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notes.txt
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notes.txt
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PART 1: THE EMAIL LOOKUP SERVER
I include this because it uses Russ Cox's fast lookup - search.db -
to test if a sequence is in the OEIS. In contrast, Superseeker,
in Part 2, uses my old grep, which is much slower. If I had more
time, I would switch over Superseeker to use search.db.
Here is the program, called "hisP"
[Handbook of Integer Sequences lookup, prim version]
It uses programs dehtml3 and getfrom2, which
are described in more detail in Part 2.
It also mentions some other files (e.g. stripped) which
are not used at present.
As emails addressed to "sequences@research.att.com" arrive, they are
piped into this program.
PART 2: SUPERSEEKER
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&
&&& Summary: Here is a summary of what Superseeker does:
&&&
&&& - Runs superprocfan (written by Mira Bernstein),
&&& which repeatedly computes inverse binomial
&&& transform of the sequence (if these triangles are
&&& glued together they form a "fan" - see the Bernstein-Sloane
&&& paper on eigensequences). If any of these are recognizable,
&&& we have a formula.
&&&
&&& - Runs proc8 (compiled version of superproc8.f)
&&& which tests if differences of some order are periodic
&&&
&&& - If the sequence only takes two values, a and b say, i.e. is a "binary" sequence,
&&& proc9 (compiled version of superproc9.f) computes the
&&& six canonical associated sequences and looks them up in the OEIS.
&&& The 6 sequences, all equivalent to the
&&& original are: replace a,b by 1,2; by 2,1; positions of a's,
&&& of b's; run lengths; and the derivative.
&&&
&&& - superproc2prim calls the "guessgf" parts of the "gfun" Maple package
&&& of Bruno Salvy and Paul Zimmermann
&&& to look for generating functions.
&&& See
&&& http://www.maplesoft.com/support/help/Maple/view.aspx?path=gfun
&&& or
&&& pictor.math.uqam.ca/~plouffe/articles/gfun.pdf
&&& for more about gfun
&&&
&&& - superproc4prim calls the "listtorec" parts of the "gfun" Maple package
&&& of Bruno Salvy and Paul Zimmermann
&&& to look for recurrences.
&&&
&&& - Uses Harm Derksen's program "superguesss" to try
&&& to guess a formula or recurrence.
&&& [Harm Derksen's program "guesss" uses Pade'-Hermite approximations
&&& - see http://www.maplesoft.com/CyberMath/share/guesss.html.
&&& That algorithm is described in:
&&& An algorithm to compute generalized Pade'-Hermite forms,
&&& Report 9403 (1994), Dept. of Math., Catholic University Nijmegen
&&& (available from http://www.math.lsa.umich.edu/~hderksen/preprints/pade.ps).]
&&&
&&& - Uses Christian Kratthentaler's Mathematica program Rate ("superrate.m") which tries to
&&& guess a closed form for a sequence ("rate" is "guess" in German).
&&& For a description of Rate, see
&&& http://radon.mat.univie.ac.at/People/kratt/rate/rate.html.
&&&
&&& - Apply many transformations to the sequence and look up
&&& the result in the OEIS.
&&& The transforms are performed using Mathematica, with the
&&& help of Olivier Gerard's program seqtranslib.m
&&& A list of the transforms used is in "supertrans".
&&&
&&& - Apply many transformations to the sequence and look up
&&& the result in a table of sequences formed
&&& by taking the first differences of all the sequences in the OEIS.
&&& Uses the compressed file of the difference sequences, "dripped".
&&& The transforms are performed using Mathematica, with the
&&& help of Olivier Gerard's program seqtranslib.m
&&& A list of the transforms used is in "supertrans".
&&&
&&& - superproc6prim calls the "listtoalgeq" parts of the "gfun" Maple package
&&& of Bruno Salvy and Paul Zimmermann
&&& to look for algebraic equations
&&&
&&& - Uses superbeattyprim, written by Simon Plouffe,
&&& to test if the sequence is a Beatty sequence
&&&
&&& - Uses John Linderman's program CheckSeq.pl
&&& to see if the sequence has a partial overlap with
&&& any existing sequence
&&&
&&& - Uses the unix utility "agrep" to look for sequences in the OEIS
&&& that have edit distnce 1, 2 or 3 from the given sequence.
&&&
&&& - (Not used at present) runs "supercorr2" to look
&&& for sequences that are highly correlated with the given sequence.
&&&
&&& - Several other people have offered the OEIS their programs for guessing
&&& a formula or explanation for a sequence, but I did not
&&& have time to incorporate them into Superseeker.
&&& Hopefully this can be done on the wiki version.
&&&
&&& Note that the file "superhelp.txt" included below
&&& gives another summary of what Superseeker does.
&&&
&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
As emails addressed to "superseeker@research.att.com" arrive, they are
piped into the program superhisP, and later are fed into superasstprim.
superproc2prim calls the guessgf sections of gfun. gfun is not included here, since it is part of Maple.