.. -*- coding: utf-8 -*-












.. role:: sref(numref)
.. role:: xref(numref)
.. Copyright (C) 2019, Wolfgang Scherer, <Wolfgang.Scherer at gmx.de>
..
.. This file is part of Development.
..
.. Permission is granted to copy, distribute and/or modify this document
.. under the terms of the GNU Free Documentation License, Version 1.3
.. or any later version published by the Free Software Foundation;
.. with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
.. A copy of the license is included in the section entitled "GNU
.. Free Documentation License".

.. inline comments (with du_comment_role)
.. role:: rem(comment)
.. role:: html(raw)
   :format: html
.. role:: shx(code)
   :language: sh

.. rst-class:: narrow xmedium xlarge xhuge xultra

##################################################
:rem:`|||:sec:|||`\ Markup converter design
##################################################
.. >>CODD See `the components of a doctoral dissertation and their order <http://site.uit.no/english/writing-style/bookstructure/>`_
.. >>CODD Dedication
.. >>CODD Epigraph
.. >>CODD Abstract

.. compound::

   pandoc(1) most probably implements a central generic DOM for markup
   conversion vs. a direct conversion between markup languages. The
   difference being development requirements of :math:`\Theta(n)`
   vs. :math:`\Theta(n^2)`.

   .. \|:here:|

.. >>CODD Introduction
.. >>CODD Chapter

.. see https://tex.stackexchange.com/questions/95162/how-to-create-a-matrix-with-20-columns-in-latex
.. raw:: latex

   \setcounter{MaxMatrixCols}{20}

==============================================================
:rem:`|||:sec:|||`\ Direct conversion between markup languages
==============================================================

For each new markup language :math:`n`, a parser supporting
:math:`n-1` renderers must be written for translating the new language
to all implemented languages. For :math:`n-1` parsers a renderer must
be added for translating the implemented languages to the new
language.

.. graphviz::

   digraph pandoc {
   layout = circo;
   RST [label="ReST"];
   MD [label="markdown"];
   HTML [label="HTML"];
   MW [label="MediaWiki"];
   JSON [label="MediaWiki"];

   RST -> MD [label="p+r>"];
   RST -> HTML [label="p+r>"];
   RST -> MW [label="p+r>"];
   RST -> JSON [label="p+r>"];

   MD -> RST [label="p+r>"];
   MD -> HTML [label="p+r>"];
   MD -> MW [label="p+r>"];
   MD -> JSON [label="p+r>"];

   HTML -> RST [label="p+r>"];
   HTML -> MD [label="p+r>"];
   HTML -> MW [label="p+r>"];
   HTML -> JSON [label="p+r>"];

   MW -> RST [label="p+r>"];
   MW -> MD [label="p+r>"];
   MW -> HTML [label="p+r>"];
   MW -> JSON [label="p+r>"];

   JSON -> RST [label="p+r>"];
   JSON -> MD [label="p+r>"];
   JSON -> HTML [label="p+r>"];
   JSON -> MW [label="p+r>"];
   }

Progression for number of nodes and total number of edges / 2:

.. math::

   \begin{matrix}
   \mbox{nodes}     & 0 & 1 & 2 & 3 & 4 & 5  & 6  & 7  & 8  & 9  & 10\\
   \mbox{edges} / 2 & 0 & 0 & 1 & 3 & 6 & 10 & 15 & 21 & 28 & 36 & 45
   \end{matrix}

Identified on `OEIS`_ as sequence `A161680`_ :math:`a(n) =
\binom{n}{2} = \frac{n^2 - n}{2}` (zero followed by `a000217`_,
triangular numbers: :math:`a(n) = \binom{n+1}{2} = \frac{n
(n+1)}{2}`).

.. _`OEIS`: https://oeis.org/
.. _`The On-Line Encyclopedia of Integer Sequences (OEIS)`: https://oeis.org/
.. _`A000217`: https://oeis.org/A000217
.. _`A161680`: https://oeis.org/A161680

=======================================================
:rem:`|||:sec:|||`\ Conversion via central abstract DOM
=======================================================

For each new markup language one parser (markup -> DOM) and one
renderer (DOM -> markup) must be written to fully support translations
between all previously implemented languages and the new language.

.. graphviz::

   digraph pandoc {
   layout = circo;
   DOM [label="DOM"];
   RST [label="ReST"];
   MD [label="markdown"];
   HTML [label="HTML"];
   MW [label="MediaWiki"];
   JSON [label="MediaWiki"];

   RST -> DOM [label="parse>"];
   MD -> DOM [label="parse>"];
   HTML -> DOM [label="parse>"];
   MW -> DOM [label="parse>"];
   JSON -> DOM [label="parse>"];

   DOM -> RST [label="render>"];
   DOM -> MD [label="render>"];
   DOM -> HTML [label="render>"];
   DOM -> MW [label="render>"];
   DOM -> JSON [label="render>"];
   }

Progression for number of nodes and total number of edges / 2:

.. math::

   \begin{matrix}
   \mbox{nodes}     & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\\
   \mbox{edges} / 2 & 0 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9
   \end{matrix}

:math:`a(n) = \max(0, n-1)` (see also `A289207`_).

.. _`A289207`: https://oeis.org/A289207

.. >>CODD Conclusion
.. >>CODD Appendix A

.. \|:here:|

.. >>CODD Notes
.. ==================================================
.. :rem:`|||:sec:|||`\ Footnotes
.. ==================================================

:html:`<hr>`

.. \[#]

.. >>CODD Reference List/Bibliography
.. ==================================================
.. :rem:`|||:sec:|||`\ References
.. ==================================================

.. include:: doc_defs.inc
.. include:: doc_defs_combined.inc
..
  .. \||<-snap->|| doc_standalone
  .. include:: doc/doc_defs_secret.inc
  .. \||<-snap->|| doc_standalone
  .. \||<-snap->|| not_doc_standalone
  .. include:: doc_defs_secret.inc
  .. \||<-snap->|| not_doc_standalone

.. _`Wolfgang Scherer`: wolfgang.scherer@gmx.de