text: import itertools
  
  from ...core import Add, Equality, Integer, Mul, Pow, Rational, S, Symbol, oo
  from ...core.function import _coeff_isneg
  from ...logic import true
  from ...utilities import default_sort_key, group
  from ..conventions import requires_partial
  from ..printer import Printer
  from ..str import sstr
  from .pretty_symbology import (annotated, greek_unicode, hobj, pretty_atom,
                                 pretty_symbol, pretty_use_unicode, vobj, xobj,
                                 xsym)
  from .stringpict import prettyForm, stringPict
  
  
  # rename for usage from outside
  pprint_use_unicode = pretty_use_unicode
  
  
  class PrettyPrinter(Printer):
      """Printer, which converts an expression into 2D ASCII-art figure."""
  
      printmethod = "_pretty"
  
      _default_settings = {
          "order": None,
          "full_prec": "auto",
          "use_unicode": None,
          "wrap_line": True,
          "num_columns": None,
      }
  
      def __init__(self, settings=None):
          Printer.__init__(self, settings)
          self.emptyPrinter = lambda x: prettyForm(str(x))
  
      @property
      def _use_unicode(self):
          if self._settings['use_unicode']:
              return True
          else:
              return pretty_use_unicode()
  
      def doprint(self, expr):
          return self._print(expr).render(**self._settings)
  
      # empty op so _print(stringPict) returns the same
      def _print_stringPict(self, e):
          return e
  
      def _print_atan2(self, e):
          pform = prettyForm(*self._print_seq(e.args).parens())
          pform = prettyForm(*pform.left('atan2'))
          return pform
  
      def _print_Symbol(self, e):
          symb = pretty_symbol(e.name)
          return prettyForm(symb)
      _print_Dummy = _print_Symbol
      _print_RandomSymbol = _print_Symbol
  
      def _print_Float(self, e):
          # we will use StrPrinter's Float printer, but we need to handle the
          # full_prec ourselves, according to the self._print_level
          full_prec = self._settings["full_prec"]
          if full_prec == "auto":
              full_prec = self._print_level == 1
          return prettyForm(sstr(e, full_prec=full_prec))
  
      def _print_Atom(self, e):
          try:
              # print atoms like Exp1 or Pi
              return prettyForm(pretty_atom(e.__class__.__name__))
          except KeyError:
              return self.emptyPrinter(e)
  
      # Infinity inherits from Number, so we have to override _print_XXX order
      _print_Infinity = _print_Atom
      _print_NegativeInfinity = _print_Atom
      _print_EmptySet = _print_Atom
      _print_Naturals = _print_Atom
      _print_Naturals0 = _print_Atom
      _print_Integers = _print_Atom
      _print_Rationals = _print_Atom
      _print_Reals = _print_Atom
  
      def _print_subfactorial(self, e):
          x = e.args[0]
          pform = self._print(x)
          # Add parentheses if needed
          if not ((x.is_Integer and x.is_nonnegative) or x.is_Symbol):
              pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left('!'))
          return pform
  
      def _print_factorial(self, e):
          x = e.args[0]
          pform = self._print(x)
          # Add parentheses if needed
          if not ((x.is_Integer and x.is_nonnegative) or x.is_Symbol):
              pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.right('!'))
          return pform
  
      def _print_factorial2(self, e):
          x = e.args[0]
          pform = self._print(x)
          # Add parentheses if needed
          if not ((x.is_Integer and x.is_nonnegative) or x.is_Symbol):
              pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.right('!!'))
          return pform
  
      def _print_binomial(self, e):
          n, k = e.args
  
          n_pform = self._print(n)
          k_pform = self._print(k)
  
          bar = ' '*max(n_pform.width(), k_pform.width())
  
          pform = prettyForm(*k_pform.above(bar))
          pform = prettyForm(*pform.above(n_pform))
          pform = prettyForm(*pform.parens('(', ')'))
  
          pform.baseline = (pform.baseline + 1)//2
  
          return pform
  
      def _print_Relational(self, e):
          op = prettyForm(' ' + xsym(e.rel_op) + ' ')
  
          l = self._print(e.lhs)
          r = self._print(e.rhs)
          pform = prettyForm(*stringPict.next(l, op, r))
          return pform
  
      def _print_Not(self, e):
          from ...logic import Equivalent, Implies
          if self._use_unicode:
              arg = e.args[0]
              pform = self._print(arg)
              if isinstance(arg, Equivalent):
                  return self._print_Equivalent(arg, altchar="\N{NOT IDENTICAL TO}")
              if isinstance(arg, Implies):
                  return self._print_Implies(arg, altchar="\N{RIGHTWARDS ARROW WITH STROKE}")
  
              if arg.is_Boolean and not arg.is_Not:
                  pform = prettyForm(*pform.parens())
  
              return prettyForm(*pform.left("\N{NOT SIGN}"))
          else:
              return self._print_Function(e)
  
      def __print_Boolean(self, e, char, sort=True):
          args = e.args
          if sort:
              args = sorted(e.args, key=default_sort_key)
          arg = args[0]
          pform = self._print(arg)
  
          if arg.is_Boolean and (not arg.is_Not and not arg.is_Atom):
              pform = prettyForm(*pform.parens())
  
          for arg in args[1:]:
              pform_arg = self._print(arg)
  
              if arg.is_Boolean and (not arg.is_Not and not arg.is_Atom):
                  pform_arg = prettyForm(*pform_arg.parens())
  
              pform = prettyForm(*pform.right(' %s ' % char))
              pform = prettyForm(*pform.right(pform_arg))
  
          return pform
  
      def _print_And(self, e):
          if self._use_unicode:
              return self.__print_Boolean(e, "\N{LOGICAL AND}")
          else:
              return self._print_Function(e, sort=True)
  
      def _print_Or(self, e):
          if self._use_unicode:
              return self.__print_Boolean(e, "\N{LOGICAL OR}")
          else:
              return self._print_Function(e, sort=True)
  
      def _print_Xor(self, e):
          if self._use_unicode:
              return self.__print_Boolean(e, "\N{XOR}")
          else:
              return self._print_Function(e, sort=True)
  
      def _print_Nand(self, e):
          if self._use_unicode:
              return self.__print_Boolean(e, "\N{NAND}")
          else:
              return self._print_Function(e, sort=True)
  
      def _print_Nor(self, e):
          if self._use_unicode:
              return self.__print_Boolean(e, "\N{NOR}")
          else:
              return self._print_Function(e, sort=True)
  
      def _print_Implies(self, e, altchar=None):
          if self._use_unicode:
              return self.__print_Boolean(e, altchar or "\N{RIGHTWARDS ARROW}", sort=False)
          else:
              return self._print_Function(e)
  
      def _print_Equivalent(self, e, altchar=None):
          if self._use_unicode:
              return self.__print_Boolean(e, altchar or "\N{IDENTICAL TO}")
          else:
              return self._print_Function(e, sort=True)
  
      def _print_conjugate(self, e):
          pform = self._print(e.args[0])
          return prettyForm( *pform.above( hobj('_', pform.width())) )
  
      def _print_Abs(self, e):
          pform = self._print(e.args[0])
          pform = prettyForm(*pform.parens('|', '|'))
          return pform
      _print_Determinant = _print_Abs
  
