applicable library operation named ** 
      with argument type(s) 
                                 Variable(x)
                               PositiveInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   FriCAS will attempt to step through and interpret the code.
   There are no library operations named ** 
      Use HyperDoc Browse or issue
                                 )what op **
      to learn if there is any operation containing " ** " in its name.

   Cannot find a definition or applicable library operation named ** 
      with argument type(s) 
                                 Variable(x)
                               PositiveInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.