trs/TODO

 - Fix BisonSyntaxError location tracking.

 - Sort polynom by its exponents?

 - No possibilities found for:
   >>> a2b3 + a2b3
   a ^ 2 * b ^ 3 + a ^ 2 * b ^ 3

 - 2 + 3 + 4 rewrites to 5 instead of 5 + 4
   -> the problem is that the 'root' of the application is actually a subtree
   of the entire expression. This means that the parent of each possibility
   root (or 'subtree') must me stored to be able to replace the subtree.

 - MESSAGES needs to be expanded.

 - rewrite match_combine_polynomes to an even more generic form:
   match_combine_factors.

 - "--ab + c" has no rewrite possibility. The graph of "--ab + c" is also
   not valid:

     -
     │
      +
    ╭─┴╮
    *  c
   ╭┴╮
   - b
   │
   a

 - The following expression gives a cycle in the possibilities:

   >>> ab + ba
   possibilities:
     Group "ab" is multiplied by 1 and 1, combine them.
   >>> (1 + 1) * ab
   (1 + 1)ab
   possibilities:
     Combine the constants 1 and 1.
     Group "1" is multiplied by 1 and 1, combine them.
     Expand a(1 + 1).
     Expand b(1 + 1).

 - Fix division by zero caused by "0/0".

smvv@multivac ~/work/trs $ printf "a/0\n??" | ./main.py
Traceback (most recent call last):
  File "./main.py", line 75, in <module>
    main()
  File "./main.py", line 64, in main
    node = p.run(debug=args.debug)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 258, in run
    self.report_last_error(filename, e)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 251, in run
    self.engine.runEngine(debug)
  File "bison_.pyx", line 592, in bison_.ParserEngine.runEngine (build/external/pybison/bison_.c:592)
  File "/home/smvv/work/trs/src/parser.py", line 195, in hook_handler
    possibilities = handler(retval)
  File "/home/smvv/work/trs/src/rules/fractions.py", line 23, in match_constant_division
    raise ZeroDivisionError('Division by zero: %s.' % node)
ZeroDivisionError: Division by zero: a / 0.

smvv@multivac ~/work/trs $ printf "0/0\n??" | ./main.py
Traceback (most recent call last):
  File "./main.py", line 75, in <module>
    main()
  File "./main.py", line 64, in main
    node = p.run(debug=args.debug)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 258, in run
    self.report_last_error(filename, e)
  File "/home/smvv/work/trs/external/pybison/src/python/bison.py", line 251, in run
    self.engine.runEngine(debug)
  File "bison_.pyx", line 592, in bison_.ParserEngine.runEngine (build/external/pybison/bison_.c:592)
  File "/home/smvv/work/trs/src/parser.py", line 195, in hook_handler
    possibilities = handler(retval)
  File "/home/smvv/work/trs/src/rules/numerics.py", line 73, in match_divide_numerics
    divide = not divmod(n.value, dv)[1]
ZeroDivisionError: integer division or modulo by zero

 - Last possibilities reduce to a similar result.

smvv@multivac ~/work/trs $ printf "0/1\n??" | ./main.py
<Possibility root="0 / 1" handler=divide_numerics args=(0, 1)>
Division of 0 by 1 reduces to 0.
Division of 0 by 1 reduces to 0.