      def _print_floor(self, e):
          if self._use_unicode:
              pform = self._print(e.args[0])
              pform = prettyForm(*pform.parens('lfloor', 'rfloor'))
              return pform
          else:
              return self._print_Function(e)
  
      def _print_ceiling(self, e):
          if self._use_unicode:
              pform = self._print(e.args[0])
              pform = prettyForm(*pform.parens('lceil', 'rceil'))
              return pform
          else:
              return self._print_Function(e)
  
      def _print_Derivative(self, deriv):
          if requires_partial(deriv) and self._use_unicode:
              deriv_symbol = '\N{PARTIAL DIFFERENTIAL}'
          else:
              deriv_symbol = r'd'
          syms = list(reversed(deriv.variables))
          x = None
  
          for sym, num in group(syms, multiple=False):
              s = self._print(sym)
              ds = prettyForm(*s.left(deriv_symbol))
  
              if num > 1:
                  ds = ds**prettyForm(str(num))
  
              if x is None:
                  x = ds
              else:
                  x = prettyForm(*x.right(' '))
                  x = prettyForm(*x.right(ds))
  
          f = prettyForm(
              binding=prettyForm.FUNC, *self._print(deriv.expr).parens())
  
          pform = prettyForm(deriv_symbol)
  
          if len(syms) > 1:
              pform = pform**prettyForm(str(len(syms)))
  
          pform = prettyForm(*pform.below(stringPict.LINE, x))
          pform.baseline = pform.baseline + 1
          pform = prettyForm(*stringPict.next(pform, f))
          pform.binding = prettyForm.MUL
  
          return pform
  
      def _print_Integral(self, integral):
          f = integral.function
  
          # Add parentheses if arg involves addition of terms and
          # create a pretty form for the argument
          prettyF = self._print(f)
          # XXX generalize parens
          if f.is_Add:
              prettyF = prettyForm(*prettyF.parens())
  
          # dx dy dz ...
          arg = prettyF
          for x in integral.limits:
              prettyArg = self._print(x[0])
              # XXX qparens (parens if needs-parens)
              if prettyArg.width() > 1:
                  prettyArg = prettyForm(*prettyArg.parens())
  
              arg = prettyForm(*arg.right(' d', prettyArg))
  
          # \int \int \int ...
          firstterm = True
          s = None
          for lim in integral.limits:
              x = lim[0]
              # Create bar based on the height of the argument
              h = arg.height()
              H = h + 2
  
              # XXX hack!
              ascii_mode = not self._use_unicode
              if ascii_mode:
                  H += 2
  
              vint = vobj('int', H)
  
              # Construct the pretty form with the integral sign and the argument
              pform = prettyForm(vint)
              pform.baseline = arg.baseline + (
                  H - h)//2    # covering the whole argument
  
              if len(lim) > 1:
                  # Create pretty forms for endpoints, if definite integral.
                  # Do not print empty endpoints.
                  if len(lim) == 2:
                      prettyA = prettyForm("")
                      prettyB = self._print(lim[1])
                  if len(lim) == 3:
                      prettyA = self._print(lim[1])
                      prettyB = self._print(lim[2])
  
                  if ascii_mode:  # XXX hack
                      # Add spacing so that endpoint can more easily be
                      # identified with the correct integral sign
                      spc = max(1, 3 - prettyB.width())
                      prettyB = prettyForm(*prettyB.left(' ' * spc))
  
                      spc = max(1, 4 - prettyA.width())
                      prettyA = prettyForm(*prettyA.right(' ' * spc))
  
                  pform = prettyForm(*pform.above(prettyB))
                  pform = prettyForm(*pform.below(prettyA))
  
              if not ascii_mode:  # XXX hack
                  pform = prettyForm(*pform.right(' '))
  
              if firstterm:
                  s = pform   # first term
                  firstterm = False
              else:
                  s = prettyForm(*s.left(pform))
  
          pform = prettyForm(*arg.left(s))
          pform.binding = prettyForm.MUL
          return pform
  
      def _print_Product(self, expr):
          func = expr.term
          pretty_func = self._print(func)
  
          horizontal_chr = xobj('_', 1)
          corner_chr = xobj('_', 1)
          vertical_chr = xobj('|', 1)
  
          if self._use_unicode:
              # use unicode corners
              horizontal_chr = xobj('-', 1)
              corner_chr = '\N{BOX DRAWINGS LIGHT DOWN AND HORIZONTAL}'
  
          func_height = pretty_func.height()
  
          first = True
          max_upper = 0
          sign_height = 0
  
          for lim in expr.limits:
              width = (func_height + 2) * 5 // 3 - 2
              sign_lines = []
              sign_lines.append(corner_chr + (horizontal_chr*width) + corner_chr)
              for i in range(func_height + 1):
                  sign_lines.append(vertical_chr + (' '*width) + vertical_chr)
  
              pretty_sign = stringPict('')
              pretty_sign = prettyForm(*pretty_sign.stack(*sign_lines))
  
              pretty_upper = self._print(lim[2])
              pretty_lower = self._print(Equality(lim[0], lim[1]))
  
              max_upper = max(max_upper, pretty_upper.height())
  
              if first:
                  sign_height = pretty_sign.height()
  
              pretty_sign = prettyForm(*pretty_sign.above(pretty_upper))
              pretty_sign = prettyForm(*pretty_sign.below(pretty_lower))
  
              if first:
                  pretty_func.baseline = 0
                  first = False
  
              height = pretty_sign.height()
              padding = stringPict('')
              padding = prettyForm(*padding.stack(*[' ']*(height - 1)))
              pretty_sign = prettyForm(*pretty_sign.right(padding))
  
              pretty_func = prettyForm(*pretty_sign.right(pretty_func))
  
          pretty_func.baseline = max_upper + sign_height//2
          pretty_func.binding = prettyForm.MUL
          return pretty_func
  
      def _print_Sum(self, expr):
          ascii_mode = not self._use_unicode
  
          def asum(hrequired, lower, upper, use_ascii):
              h = max(hrequired, 2)
              d = h//2
              w = d + 1
              more = hrequired % 2
  
              lines = []
              if use_ascii:
                  lines.append("_"*w + ' ')
                  lines.append(r"\%s`" % (' '*(w - 1)))
                  for i in range(1, d):
                      lines.append('%s\\%s' % (' '*i, ' '*(w - i)))
                  if more:
                      lines.append('%s)%s' % (' '*d, ' '*(w - d)))
                  for i in reversed(range(1, d)):
                      lines.append('%s/%s' % (' '*i, ' '*(w - i)))
                  lines.append("/" + "_"*(w - 1) + ',')
                  return d, h + more, lines, 0
              else:
                  w = w + more
                  d = d + more
                  vsum = vobj('sum', 4)
                  lines.append("_"*w)
                  for i in range(d):
                      lines.append('%s%s%s' % (' '*i, vsum[2], ' '*(w - i - 1)))
                  for i in reversed(range(d)):
                      lines.append('%s%s%s' % (' '*i, vsum[4], ' '*(w - i - 1)))
                  lines.append(vsum[8]*w)
                  return d, h + 2*more, lines, more
  
          f = expr.function
  
          prettyF = self._print(f)
  
          if f.is_Add:  # add parens
              prettyF = prettyForm(*prettyF.parens())
  
