W. Lang: Formatting of sequences

2001, updated for maple12: Feb 2009

Old Maple V version (no column widths adjustments, hence faster)


Formatting EIS   tabl and tabf arrays

lower triangular matrix (tabl),   staircase matrix (tabf)

offset for rows and columns (integers):           

Id-number for output caption (will be the EIS A-number if used in 'a-sequence' below)   


a-sequence: 

If the 'tabl' option is valid skip the next parts, go to 'Chose width of the output page', then 'SEND'.

For tabf arrays a second sequence, called the tabf shape sequence, is needed:

either row length sequence,   or step length sequence


shape sequence: 
Entry irrelevant if preset shape sequence from pull down menue has been chosen.

Chose width of output page    

   
CLEAR


Explanations:

  • Select either 'tabl', if the 'a-sequence' should be formatted as a lower triangular matrix arrays , or 'tabf' for other (irregular) arrays.
  • The output will have numbered rows and columns starting with the two 'off set' values. The default values are [0,0].
  • The output caption will quote the 'Id-number' (with an 'A' in front). It will automatically be the EIS A-number if this option is chosen for the 'a-sequence'.
  • The 'a-sequence' input can be an EIS A-number representing the tabl or tabf sequence as defined in EIS under 'Keywords'.
    If a sequence is typed in (use the pull down menue for 'a-sequence'), it should be a string of integers, enclosed by brackets [ ] and separated by commas (insensitive to blanks, no comma at the end), representing a tabl or tabf sequence.
  • For 'tabf' arrays a 'shape sequence' is needed in addition to the 'a-sequence'. One can choose either the row lengths or the step widths (the difference of the number of entries in consecutive rows, starting with the number of entries of the first row). No negative numbers are allowed for row lengths sequence entries.
  • The width of the output page entry (in number of characters) influences the row number of the output array (tabl or tabf type).
The output will be a complete matrix type array (the 'alist' string is cut off, depeding on the 'shape sequence' which in the tabl case is the sequence of ten 1's). If the EIS A-number for 'a-sequence' or the tabf shape sequence is known one could also use the 'type in ...' option and paste and copy from the EIS files. One can get the sequence, say A000108, from the address http://www.research.att.com/~njas/sequences/A000108.

Acknowledgements:

This application would not exist without advice and help from Bernd Feucht, Gerrit Jahn, Christian Kaufhold, Christoph Mayer and, especially, from Dr. Thomas Hahn. Thanks go also to Dr. N. J. A. Sloane who suggested to allow as input also EIS A-numbers as well as row length sequences in the tabf case.



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