Edit detail for #223 Legendre Polynomials revision 1 of 2

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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  

From billpage Sun Oct 23 12:50:48 -0500 2005
From: billpage
Date: Sun, 23 Oct 2005 12:50:48 -0500
Subject: Legendre example
Message-ID: <20051023125048-0500@wiki.axiom-developer.org>

Axiom book page 720:

\begin{axiom}
L n ==
  n = 0 => 1
  n = 1 => x
  (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
\end{axiom}
\begin{axiom}
dx := operator("D") :: OP(POLY FRAC INT)
Dp(p) == D(p, 'x)
-- use an explicit function instead of anonymous
evaluate(dx, Dp)
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
\end{axiom}
\begin{axiom}
L 15
E 15
(E 15)(L 15)
\end{axiom}

Submitted by : (unknown) at: 2007-11-17T22:11:25-08:00 (16 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : general Severity : critical serious normal minor wishlist Status : open pending closed Optional subject :   Optional comment :

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

Legendre example --billpage, Sun, 23 Oct 2005 12:50:48 -0500 reply

Axiom book page 720:

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

Type: Void

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

(1)

Type: Operator Polynomial Fraction Integer

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

Type: Void

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

axiom

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

(2)

Type: Operator Polynomial Fraction Integer

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

Type: Void

axiom
L 15

axiom

Compiling function L with type Integer -> Polynomial Fraction 
      Integer

axiom

Compiling function L as a recurrence relation.

(3)

Type: Polynomial Fraction Integer

axiom
E 15

axiom

Compiling function E with type PositiveInteger -> Operator 
      Polynomial Fraction Integer

(4)

Type: Operator Polynomial Fraction Integer

axiom
(E 15)(L 15)

(5)

Type: Polynomial Fraction Integer