          H = prettyF.height() + 2
  
          # \sum \sum \sum ...
          first = True
          max_upper = 0
          sign_height = 0
  
          for lim in expr.limits:
              assert len(lim) == 3  # no support for indefinite sums yet
              prettyUpper = self._print(lim[2])
              prettyLower = self._print(Equality(lim[0], lim[1],
                                                 evaluate=False))
  
              max_upper = max(max_upper, prettyUpper.height())
  
              # Create sum sign based on the height of the argument
              d, h, slines, adjustment = asum(
                  H, prettyLower.width(), prettyUpper.width(), ascii_mode)
              prettySign = stringPict('')
              prettySign = prettyForm(*prettySign.stack(*slines))
  
              if first:
                  sign_height = prettySign.height()
  
              prettySign = prettyForm(*prettySign.above(prettyUpper))
              prettySign = prettyForm(*prettySign.below(prettyLower))
  
              if first:
                  # change F baseline so it centers on the sign
                  prettyF.baseline -= d - (prettyF.height()//2 -
                                           prettyF.baseline) - adjustment
                  first = False
  
              # put padding to the right
              pad = stringPict('')
              pad = prettyForm(*pad.stack(*[' ']*h))
              prettySign = prettyForm(*prettySign.right(pad))
              # put the present prettyF to the right
              prettyF = prettyForm(*prettySign.right(prettyF))
  
          prettyF.baseline = max_upper + sign_height//2
          prettyF.binding = prettyForm.MUL
          return prettyF
  
      def _print_Limit(self, l):
          e, z, z0, dir = l.args
  
          E = self._print(e)
          if e.is_Add or e.is_Relational:
              E = prettyForm(*E.parens())
          Lim = prettyForm('lim')
  
          LimArg = self._print(z)
          if self._use_unicode:
              LimArg = prettyForm(*LimArg.right('\N{BOX DRAWINGS LIGHT HORIZONTAL}\N{RIGHTWARDS ARROW}'))
          else:
              LimArg = prettyForm(*LimArg.right('->'))
          LimArg = prettyForm(*LimArg.right(self._print(z0)))
  
          if str(dir) == "real" or z0 in (oo, -oo):
              dir = ""
          else:
              if self._use_unicode:
                  dir = '\N{SUPERSCRIPT PLUS SIGN}' if str(dir) == "+" else '\N{SUPERSCRIPT MINUS}'
  
          LimArg = prettyForm(*LimArg.right(self._print(dir)))
  
          Lim = prettyForm(*Lim.below(LimArg))
          Lim = prettyForm(*Lim.right(E))
  
          return Lim
  
      def _print_matrix_contents(self, e):
          """
          This method factors out what is essentially grid printing.
          """
          M = e   # matrix
          Ms = {}  # i,j -> pretty(M[i,j])
          for i in range(M.rows):
              for j in range(M.cols):
                  Ms[i, j] = self._print(M[i, j])
  
          # h- and v- spacers
          hsep = 2
          vsep = 1
  
          # max width for columns
          maxw = [-1] * M.cols
  
          for j in range(M.cols):
              maxw[j] = max([Ms[i, j].width() for i in range(M.rows)] or [0])
  
          # drawing result
          D = None
  
          for i in range(M.rows):
  
              D_row = None
              for j in range(M.cols):
                  s = Ms[i, j]
  
                  # reshape s to maxw
                  # XXX this should be generalized, and go to stringPict.reshape ?
                  assert s.width() <= maxw[j]
  
                  # hcenter it, +0.5 to the right                        2
                  # ( it's better to align formula starts for say 0 and r )
                  # XXX this is not good in all cases -- maybe introduce vbaseline?
                  wdelta = maxw[j] - s.width()
                  wleft = wdelta // 2
                  wright = wdelta - wleft
  
                  s = prettyForm(*s.right(' '*wright))
                  s = prettyForm(*s.left(' '*wleft))
  
                  # we don't need vcenter cells -- this is automatically done in
                  # a pretty way because when their baselines are taking into
                  # account in .right()
  
                  if D_row is None:
                      D_row = s   # first box in a row
                      continue
  
                  D_row = prettyForm(*D_row.right(' '*hsep))  # h-spacer
                  D_row = prettyForm(*D_row.right(s))
  
              if D is None:
                  D = D_row       # first row in a picture
                  continue
  
              # v-spacer
              for _ in range(vsep):
                  D = prettyForm(*D.below(' '))
  
              D = prettyForm(*D.below(D_row))
  
          if D is None:
              D = prettyForm('')  # Empty Matrix
  
          return D
  
      def _print_MatrixBase(self, e):
          D = self._print_matrix_contents(e)
          D.baseline = D.height()//2
          D = prettyForm(*D.parens('[', ']'))
          return D
      _print_ImmutableMatrix = _print_MatrixBase
      _print_Matrix = _print_MatrixBase
  
      def _print_Trace(self, e):
          D = self._print(e.arg)
          D = prettyForm(*D.parens('(', ')'))
          D.baseline = D.height()//2
          D = prettyForm(*D.left('\n'*0 + 'tr'))
          return D
  
      def _print_MatrixElement(self, expr):
          from ...matrices import MatrixSymbol
          if (isinstance(expr.parent, MatrixSymbol)
                  and expr.i.is_number and expr.j.is_number):
              return self._print(
                  Symbol(expr.parent.name + '_%d%d' % (expr.i, expr.j)))
          else:
              prettyFunc = self._print(expr.parent)
              prettyIndices = self._print_seq((expr.i, expr.j),
                                              delimiter=', ').parens(left='[',
                                                                     right=']')[0]
              pform = prettyForm(binding=prettyForm.FUNC,
                                 *stringPict.next(prettyFunc, prettyIndices))
  
              # store pform parts so it can be reassembled e.g. when powered
              pform.prettyFunc = prettyFunc
              pform.prettyArgs = prettyIndices
  
              return pform
  
      def _print_Transpose(self, expr):
          pform = self._print(expr.arg)
          from ...matrices import MatrixSymbol
          if not isinstance(expr.arg, MatrixSymbol):
              pform = prettyForm(*pform.parens())
          pform = pform**(prettyForm('T'))
          return pform
  
      def _print_Adjoint(self, expr):
          pform = self._print(expr.arg)
          if self._use_unicode:
              dag = prettyForm('\N{DAGGER}')
          else:
              dag = prettyForm('+')
          from ...matrices import MatrixSymbol
          if not isinstance(expr.arg, MatrixSymbol):
              pform = prettyForm(*pform.parens())
          pform = pform**dag
          return pform
  
      def _print_MatAdd(self, expr):
          return self._print_seq(expr.args, None, None, ' + ')
  
      def _print_MatMul(self, expr):
          args = list(expr.args)
          from ...matrices import MatAdd, HadamardProduct
          for i, a in enumerate(args):
              if (isinstance(a, (Add, MatAdd, HadamardProduct))
                      and len(expr.args) > 1):
                  args[i] = prettyForm(*self._print(a).parens())
              else:
                  args[i] = self._print(a)
  
          return prettyForm.__mul__(*args)
  
      def _print_MatPow(self, expr):
          pform = self._print(expr.base)
          from ...matrices import MatrixSymbol
          if not isinstance(expr.base, MatrixSymbol):
              pform = prettyForm(*pform.parens())
          pform = pform**(self._print(expr.exp))
          return pform
  
