Support ProductOrder's in core

[skirpichev]

Right now Expr.as_ordered_terms() raises an exception:

In [1]: from diofant.polys.orderings import build_product_order, lex

In [2]: O = build_product_order(((lex, z), (lex, x, y)), [x, y, z])

In [3]: F = [x**2 + y + z - 1, x + y**2 + z - 1, x + y + z**2 - 1]

In [4]: groebner(F, x, y, z, order=O)
Out[4]: ---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
File ~/venv/dev3.11/lib/python3.11/site-packages/IPython/core/formatters.py:706, in PlainTextFormatter.__call__(self, obj)
    699 stream = StringIO()
    700 printer = pretty.RepresentationPrinter(stream, self.verbose,
    701     self.max_width, self.newline,
    702     max_seq_length=self.max_seq_length,
    703     singleton_pprinters=self.singleton_printers,
    704     type_pprinters=self.type_printers,
    705     deferred_pprinters=self.deferred_printers)
--> 706 printer.pretty(obj)
    707 printer.flush()
    708 return stream.getvalue()

File ~/venv/dev3.11/lib/python3.11/site-packages/IPython/lib/pretty.py:407, in RepresentationPrinter.pretty(self, obj)
    405     meth = cls._repr_pretty_
    406     if callable(meth):
--> 407         return meth(obj, self, cycle)
    408 if cls is not object \
    409         and callable(cls.__dict__.get('__repr__')):
    410     return _repr_pprint(obj, self, cycle)

File ~/src/diofant/diofant/core/basic.py:164, in Basic._repr_pretty_(self, p, cycle)
    162 def _repr_pretty_(self, p, cycle):
    163     from ..printing import pretty
--> 164     p.text(pretty(self))

File ~/src/diofant/diofant/printing/pretty/pretty.py:1591, in pretty(expr, **settings)
   1588 uflag = pretty_use_unicode(use_unicode)
   1590 try:
-> 1591     return pp.doprint(expr)
   1592 finally:
   1593     pretty_use_unicode(uflag)

File ~/src/diofant/diofant/printing/pretty/pretty.py:47, in PrettyPrinter.doprint(self, expr)
     46 def doprint(self, expr):
---> 47     return self._print(expr).render(**self._settings)

File ~/src/diofant/diofant/printing/printer.py:211, in Printer._print(self, expr, *args, **kwargs)
    208         if cls.__class__.__name__ == 'UndefinedFunction':
    209             # XXX a hack for sympy/sympy#6853
    210             continue
--> 211         return getattr(self, printmethod)(expr, *args, **kwargs)
    213 # Unknown object, fall back to the emptyPrinter.
    214 return self.emptyPrinter(expr)

File ~/src/diofant/diofant/printing/pretty/pretty.py:1506, in PrettyPrinter._print_GroebnerBasis(self, basis)
   1505 def _print_GroebnerBasis(self, basis):
-> 1506     exprs = [self._print_Add(arg, order=basis.order)
   1507              for arg in basis.exprs]
   1508     exprs = prettyForm(*self.join(', ', exprs).parens(left='[', right=']'))
   1510     gens = [self._print(gen) for gen in basis.gens]

File ~/src/diofant/diofant/printing/pretty/pretty.py:1506, in <listcomp>(.0)
   1505 def _print_GroebnerBasis(self, basis):
-> 1506     exprs = [self._print_Add(arg, order=basis.order)
   1507              for arg in basis.exprs]
   1508     exprs = prettyForm(*self.join(', ', exprs).parens(left='[', right=']'))
   1510     gens = [self._print(gen) for gen in basis.gens]

File ~/src/diofant/diofant/printing/pretty/pretty.py:1073, in PrettyPrinter._print_Add(self, expr, order)
   1071     terms = list(expr.args)
   1072 else:
-> 1073     terms = expr.as_ordered_terms(order=order or self.order)
   1074 pforms, indices = [], []
   1076 def pretty_negative(pform, index):

File ~/src/diofant/diofant/core/expr.py:793, in Expr.as_ordered_terms(self, order, data)
    790 terms, gens = self.as_terms()
    792 if not any(term.is_Order for term, _ in terms):
--> 793     ordered = sorted(terms, key=key, reverse=reverse)
    794 else:
    795     _terms, _order = [], []

File ~/src/diofant/diofant/core/expr.py:767, in Expr._parse_order.<locals>.key(term)
    764 def key(term):
    765     _, ((re, im), monom, ncpart) = term
--> 767     monom = neg(monom_key(monom))
    768     ncpart = tuple(e.sort_key(order=order) for e in ncpart)
    769     coeff = ((bool(im), im), (re, im))

File ~/src/diofant/diofant/polys/orderings.py:109, in ProductOrder.__call__(self, monomial)
    108 def __call__(self, monomial):
--> 109     return tuple(O(lamda(monomial)) for (O, lamda) in self.args)

File ~/src/diofant/diofant/polys/orderings.py:109, in <genexpr>(.0)
    108 def __call__(self, monomial):
--> 109     return tuple(O(lamda(monomial)) for (O, lamda) in self.args)

File ~/src/diofant/diofant/polys/orderings.py:246, in _ItemGetter.__call__(self, m)
    245 def __call__(self, m):
--> 246     return tuple(m[idx] for idx in self.seq)

File ~/src/diofant/diofant/polys/orderings.py:246, in <genexpr>(.0)
    245 def __call__(self, m):
--> 246     return tuple(m[idx] for idx in self.seq)

IndexError: tuple index out of range