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#222 FramedNonAssociativeAlgebraFunctions2 and map ←	↑	→ #224 ICARD fails to display database info

#223 Legendre Polynomials

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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added:

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:

fricas

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

Type: Void

fricas

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

$\label{eq1}D$

(1)

Type: Operator(Polynomial(Fraction(Integer)))

fricas

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

Type: Void

fricas

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

fricas

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

$\label{eq2}D$

(2)

Type: Operator(Polynomial(Fraction(Integer)))

fricas

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

Type: Void

fricas

L 15

fricas

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

fricas

Compiling function L as a recurrence relation.

$\label{eq3}\begin{array}{@{}l} \displaystyle {{\frac{9694845}{2048}}\ {{x}^{15}}}-{{\frac{35102025}{2048}}\ {{x}^{13}}}+ \ \ \displaystyle {{\frac{50702925}{2048}}\ {{x}^{11}}}-{{\frac{37182145}{2048}}\ {{x}^{9}}}+ \ \ \displaystyle {{\frac{14549535}{2048}}\ {{x}^{7}}}-{{\frac{2909907}{2048}}\ {{x}^{5}}}+ \ \ \displaystyle {{\frac{255255}{2048}}\ {{x}^{3}}}-{{\frac{6435}{2048}}\ x}$

(3)

Type: Polynomial(Fraction(Integer))

fricas

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.

... --kratt6, Thu, 20 Dec 2007 01:02:10 -0800 reply

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