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Submitted by : (unknown) at: 2007-11-17T22:11:25-08:00 (10 years ago)
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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

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)

\label{eq1}D(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))

\label{eq2}D(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.

\label{eq3}\begin{array}{@{}l}
\displaystyle
{{{9694845}\over{2048}}\ {x^{15}}}-{{{35102025}\over{2048}}\ {x^{13}}}+{{{50702925}\over{2048}}\ {x^{11}}}- 
\
\
\displaystyle
{{{37182145}\over{2048}}\ {x^9}}+{{{14549535}\over{2048}}\ {x^7}}-{{{2909907}\over{2048}}\ {x^5}}+{{{255255}\over{2048}}\ {x^3}}- 
\
\
\displaystyle
{{{6435}\over{2048}}\  x}
(3)
Type: Polynomial(Fraction(Integer))
axiom
E 15
axiom
Compiling function E with type PositiveInteger -> Operator(
      Polynomial(Fraction(Integer)))

\label{eq4}{240}-{2 \  x \  D}+{{\left(-{x^2}+ 1 \right)}\ {D^2}}(4)
Type: Operator(Polynomial(Fraction(Integer)))
axiom
(E 15)(L 15)

\label{eq5}0(5)
Type: Polynomial(Fraction(Integer))

Category: Axiom on Linux => Axiom Documentation Status: open => closed




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