      _print_MatrixSymbol = _print_Symbol
  
      def _print_BasisDependent(self, expr):
          from ...vector import Vector
  
          if not self._use_unicode:  # pragma: no cover
              raise NotImplementedError("ASCII pretty printing of BasisDependent is not implemented")
  
          if expr == expr.zero:
              return prettyForm(expr.zero._pretty_form)
          o1 = []
          vectstrs = []
          if isinstance(expr, Vector):
              items = expr.separate().items()
          else:
              items = [(0, expr)]
          for system, vect in items:
              inneritems = list(vect.components.items())
              inneritems.sort(key=lambda x: x[0].__str__())
              for k, v in inneritems:
                  # If the coef of the basis vector is 1 - we skip the 1
                  if v == 1:
                      o1.append("" + k._pretty_form)
  
                  # Same for -1
                  elif v == -1:
                      o1.append("(-1) " + k._pretty_form)
  
                  else:
                      # We always wrap the measure numbers in #parentheses
                      arg_str = self._print(v).parens()[0]
  
                      o1.append(arg_str + ' ' + k._pretty_form)
                  vectstrs.append(k._pretty_form)
  
          # Fixing the newlines
          lengths = []
          strs = ['']
          for i, partstr in enumerate(o1):
              # XXX: What is this hack?
              if '\n' in partstr:
                  tempstr = partstr
                  tempstr = tempstr.replace(vectstrs[i], '')
                  tempstr = tempstr.replace('\N{RIGHT PARENTHESIS UPPER HOOK}',
                                            '\N{RIGHT PARENTHESIS UPPER HOOK}'
                                            + ' ' + vectstrs[i])
                  o1[i] = tempstr
          o1 = [x.split('\n') for x in o1]
          n_newlines = max(len(x) for x in o1)
          for parts in o1:
              lengths.append(len(parts[0]))
              for j in range(n_newlines):
                  if j+1 <= len(parts):
                      if j >= len(strs):
                          strs.append(' ' * (sum(lengths[:-1]) +
                                             3*(len(lengths) - 1)))
                      if j == 0:
                          strs[0] += parts[0] + ' + '
                      else:
                          strs[j] += parts[j] + ' ' * (lengths[-1] -
                                                       len(parts[j]) + 3)
                  else:
                      if j >= len(strs):
                          strs.append(' ' * (sum(lengths[:-1]) +
                                             3*(len(lengths) - 1)))
                      strs[j] += ' '*(lengths[-1]+3)
  
          return prettyForm('\n'.join([s[:-3] for s in strs]))
  
      def _print_NDimArray(self, expr):
          from ...matrices import ImmutableMatrix
  
          if expr.rank() == 0:
              return self._print(expr[()])
  
          level_str = [[]] + [[] for i in range(expr.rank())]
          shape_ranges = [list(range(i)) for i in expr.shape]
          for outer_i in itertools.product(*shape_ranges):
              level_str[-1].append(expr[outer_i])
              even = True
              for back_outer_i in range(expr.rank()-1, -1, -1):
                  if len(level_str[back_outer_i+1]) < expr.shape[back_outer_i]:
                      break
                  if even:
                      level_str[back_outer_i].append(level_str[back_outer_i+1])
                  else:
                      level_str[back_outer_i].append(ImmutableMatrix(level_str[back_outer_i+1]))
                      if len(level_str[back_outer_i + 1]) == 1:
                          level_str[back_outer_i][-1] = ImmutableMatrix([[level_str[back_outer_i][-1]]])
                  even = not even
                  level_str[back_outer_i+1] = []
  
          out_expr = level_str[0][0]
          if expr.rank() % 2 == 1:
              out_expr = ImmutableMatrix([out_expr])
  
          return self._print(out_expr)
  
      _print_ImmutableDenseNDimArray = _print_NDimArray
      _print_ImmutableSparseNDimArray = _print_NDimArray
      _print_MutableDenseNDimArray = _print_NDimArray
      _print_MutableSparseNDimArray = _print_NDimArray
  
      def _print_Piecewise(self, pexpr):
  
          P = {}
          for n, ec in enumerate(pexpr.args):
              P[n, 0] = self._print(ec.expr)
              if ec.cond == true:
                  P[n, 1] = prettyForm('otherwise')
              else:
                  P[n, 1] = prettyForm(
                      *prettyForm('for ').right(self._print(ec.cond)))
          hsep = 2
          vsep = 1
          len_args = len(pexpr.args)
  
          # max widths
          maxw = [max(P[i, j].width() for i in range(len_args))
                  for j in range(2)]
  
          # FIXME: Refactor this code and matrix into some tabular environment.
          # drawing result
          D = None
  
          for i in range(len_args):
              D_row = None
              for j in range(2):
                  p = P[i, j]
                  assert p.width() <= maxw[j]
  
                  wdelta = maxw[j] - p.width()
                  wleft = wdelta // 2
                  wright = wdelta - wleft
  
                  p = prettyForm(*p.right(' '*wright))
                  p = prettyForm(*p.left(' '*wleft))
  
                  if D_row is None:
                      D_row = p
                      continue
  
                  D_row = prettyForm(*D_row.right(' '*hsep))  # h-spacer
                  D_row = prettyForm(*D_row.right(p))
              if D is None:
                  D = D_row       # first row in a picture
                  continue
  
              # v-spacer
              for _ in range(vsep):
                  D = prettyForm(*D.below(' '))
  
              D = prettyForm(*D.below(D_row))
  
          D = prettyForm(*D.parens('{', ''))
          D.baseline = D.height()//2
          D.binding = prettyForm.OPEN
          return D
  
      def _hprint_vec(self, v):
          D = None
  
          for a in v:
              p = a
              if D is None:
                  D = p
              else:
                  D = prettyForm(*D.right(', '))
                  D = prettyForm(*D.right(p))
          if D is None:
              D = stringPict(' ')
  
          return D
  
      def _hprint_vseparator(self, p1, p2):
          tmp = prettyForm(*p1.right(p2))
          sep = stringPict(vobj('|', tmp.height()), baseline=tmp.baseline)
          return prettyForm(*p1.right(sep, p2))
  
      def _print_hyper(self, e):
          # FIXME refactor Matrix, Piecewise, and this into a tabular environment
          ap = [self._print(a) for a in e.ap]
          bq = [self._print(b) for b in e.bq]
  
          P = self._print(e.argument)
          P.baseline = P.height()//2
  
          # Drawing result - first create the ap, bq vectors
          D = None
          for v in [ap, bq]:
              D_row = self._hprint_vec(v)
              if D is None:
                  D = D_row       # first row in a picture
              else:
                  D = prettyForm(*D.below(' '))
                  D = prettyForm(*D.below(D_row))
  
