/usr/lib/open-axiom/input/opalg.input is in open-axiom-test 1.4.1+svn~2626-2ubuntu2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | --Copyright The Numerical Algorithms Group Limited 1991, 1995.
)cl all
-- This is the recursive definition of the Legendre polynomials
L n ==
n = 0 => 1
n = 1 => x
(2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2)
L 5
-- Create the differential operator d/dx on Q[x]
dx := operator("D")::OP(POLY FRAC INT)
-- and attach the map d/dx to it:
evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT)
-- This is the differential equation satisfied by the nth Legendre poly:
E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)
E 5
[L i for i in 1..10]
[E i for i in 1..10]
[(E i)(L i) for i in 1..10]
|