#15395: Wrong limit for squence involving Fibonacci sequence, 0 instead of
golden
ratio
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Reporter: aginiewicz | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: calculus | Keywords: limit,golden_ratio
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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I tried to define Fibonacci sequence using golden ratio in two ways, using
values:
{{{
sage: value_1 = 1-golden_ratio
sage: value_2 = -golden_ratio^(-1)
sage: bool(value_1 == value_2)
true
}}}
(gives true, so two definitions, F1 and F2 below should be equal, even
though they are not according to Sage)
{{{
sage: F1(k) = (golden_ratio^k-(value_1)^(k))/sqrt(5)
sage: F2(k) = (golden_ratio^k-(value_2)^(k))/sqrt(5)
sage: bool(F1(k) != F2(k))
true
}}}
When simplified everything seems to be equal at least for first 10 or 1000
elements:
{{{
sage: [(F1(j)-F2(j)).full_simplify() for j in range(10)]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
}}}
Anyway, now to the error: limit for F1 gives wrong result:
{{{
sage: limit(F1(k+1)/F1(k), k=oo)
0
}}}
and for F2 works OK:
{{{
sage: limit(F2(k+1)/F2(k), k=oo)
1/2*sqrt(5) + 1/2
}}}
I've tested it with Sage 5.12 and 5.11, with same result. This can be as
simple as some thing with how golden ratio is handled, or something far
more involved maybe?
--
Ticket URL: <http://trac.sagemath.org/ticket/15395>
Sage <http://www.sagemath.org>
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