          # make sure that the argument `z' is centred vertically
          D.baseline = D.height()//2
  
          # insert horizontal separator
          P = prettyForm(*P.left(' '))
          D = prettyForm(*D.right(' '))
  
          # insert separating `|`
          D = self._hprint_vseparator(D, P)
  
          # add parens
          D = prettyForm(*D.parens('(', ')'))
  
          # create the F symbol
          above = D.height()//2 - 1
          below = D.height() - above - 1
  
          sz, t, b, add, img = annotated('F')
          F = prettyForm('\n' * (above - t) + img + '\n' * (below - b),
                         baseline=above + sz)
          add = (sz + 1)//2
  
          F = prettyForm(*F.left(self._print(len(e.ap))))
          F = prettyForm(*F.right(self._print(len(e.bq))))
          F.baseline = above + add
  
          D = prettyForm(*F.right(' ', D))
  
          return D
  
      def _print_meijerg(self, e):
          # FIXME refactor Matrix, Piecewise, and this into a tabular environment
  
          v = {}
          v[(0, 0)] = [self._print(a) for a in e.an]
          v[(0, 1)] = [self._print(a) for a in e.aother]
          v[(1, 0)] = [self._print(b) for b in e.bm]
          v[(1, 1)] = [self._print(b) for b in e.bother]
  
          P = self._print(e.argument)
          P.baseline = P.height()//2
  
          vp = {}
          for idx in v:
              vp[idx] = self._hprint_vec(v[idx])
  
          for i in range(2):
              maxw = max(vp[(0, i)].width(), vp[(1, i)].width())
              for j in range(2):
                  s = vp[(j, i)]
                  left = (maxw - s.width()) // 2
                  right = maxw - left - s.width()
                  s = prettyForm(*s.left(' ' * left))
                  s = prettyForm(*s.right(' ' * right))
                  vp[(j, i)] = s
  
          D1 = prettyForm(*vp[(0, 0)].right('  ', vp[(0, 1)]))
          D1 = prettyForm(*D1.below(' '))
          D2 = prettyForm(*vp[(1, 0)].right('  ', vp[(1, 1)]))
          D = prettyForm(*D1.below(D2))
  
          # make sure that the argument `z' is centred vertically
          D.baseline = D.height()//2
  
          # insert horizontal separator
          P = prettyForm(*P.left(' '))
          D = prettyForm(*D.right(' '))
  
          # insert separating `|`
          D = self._hprint_vseparator(D, P)
  
          # add parens
          D = prettyForm(*D.parens('(', ')'))
  
          # create the G symbol
          above = D.height()//2 - 1
          below = D.height() - above - 1
  
          sz, t, b, add, img = annotated('G')
          F = prettyForm('\n' * (above - t) + img + '\n' * (below - b),
                         baseline=above + sz)
  
          pp = self._print(len(e.ap))
          pq = self._print(len(e.bq))
          pm = self._print(len(e.bm))
          pn = self._print(len(e.an))
  
          def adjust(p1, p2):
              diff = p1.width() - p2.width()
              if diff == 0:
                  return p1, p2
              elif diff > 0:
                  return p1, prettyForm(*p2.left(' '*diff))
              else:
                  return prettyForm(*p1.left(' '*-diff)), p2
          pp, pm = adjust(pp, pm)
          pq, pn = adjust(pq, pn)
          pu = prettyForm(*pm.right(', ', pn))
          pl = prettyForm(*pp.right(', ', pq))
  
          ht = F.baseline - above - 2
          pu = prettyForm(*pu.below('\n'*ht))
          p = prettyForm(*pu.below(pl))
  
          F.baseline = above
          F = prettyForm(*F.right(p))
  
          F.baseline = above + add
  
          D = prettyForm(*F.right(' ', D))
  
          return D
  
      def _print_Function(self, e, sort=False):
          # XXX works only for applied functions
          func = e.func
          args = e.args
          if sort:
              args = sorted(args, key=default_sort_key)
  
          func_name = func.__name__
  
          prettyFunc = self._print(Symbol(func_name))
          prettyArgs = prettyForm(*self._print_seq(args).parens())
  
          pform = prettyForm(
              binding=prettyForm.FUNC, *stringPict.next(prettyFunc, prettyArgs))
  
          # store pform parts so it can be reassembled e.g. when powered
          pform.prettyFunc = prettyFunc
          pform.prettyArgs = prettyArgs
  
          return pform
  
      def _print_GeometryEntity(self, expr):
          # GeometryEntity is based on Tuple but should not print like a Tuple
          return self.emptyPrinter(expr)
  
      def _print_Lambda(self, e):
          vars, expr = e.args
          if self._use_unicode:
              arrow = " \N{RIGHTWARDS ARROW FROM BAR} "
          else:
              arrow = " -> "
          if len(vars) == 1:
              var_form = self._print(vars[0])
          else:
              var_form = self._print(tuple(vars))
  
          return prettyForm(*stringPict.next(var_form, arrow, self._print(expr)), binding=8)
  
      def _print_Order(self, expr):
          pform = self._print(expr.expr)
          if ((expr.point and any(p != 0 for p in expr.point)) or
                  len(expr.variables) > 1):
              pform = prettyForm(*pform.right("; "))
              if len(expr.variables) > 1:
                  pform = prettyForm(*pform.right(self._print(expr.variables)))
              else:
                  pform = prettyForm(*pform.right(self._print(expr.variables[0])))
              if self._use_unicode:
                  pform = prettyForm(*pform.right(" \N{RIGHTWARDS ARROW} "))
              else:
                  pform = prettyForm(*pform.right(" -> "))
              if len(expr.point) > 1:
                  pform = prettyForm(*pform.right(self._print(expr.point)))
              else:
                  pform = prettyForm(*pform.right(self._print(expr.point[0])))
          pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left("O"))
          return pform
  
      def _print_gamma(self, e):
          if self._use_unicode:
              pform = self._print(e.args[0])
              pform = prettyForm(*pform.parens())
              pform = prettyForm(*pform.left(greek_unicode['Gamma']))
              return pform
          else:
              return self._print_Function(e)
  
      def _print_uppergamma(self, e):
          if self._use_unicode:
              pform = self._print(e.args[0])
              pform = prettyForm(*pform.right(', ', self._print(e.args[1])))
              pform = prettyForm(*pform.parens())
              pform = prettyForm(*pform.left(greek_unicode['Gamma']))
              return pform
          else:
              return self._print_Function(e)
  
      def _print_lowergamma(self, e):
          if self._use_unicode:
              pform = self._print(e.args[0])
              pform = prettyForm(*pform.right(', ', self._print(e.args[1])))
              pform = prettyForm(*pform.parens())
              pform = prettyForm(*pform.left(greek_unicode['gamma']))
              return pform
          else:
              return self._print_Function(e)
  
      def _print_DiracDelta(self, e):
          if self._use_unicode:
              pform = self._print(e.args[0])
              pform = prettyForm(*pform.parens())
              delta = self._print(greek_unicode['delta'])
              if len(e.args) > 1 and e.args[1] != 0:
                  k = prettyForm(*self._print(e.args[1]).parens())
                  delta = delta**k
              pform = prettyForm(*pform.left(delta))
              return pform
          else:
              return self._print_Function(e)
  
      def _print_expint(self, e):
          from ...core import Function
          if e.args[0].is_Integer and self._use_unicode:
              return self._print_Function(Function('E_%s' % e.args[0])(e.args[1]))
          return self._print_Function(e)
  
      def _print_Chi(self, e):
          # This needs a special case since otherwise it comes out as greek
          # letter chi...
          prettyFunc = prettyForm("Chi")
          prettyArgs = prettyForm(*self._print_seq(e.args).parens())
  
          pform = prettyForm(
              binding=prettyForm.FUNC, *stringPict.next(prettyFunc, prettyArgs))
  
