Table formatting proposal

Tue Jul 27 20:38:18 CEST 1999

Here's the original message to which David Wilson responded.  Sorry for
any confusion the reply-before-actual-message caused...

-E

On Mon, 26 Jul 1999, N. J. A. Sloane wrote:

> i think david wilson's proposal is brilliant, and would indeed
> many of the indexing problems.

Although Neil's opinion is the one that really matters on such issues :),
I also think David has a great idea here.

> if only he had suggested this 10 years ago
> 
> rather than changing all 50,000 %O lines, a more feasible way to
> follow his suggestion would be to mention this in Comment (%C) lines:  
> Indexed by A012345 (say).

IMHO, I think the comment line should stay comments-only (and not include
actual content information like index sequences).

However, here's a fairly detailed, but I think very general and precise,
proposal for dealing with the general problem of tabular sequences.  How
about adding a new optional tag (say %f for "formatting") which could
specify, for a tabl/tabf sequence, the sequence numbers indexing the
sequence at hand, the offsets, a reference sequence giving the number of
elements in each row, and the preferred alignment of rows = C, L, or R?  
I think this would fairly precisely specify the format of a tabular
sequence (somebody correct me if there are ambiguities which have escaped
me).

Take, for example, Pascal's triangle read by rows

ID Number: A007318 (Formerly M0082)
Sequence:  1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,1,6,15,20,15,6,
           1,1,7,21,35,35,21,7,1,1,8,28,56,70,56,28,8,1,1,9,36,84,126,
           126,84,36,9,1,1,10,45,120,210,252,210,120,45,10,1,1,11,55,
           165,330,462,462,330,165,55,11,1
Name:      Pascal triangle read by rows.

       1                      (0,0)
     1   1                (1,0)   (1,1)
   1   2   1            (2,0)  (2,1)  (2,2)
 1   3   3   1       (3,0)  (3,1) (3,2)  (3,3)

This would have an %i entry something like
%i A003056,A002262 (0,0) A000027 C 

where the indexing sequences are

ID Number: A003056
Sequence:  0,1,1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,
           7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,10,10,10,
           10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,
           12,12,12
Name:      n appears n+1 times.

ID Number: A002262
Sequence:  0,0,1,0,1,2,0,1,2,3,0,1,2,3,4,0,1,2,3,4,5,0,1,2,3,4,5,6,0,1,
           2,3,4,5,6,7,0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,
           5,6,7,8,9,10,0,1,2,3,4,5,6,7,8,9,10,11,0,1,2,3,4,5,6,7,8,9,
           10,11,12,0,1,2,3,4,5
Name:      Integers 0 to n followed by integers 0 to n+1 etc.

The offsets from start of the indexing sequences are (0,0).

The number of lines on successive rows for formatting are

ID Number: A000027 (Formerly M0472 and N0173)
Sequence:  1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
           24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
           44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
           64,65,66,67,68,69,70,71,72,73,74,75,76,77
Name:      The natural numbers.

And the rows themselves are to be centered (C).

Although I haven't thought it all the way through, the %f line could be
generated semi-automatically in the Maple and Mathematica scripts for
automatic sequence formatting.  Some of the looking up and specification
of the reference sequences could be automated.  For example, instead of
feeding the parser flat lists, nested lists could be used.  (I currently
generate nested lists for tabl entries anyway but flatten them out, thus
losing the row length information.)  This would give you a list of row
lengths right away.  Furthermore, giving lists like { {{{0,0},1}},
{{{1,0},1},{{1,1},1}}, ... } to a special command could automatically pull
out the indexing sequences and create a set of sequence lookup lines to be
e-mailed to sequences, with the resulting sequence numbers then being
inserted in the script FormatSequence[] (or whatever the Maple equivalent
is) command to specify the %i line.

In practice, you could also make assumptions that the index sequences were
"simple" and so have some database of %A numbers corresponding to common
indexing sequences and row lengths built in to the parsing scripts.

If you didn't like the %i line, you could just ignore it.

Does this sound like too much trouble or perhaps potentially useful?  I
personally think it would add value to the precise specification of
tabular sequences, although I'll back off if someone points out any
reasons why it won't work...

Cheers,
-Eric

--------------------------------------------------------------------
* Eric W. Weisstein                                                *
* Encyclopedist             phone:  217-398-0700 x599              *
* Wolfram Research, Inc.    FAX:    217-398-0747                   *
* 100 Trade Center Drive    e-mail: eww at wolfram.com                *
* Champaign, IL 61820-7237  WWW: www.treasure-troves.com/eric.html *
--------------------------------------------------------------------