[seqfan] Re: Worry about old sequence, A030077, paths in K_n

[Allan Wechsler]

Are there any good examples of nontrivial equivalences? I'm thinking that
we might be able to *characterize* nontrivial equivalences, and thus be
able to prove two paths to be unequal in a sort of "combinatorial" way,
without resorting to extended arithmetic.

On Sat, Apr 2, 2022 at 3:03 PM Sean A. Irvine <sairvin at gmail.com> wrote:

> By the way, my code is using computable reals not floating-point, but it
> still faces the problem of deciding equality.  I've been using 50 decimal
> digits for this problem. I could easily rerun with higher precision, but I
> would like to remove the need for the approximation altogether.
>
> Sean.
>
>
> On Sun, 3 Apr 2022 at 02:04, David Applegate <david at bcda.us> wrote:
>
> > I worry about using floating point (extended or not) to check if
> > different sums of square roots are equal or not.  Using finite precision
> > for this is extremely tricky This is a notoriously hard problem in
> > general.  For example, to see that
> > sqrt(7)+sqrt(14)+sqrt(39)+sqrt(70)+sqrt(72)+sqrt(76)+sqrt(85) !=
> > sqrt(13)+sqrt(16)+sqrt(55)+sqrt(67)+sqrt(73)+sqrt(79) you already need
> > more than double-precision floating point (their difference is 10^-19,
> > see
> >
> >
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.156.3838&rep=rep1&type=pdf
> > ).
> > There is a randomized polynomial time algorithm for testing equality,
> > but it isn't just compute the result to enough precision.
> >
> > Some links with additional information:
> >
> >
> https://cstheory.stackexchange.com/questions/79/problems-between-p-and-npc/4010#4010
> > https://topp.openproblem.net/p33
> >
> >
> https://refubium.fu-berlin.de/bitstream/handle/fub188/18449/1993-13.pdf;jsessionid=89F489131478714C98250CFA34AFBFE7?sequence=1
> >
> > -Dave
> >
> > On 4/2/2022 5:05 AM, Sean A. Irvine wrote:
> > > So far I can verify to A030077(14):
> > >
> > > 2022-04-02 21:46:54 1
> > > 2022-04-02 21:46:54 1
> > > 2022-04-02 21:46:54 1
> > > 2022-04-02 21:46:54 3
> > > 2022-04-02 21:46:54 5
> > > 2022-04-02 21:46:54 17
> > > 2022-04-02 21:46:54 28
> > > 2022-04-02 21:46:54 105
> > > 2022-04-02 21:46:54 161
> > > 2022-04-02 21:46:54 670
> > > 2022-04-02 21:46:55 1001
> > > 2022-04-02 21:47:00 2869
> > > 2022-04-02 21:47:58 6188
> > > 2022-04-02 22:01:58 26565
> > >
> > > I adapted my existing program for A007874 to this case.  I'm not sure
> > why I
> > > skipped over it before, but perhaps the dihedral group confused me.
> The
> > > program uses 50 digits of precision for the length determination. I
> feel
> > > like it should be possible to do this without any kind of precision
> > limit,
> > > but I don't have the time for that now.  I'll leave it running
> overnight.
> > >
> > > I'll also start a run for A007874 itself which also has four additional
> > > terms with a(15) looking a little suspicious.
> > >
> > > Sean.
> > >
> > >
> > >
> > > On Sat, 2 Apr 2022 at 16:22, Neil Sloane <njasloane at gmail.com> wrote:
> > >
> > >> To Seq Fans, The creator of an interesting sequence,  A030077, Daniel
> > >> Gittelson, submitted 12 terms in 1999, and 4 more terms were added in
> > 2007
> > >> by a former editor. Daniel G. wrote to me today, expressing doubt
> about
> > the
> > >> 4 additional terms.
> > >>
> > >> He says he interrupted his study of sequences to pursue a medical
> > career,
> > >> but now that he is retired, he can return to combinatorics.
> > >>
> > >> It would be nice if someone could verify the terms! (It is not at all
> > >> obvious to me how to do this.)
> > >>
> > >> Neil Sloane
> > >>
> > >> --
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >>
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> > --
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> >
>
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