          # store pform parts so it can be reassembled e.g. when powered
          pform.prettyFunc = prettyFunc
          pform.prettyArgs = prettyArgs
  
          return pform
  
      def _print_elliptic_e(self, e):
          pforma0 = self._print(e.args[0])
          if len(e.args) == 1:
              pform = pforma0
          else:
              pforma1 = self._print(e.args[1])
              pform = self._hprint_vseparator(pforma0, pforma1)
          pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left('E'))
          return pform
  
      def _print_elliptic_k(self, e):
          pform = self._print(e.args[0])
          pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left('K'))
          return pform
  
      def _print_elliptic_f(self, e):
          pforma0 = self._print(e.args[0])
          pforma1 = self._print(e.args[1])
          pform = self._hprint_vseparator(pforma0, pforma1)
          pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left('F'))
          return pform
  
      def _print_elliptic_pi(self, e):
          name = greek_unicode['Pi'] if self._use_unicode else 'Pi'
          pforma0 = self._print(e.args[0])
          pforma1 = self._print(e.args[1])
          if len(e.args) == 2:
              pform = self._hprint_vseparator(pforma0, pforma1)
          else:
              pforma2 = self._print(e.args[2])
              pforma = self._hprint_vseparator(pforma1, pforma2)
              pforma = prettyForm(*pforma.left('; '))
              pform = prettyForm(*pforma.left(pforma0))
          pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left(name))
          return pform
  
      def _print_Mod(self, expr):
          pform = self._print(expr.args[0])
          if pform.binding > prettyForm.MUL:
              pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.right(' mod '))
          pform = prettyForm(*pform.right(self._print(expr.args[1])))
          pform.binding = prettyForm.OPEN
          return pform
  
      def _print_GoldenRatio(self, expr):
          if self._use_unicode:
              return prettyForm(pretty_symbol('phi'))
          return self._print(Symbol("GoldenRatio"))
  
      def _print_EulerGamma(self, expr):
          if self._use_unicode:
              return prettyForm(pretty_symbol('gamma'))
          return self._print(Symbol("EulerGamma"))
  
      def _print_Add(self, expr, order=None):
          if self.order == 'none':
              terms = list(expr.args)
          else:
              terms = expr.as_ordered_terms(order=order or self.order)
          pforms, indices = [], []
  
          def pretty_negative(pform, index):
              """Prepend a minus sign to a pretty form. """
              # TODO: Move this code to prettyForm
              if index == 0:
                  if pform.height() > 1:
                      pform_neg = '- '
                  else:
                      pform_neg = '-'
              else:
                  pform_neg = ' - '
  
              if pform.binding > prettyForm.NEG:
                  p = stringPict(*pform.parens())
              else:
                  p = pform
              p = stringPict.next(pform_neg, p)
              # Lower the binding to NEG, even if it was higher. Otherwise, it
              # will print as a + ( - (b)), instead of a - (b).
              return prettyForm(binding=prettyForm.NEG, *p)
  
          for i, term in enumerate(terms):
              if term.is_Mul and _coeff_isneg(term):
                  coeff, other = term.as_coeff_mul(rational=False)
                  pform = self._print(Mul(-coeff, *other, evaluate=False))
                  pforms.append(pretty_negative(pform, i))
              elif term.is_Rational and term.denominator > 1:
                  pforms.append(None)
                  indices.append(i)
              elif term.is_Number and term < 0:
                  pform = self._print(-term)
                  pforms.append(pretty_negative(pform, i))
              elif term.is_Relational:
                  pforms.append(prettyForm(*self._print(term).parens()))
              else:
                  pforms.append(self._print(term))
  
          if indices:
              large = True
  
              for pform in pforms:
                  if pform is not None and pform.height() > 1:
                      break
              else:
                  large = False
  
              for i in indices:
                  term, negative = terms[i], False
  
                  if term < 0:
                      term, negative = -term, True
  
                  if large:
                      pform = prettyForm(str(term.numerator))/prettyForm(str(term.denominator))
                  else:
                      pform = self._print(term)
  
                  if negative:
                      pform = pretty_negative(pform, i)
  
                  pforms[i] = pform
  
          return prettyForm.__add__(*pforms)
  
      def _print_Mul(self, product):
          a = []  # items in the numerator
          b = []  # items that are in the denominator (if any)
  
          if self.order != 'none':
              args = product.as_ordered_factors()
          else:
              args = product.args
  
          multiple_ones = len([x for x in args if x == 1]) > 1
  
          # Gather terms for numerator/denominator
          for item in args:
              if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
                  if item.exp != -1:
                      b.append(Pow(item.base, -item.exp, evaluate=False))
                  else:
                      b.append(Pow(item.base, -item.exp))
              elif item.is_Rational and item is not oo:
                  if item.numerator != 1 or multiple_ones:
                      a.append(Rational(item.numerator))
                  if item.denominator != 1:
                      b.append(Rational(item.denominator))
              else:
                  a.append(item)
  
          from ...functions import Piecewise
          from ...concrete import Product, Sum
          from ...integrals import Integral
  
          # Convert to pretty forms. Add parens to Add instances if there
          # is more than one term in the numer/denom
          for i in range(len(a)):
              if (a[i].is_Add and len(a) > 1) or (i != len(a) - 1 and
                                                  isinstance(a[i], (Integral, Piecewise, Product, Sum))):
                  a[i] = prettyForm(*self._print(a[i]).parens())
              elif a[i].is_Relational:
                  a[i] = prettyForm(*self._print(a[i]).parens())
              else:
                  a[i] = self._print(a[i])
  
          for i in range(len(b)):
              if (b[i].is_Add and len(b) > 1) or (i != len(b) - 1 and
                                                  isinstance(b[i], (Integral, Piecewise, Product, Sum))):
                  b[i] = prettyForm(*self._print(b[i]).parens())
              else:
                  b[i] = self._print(b[i])
  
          # Construct a pretty form
          if len(b) == 0:
              return prettyForm.__mul__(*a)
          else:
              if len(a) == 0:
                  a.append( self._print(Integer(1)) )
              return prettyForm.__mul__(*a)/prettyForm.__mul__(*b)
  
      # A helper function for _print_Pow to print x**(1/n)
      def _print_nth_root(self, base, expt):
          bpretty = self._print(base)
  
