#11802: Generation of Lucas sequences modulo an integer
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Reporter: somindu | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.7.2
Component: basic arithmetic | Keywords: Lucas sequence
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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The Lucas sequence modulo an integer n is given by {{{V_k = PV_{k-1} - Q
V_{k-2} mod n}}} with {{{V_0 = 2 and V_1 = P}}}. This is not implemented
in Sage. There are algorithms {{{fast_lucas}}} and {{{slow_lucas}}} that
compute this sequence only for the special case {{{Q=1}}}.
{{{
sage: from sage.rings.finite_rings.integer_mod import fast_lucas
sage: [fast_lucas(i, Mod(8,11)) for i in range(15)]
[2, 8, 7, 4, 3, 9, 3, 4, 7, 8, 2, 8, 7, 4, 3]
}}}
{{{
sage: from sage.rings.finite_rings.integer_mod import slow_lucas
sage: [slow_lucas(i, Mod(8,11)) for i in range(15)]
[2, 8, 7, 4, 3, 9, 3, 4, 7, 8, 2, 8, 7, 4, 3]
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11802>
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