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last edited 16 years ago by kratt6 |
Edit detail for #223 Legendre Polynomials revision 2 of 2
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Editor: kratt6
Time: 2007/12/20 01:02:10 GMT-8 |
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From kratt6 Thu Dec 20 01:02:10 -0800 2007
From: kratt6
Date: Thu, 20 Dec 2007 01:02:10 -0800
Subject:
Message-ID: <20071220010210-0800@axiom-wiki.newsynthesis.org>
Category: Axiom on Linux => Axiom Documentation
Status: open => closed
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.
![\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}](images/5004167004370473973-16.0px.png "\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))) | (4) |
Type: Operator(Polynomial(Fraction(Integer)))
axiom
(E 15)(L 15)
 | (5) |
Type: Polynomial(Fraction(Integer))
Category: Axiom on Linux => Axiom Documentation
Status: open => closed