          # Construct root sign, start with the \/ shape
          _zZ = xobj('/', 1)
          rootsign = xobj('\\', 1) + _zZ
          # Make exponent number to put above it
          if isinstance(expt, Rational):
              exp = str(expt.denominator)
              if exp == '2':
                  exp = ''
          else:
              exp = str(expt.args[0])
          exp = exp.ljust(2)
          if len(exp) > 2:
              rootsign = ' '*(len(exp) - 2) + rootsign
          # Stack the exponent
          rootsign = stringPict(exp + '\n' + rootsign)
          rootsign.baseline = 0
          # Diagonal: length is one less than height of base
          linelength = bpretty.height() - 1
          diagonal = stringPict('\n'.join(
              ' '*(linelength - i - 1) + _zZ + ' '*i
              for i in range(linelength)
          ))
          # Put baseline just below lowest line: next to exp
          diagonal.baseline = linelength - 1
          # Make the root symbol
          rootsign = prettyForm(*rootsign.right(diagonal))
          # Det the baseline to match contents to fix the height
          # but if the height of bpretty is one, the rootsign must be one higher
          rootsign.baseline = max(1, bpretty.baseline)
          # build result
          s = prettyForm(hobj('_', 2 + bpretty.width()))
          s = prettyForm(*bpretty.above(s))
          s = prettyForm(*s.left(rootsign))
          return s
  
      def _print_Pow(self, power):
          from ...simplify import fraction
          from ...series import Limit
          b, e = power.as_base_exp()
          if power.is_commutative and not e.is_Float:
              if e == -1:
                  return prettyForm("1")/self._print(b)
              n, d = fraction(e)
              if n == 1 and d.is_Atom and not e.is_Integer:
                  return self._print_nth_root(b, e)
              if e.is_Rational and e < 0:
                  return prettyForm("1")/self._print(Pow(b, -e, evaluate=False))
  
          if b.is_Relational or isinstance(b, Limit):
              return prettyForm(*self._print(b).parens()).__pow__(self._print(e))
  
          return self._print(b)**self._print(e)
  
      def __print_numer_denom(self, p, q):
          if q == 1:
              if p < 0:
                  return prettyForm(str(p), binding=prettyForm.NEG)
              else:
                  return prettyForm(str(p))
          elif abs(p) >= 10 and abs(q) >= 10:
              # If more than one digit in numer and denom, print larger fraction
              if p < 0:
                  return prettyForm(str(p), binding=prettyForm.NEG)/prettyForm(str(q))
                  # Old printing method:
                  # pform = prettyForm(str(-p))/prettyForm(str(q))
                  # return prettyForm(binding=prettyForm.NEG, *pform.left('- '))
              else:
                  return prettyForm(str(p))/prettyForm(str(q))
          else:
              return
  
      def _print_Rational(self, expr):
          result = self.__print_numer_denom(expr.numerator, expr.denominator)
  
          if result is not None:
              return result
          else:
              return self.emptyPrinter(expr)
  
      def _print_ProductSet(self, p):
          prod_char = "\N{MULTIPLICATION SIGN}" if self._use_unicode else 'x'
          return self._print_seq(p.sets, None, None, ' %s ' % prod_char,
                                 parenthesize=lambda set: set.is_Union or
                                 set.is_Intersection or set.is_ProductSet)
  
      def _print_FiniteSet(self, s):
          items = sorted(s.args, key=default_sort_key)
          return self._print_seq(items, '{', '}', ', ' )
  
      def _print_set(self, l):
          return self._print_seq(sorted(l, key=default_sort_key), '{', '}')
  
      def _print_Range(self, s):
  
          if self._use_unicode:
              dots = "\N{HORIZONTAL ELLIPSIS}"
          else:
              dots = '...'
  
          if s.start == -oo:
              it = iter(s)
              printset = s.start, dots, s._last_element - s.step, s._last_element
          elif s.stop is oo or len(s) > 4:
              it = iter(s)
              printset = next(it), next(it), dots, s._last_element
          else:
              printset = tuple(s)
  
          return self._print_seq(printset, '{', '}', ', ' )
  
      def _print_Interval(self, i):
          if i.left_open:
              left = '('
          else:
              left = '['
  
          if i.right_open:
              right = ')'
          else:
              right = ']'
  
          return self._print_seq(i.args[:2], left, right)
  
      def _print_Intersection(self, u):
  
          delimiter = ' %s ' % pretty_atom('Intersection', 'n')
  
          return self._print_seq(u.args, None, None, delimiter,
                                 parenthesize=lambda set: set.is_ProductSet or
                                 set.is_Union or set.is_Complement)
  
      def _print_Union(self, u):
  
          union_delimiter = ' %s ' % pretty_atom('Union', 'U')
  
          return self._print_seq(u.args, None, None, union_delimiter,
                                 parenthesize=lambda set: set.is_ProductSet or
                                 set.is_Intersection or set.is_Complement)
  
      def _print_SymmetricDifference(self, u):
          if not self._use_unicode:
              raise NotImplementedError("ASCII pretty printing of SymmetricDifference is not implemented")
  
          sym_delimeter = ' %s ' % pretty_atom('SymmetricDifference')
  
          return self._print_seq(u.args, None, None, sym_delimeter)
  
      def _print_Complement(self, u):
  
          delimiter = r' \ '
  
          return self._print_seq(u.args, None, None, delimiter,
                                 parenthesize=lambda set: set.is_ProductSet or set.is_Intersection
                                 or set.is_Union)
  
      def _print_Contains(self, e):
          var, set = e.args
          if self._use_unicode:
              el = " \N{ELEMENT OF} "
              return prettyForm(*stringPict.next(self._print(var),
                                                 el, self._print(set)), binding=8)
          else:
              return prettyForm(sstr(e))
  
      def _print_seq(self, seq, left=None, right=None, delimiter=', ',
                     parenthesize=lambda x: False):
          s = None
  
          for item in seq:
              pform = self._print(item)
  
              if parenthesize(item):
                  pform = prettyForm(*pform.parens())
              if s is None:
                  # first element
                  s = pform
              else:
                  s = prettyForm(*stringPict.next(s, delimiter))
                  s = prettyForm(*stringPict.next(s, pform))
  
          if s is None:
              s = stringPict('')
  
          s = prettyForm(*s.parens(left, right, ifascii_nougly=True))
          return s
  
      def join(self, delimiter, args):
          pform = None
  
          for arg in args:
              if pform is None:
                  pform = arg
              else:
                  pform = prettyForm(*pform.right(delimiter))
                  pform = prettyForm(*pform.right(arg))
  
          if pform is None:
              return prettyForm("")
          else:
              return pform
  
      def _print_list(self, l):
          return self._print_seq(l, '[', ']')
  
      def _print_tuple(self, t):
          if len(t) == 1:
              ptuple = prettyForm(*stringPict.next(self._print(t[0]), ','))
              return prettyForm(*ptuple.parens('(', ')', ifascii_nougly=True))
          else:
              return self._print_seq(t, '(', ')')
  
      def _print_Tuple(self, expr):
          return self._print_tuple(expr)
  
      def _print_dict(self, d):
          keys = sorted(d, key=default_sort_key)
          items = []
  
          for k in keys:
              K = self._print(k)
              V = self._print(d[k])
              s = prettyForm(*stringPict.next(K, ': ', V))
  
              items.append(s)
  
          return self._print_seq(items, '{', '}')
  
      def _print_Dict(self, d):
          return self._print_dict(d)
  
      def _print_frozenset(self, s):
          items = sorted(s, key=default_sort_key)
          pretty = self._print_seq(items, '{', '}')
          pretty = prettyForm(*pretty.parens('(', ')', ifascii_nougly=True))
          pretty = prettyForm(*stringPict.next(type(s).__name__, pretty))
          return pretty
  
