[seqfan] Re: Periodicity of seqs mod m - research idea

[Zak Seidov]

Are there similar tools in PARI?
If yes one at least can compare PARI/Mma results.


>Воскресенье, 19 февраля 2017, 5:03 +03:00 от Neil Sloane <njasloane at gmail.com>:
>
>Harvey said:  "a new function in Mathematica version 10 is
>FindTransientRepeat."
>This worries me. Without independent verification I would not accept the
>results of a secret program like that. Especially if their program says
>there are no cycles.
>What method do they use? Is it probabilistic or deterministic? Certainly if
>they claim to find a cycle that can be checked but one would still need to
>check that there is no shorter cycle and that their cycle does not begin
>any earlier than they claim.
>
>I wrote a Fortran implementation of Floyd's algorithm in 2010 that I would
>be happy to send anyone. It is quite short. There is also a C translation.
>
>Best regards
>Neil
>
>Neil J. A. Sloane, President, OEIS Foundation.
>11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>Phone: 732  828 6098 ; home page:  http://NeilSloane.com
>Email:  njasloane at gmail.com
>
>
>On Sat, Feb 18, 2017 at 5:59 PM, Harvey P. Dale < hpd at hpdale.org > wrote:
>
>>         A fairly new function in Mathematica version 10 is
>> FindTransientRepeat. For folks using Mathematica, employing that function
>> may assist in identifying periodic cycles.
>>         Best,
>>         Harvey
>>
>>
>> -----Original Message-----
>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Marc
>> LeBrun
>> Sent: Saturday, February 18, 2017 3:23 PM
>> To: Sequence Fanatics Discussion list < seqfan at list.seqfan.eu >
>> Subject: [seqfan] Re: Periodicity of seqs mod m - research idea
>>
>> On Feb 18, 2017, at 11:44 AM, Neil Sloane < njasloane at gmail.com > wrote:
>>
>> > To test for the presence of a cycle (which in general won't start at
>> > the beginning of the sequence) the standard alg. is Floyd's hare and
>> > tortoise alg.  There is a Wikipedia article on Cycle Detection.
>>
>> In some situations Gosper’s algorithm (cited but not described in
>> Wikipedia) is nice  http://www.inwap.com/pdp10/hbaker/hakmem/flows.html
>> ITEM 132 (Gosper): LOOP DETECTOR
>>
>>
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