This file is indexed.

/usr/lib/open-axiom/input/contfrac.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
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
--Copyright The Numerical Algorithms Group Limited 1991.

)clear all
r1 := 3/4
r2 := 314159/100000
 
c1 := r1 :: ContinuedFraction Integer
c2 := r2 :: ContinuedFraction Integer
 
-- We can view these in the list notation
partialQuotients c1
partialQuotients c2
 
-- These are algebraic objects, so we can manipulate them accordingly
c1 + c2
c1 * c2
1 / c2
c1 - c2
c2 - c1
 
-- and can convert them back to rational numbers.
convergents %
 
 
)clear all
-- Continued fractions over other Euclidean domains
a0 := ((-122 + 597* %i)/(4 - 4*%i))
b0 := ((-595 - %i)/(3 - 4*%i))
a  := continuedFraction(a0)
b  := continuedFraction(b0)
a + b
convergents % 
last % - (a0 + b0)
a / b
convergents %
last % - (a0/b0)

(a = b)::Boolean
c := continuedFraction(3 + 4*%i, repeating [1 + %i], repeating [5 - %i])
a/c
-- (a = c)::Boolean -- should give error
d := complete continuedFraction(3+4*%i, repeating [1+%i],[i-%i for i in 1..5])
(a = d)::Boolean


q : Fraction UnivariatePolynomial('x, Fraction Integer) 
q := (2*x**2 - x + 1) / (3*x**3 - x + 8)
 
c := continuedFraction q
d := continuedFraction differentiate q
c/d
convergents %
q/differentiate q

)clear all
-- This file illustrates continued fractions.
 
)set streams calculate 7
 
-- Use the notation Phi(ai/bi, i = 1..n) for continued fractions
-- a1/(b1 + (a2/b2 + ... (an/bn) ...))
 
-- 1/(e-1) may be written  Phi(i/i, i = 1..)
s := continuedFraction(0, expand [1..], expand [1..])
-- Euler discovered the relation (e-1)/(e+1) = Phi(1/(4i-2), i = 1..)
t := reducedContinuedFraction(0, [4*i-2 for i in 1..])
-- Arithmetic on infinite continued fractions is supported.
-- The results are given in reduced form.  We illustrate by using the
-- values s = 1/(e-1) and t = (e-1)/(e+1) to recover the expansion for e.
e := 1/(s*t) - 1
c := convergents e
for i in 1..15 repeat
  output numeric c.i
(s = t)::Boolean