      def _print_PolyElement(self, poly):
          return prettyForm(sstr(poly))
  
      def _print_FracElement(self, frac):
          return prettyForm(sstr(frac))
  
      def _print_AlgebraicElement(self, expr):
          return self._print(expr.parent.to_expr(expr))
  
      def _print_RootOf(self, expr):
          args = [self._print_Add(expr.expr, order='lex')]
          if expr.free_symbols:
              args += expr.args[1:]
          else:
              args += [expr.index]
          pform = prettyForm(*self._print_seq(args).parens())
          pform = prettyForm(*pform.left('RootOf'))
          return pform
  
      def _print_RootSum(self, expr):
          args = [self._print_Add(expr.expr, order='lex')]
  
          if expr.fun is not S.IdentityFunction:
              args.append(self._print(expr.fun))
  
          pform = prettyForm(*self._print_seq(args).parens())
          pform = prettyForm(*pform.left('RootSum'))
  
          return pform
  
      def _print_FiniteField(self, expr):
          if self._use_unicode:
              form = '\N{MATHEMATICAL DOUBLE-STRUCK CAPITAL F}_%d'
          else:
              form = 'GF(%d)'
  
          return prettyForm(pretty_symbol(form % expr.order))
  
      def _print_IntegerRing(self, expr):
          if self._use_unicode:
              return prettyForm('\N{DOUBLE-STRUCK CAPITAL Z}')
          else:
              return prettyForm('ZZ')
  
      def _print_RationalField(self, expr):
          if self._use_unicode:
              return prettyForm('\N{DOUBLE-STRUCK CAPITAL Q}')
          else:
              return prettyForm('QQ')
  
      def _print_RealField(self, domain):
          if self._use_unicode:
              prefix = '\N{DOUBLE-STRUCK CAPITAL R}'
          else:
              prefix = 'RR'
  
          if domain.has_default_precision:
              return prettyForm(prefix)
          else:
              return self._print(pretty_symbol(prefix + "_" + str(domain.precision)))
  
      def _print_PolynomialRing(self, expr):
          args = list(expr.symbols)
  
          if not expr.order.is_default:
              order = prettyForm(*prettyForm("order=").right(self._print(expr.order)))
              args.append(order)
  
          pform = self._print_seq(args, '[', ']')
          pform = prettyForm(*pform.left(self._print(expr.domain)))
  
          return pform
  
      def _print_FractionField(self, expr):
          args = list(expr.symbols)
  
          if not expr.order.is_default:
              order = prettyForm(*prettyForm("order=").right(self._print(expr.order)))
              args.append(order)
  
          pform = self._print_seq(args, '(', ')')
          pform = prettyForm(*pform.left(self._print(expr.domain)))
  
          return pform
  
      def _print_GroebnerBasis(self, basis):
          exprs = [ self._print_Add(arg, order=basis.order)
                    for arg in basis.exprs ]
          exprs = prettyForm(*self.join(", ", exprs).parens(left="[", right="]"))
  
          gens = [ self._print(gen) for gen in basis.gens ]
  
          domain = prettyForm(
              *prettyForm("domain=").right(self._print(basis.domain)))
          order = prettyForm(
              *prettyForm("order=").right(self._print(basis.order)))
  
          pform = self.join(", ", [exprs] + gens + [domain, order])
  
          pform = prettyForm(*pform.parens())
          pform = prettyForm(*pform.left(basis.__class__.__name__))
  
          return pform
  
      def _print_Subs(self, e):
          pform = self._print(e.expr)
          pform = prettyForm(*pform.parens())
  
          h = pform.height() if pform.height() > 1 else 2
          rvert = stringPict(vobj('|', h), baseline=pform.baseline)
          pform = prettyForm(*pform.right(rvert))
  
          b = pform.baseline
          pform.baseline = pform.height() - 1
          pform = prettyForm(*pform.right(self._print_seq([
              self._print_seq((self._print(v[0]), xsym('=='), self._print(v[1])),
                              delimiter='') for v in zip(e.variables, e.point) ])))
  
          pform.baseline = b
          return pform
  
      def _print_euler(self, e):
          pform = prettyForm("E")
          arg = self._print(e.args[0])
          pform_arg = prettyForm(" "*arg.width())
          pform_arg = prettyForm(*pform_arg.below(arg))
          pform = prettyForm(*pform.right(pform_arg))
          return pform
  
      def _print_catalan(self, e):
          pform = prettyForm("C")
          arg = self._print(e.args[0])
          pform_arg = prettyForm(" "*arg.width())
          pform_arg = prettyForm(*pform_arg.below(arg))
          pform = prettyForm(*pform.right(pform_arg))
          return pform
  
      def _print_KroneckerDelta(self, e):
          pform = self._print(e.args[0])
          pform = prettyForm(*pform.right((prettyForm(','))))
          pform = prettyForm(*pform.right((self._print(e.args[1]))))
          if self._use_unicode:
              a = stringPict(pretty_symbol('delta'))
          else:
              a = stringPict('d')
          b = pform
          top = stringPict(*b.left(' '*a.width()))
          bot = stringPict(*a.right(' '*b.width()))
          return prettyForm(binding=prettyForm.POW, *bot.below(top))
  
      def _print_RandomDomain(self, d):
          pform = self._print('Domain: ')
          pform = prettyForm(*pform.right(self._print(d.as_boolean())))
          return pform
  
      def _print_BaseScalarField(self, field):
          string = field._coord_sys._names[field._index]
          return self._print(pretty_symbol(string))
  
      def _print_BaseVectorField(self, field):
          s = '\N{PARTIAL DIFFERENTIAL}' + '_' + field._coord_sys._names[field._index]
          return self._print(pretty_symbol(s))
  
      def _print_Tr(self, p):
          # TODO: Handle indices
          pform = self._print(p.args[0])
          pform = prettyForm(*pform.left('%s(' % (p.__class__.__name__)))
          pform = prettyForm(*pform.right(')'))
          return pform
  
  
  def pretty(expr, **settings):
      """Returns a string containing the prettified form of expr.
  
      For information on keyword arguments see pretty_print function.
  
      """
      pp = PrettyPrinter(settings)
  
      # XXX: this is an ugly hack, but at least it works
      use_unicode = pp._settings['use_unicode']
      uflag = pretty_use_unicode(use_unicode)
  
      try:
          return pp.doprint(expr)
      finally:
          pretty_use_unicode(uflag)
  
  
  def pretty_print(expr, **settings):
      """Prints expr in pretty form.
  
      pprint is just a shortcut for this function.
  
  
      Parameters
      ==========
  
      expr : expression
          the expression to print
      wrap_line : bool, optional
          line wrapping enabled/disabled, defaults to True
      num_columns : int or None, optional
          number of columns before line breaking (default to None which reads
          the terminal width), useful when using Diofant without terminal.
      use_unicode : bool or None, optional
          use unicode characters, such as the Greek letter pi instead of
          the string pi.
      full_prec : bool or string, optional
          use full precision. Default to "auto"
      order : bool or string, optional
          set to 'none' for long expressions if slow; default is None
  
      """
      print(pretty(expr, **settings))
  
  
  #:
  pprint = pretty_print
  