#11802: Generation of Lucas sequences modulo an integer
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Reporter: somindu | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.1
Component: basic arithmetic | Resolution:
Keywords: Lucas sequence | Merged in:
ecc2011 | Reviewers:
Authors: Somindu Chaya | Work issues:
Ramanna, Shashank Singh, Srinivas | Commit:
Vivek Venkatesh | 632255798b7721896673d9d75e96a280ef4d59cc
Report Upstream: N/A | Stopgaps:
Branch: |
public/arith/lucas_seqences-11802 |
Dependencies: |
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Changes (by tscrim):
* commit: => 632255798b7721896673d9d75e96a280ef4d59cc
* branch: => public/arith/lucas_seqences-11802
Comment:
Here's a branch version of this (no rebasing was required) and I fixed up
some docstring formatting and deprecated `slow_lucas()` (see below).
Currently `slow_lucas` uses the recursive definition which works for
arbitrary integers, whereas the fast `Q=1` and general both only work in
modular arithmetic? Although from the code, there doesn't seem to be
anything that explicitly uses `n`, so I would (naively) think that this
could work for general integers. I vote to keep the specialized `Q=1`
implementation since it is faster.
I've deprecated `slow_lucas` since the more general
`BinaryRecurrenceSequence` is faster:
{{{
sage: from sage.rings.finite_rings.integer_mod import slow_lucas
sage: %timeit L = [slow_lucas(k,1,-1) for k in range(20)]
10 loops, best of 3: 16.4 ms per loop
sage: %timeit L = [slow_lucas(k,1,-1) for k in range(20)]
10 loops, best of 3: 16 ms per loop
sage: %timeit B = BinaryRecurrenceSequence(1, 1, 2, 1)
100000 loops, best of 3: 4.67 us per loop
sage: B = BinaryRecurrenceSequence(1, 1, 2, 1)
sage: %timeit LB = [B(k) for k in range(20)]
1 loops, best of 3: 15.1 ms per loop
sage: %timeit LB = [B(k) for k in range(20)] # There's caching going on
100 loops, best of 3: 7.7 ms per loop
}}}
Best,[[BR]]
Travis
----
New commits:
||[[http://git.sagemath.org/sage.git/commit/?id=6322557|6322557]]||{{{Deprecated
slow_lucas().}}}||
||[[http://git.sagemath.org/sage.git/commit/?id=b9f0603|b9f0603]]||{{{Some
review tweaks.}}}||
||[[http://git.sagemath.org/sage.git/commit/?id=d8c854c|d8c854c]]||{{{Ticket
#11802 (Generating Lucas sequences modulo an integer)}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/11802#comment:10>
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