text: """sympify -- convert objects SymPy internal format"""
  
  from __future__ import print_function, division
  
  from inspect import getmro
  
  from .core import all_classes as sympy_classes
  from .compatibility import iterable, string_types, range
  from .evaluate import global_evaluate
  
  
  class SympifyError(ValueError):
      def __init__(self, expr, base_exc=None):
          self.expr = expr
          self.base_exc = base_exc
  
      def __str__(self):
          if self.base_exc is None:
              return "SympifyError: %r" % (self.expr,)
  
          return ("Sympify of expression '%s' failed, because of exception being "
              "raised:\n%s: %s" % (self.expr, self.base_exc.__class__.__name__,
              str(self.base_exc)))
  
  converter = {}  # See sympify docstring.
  
  class CantSympify(object):
      """
      Mix in this trait to a class to disallow sympification of its instances.
  
      Examples
      ========
  
      >>> from sympy.core.sympify import sympify, CantSympify
  
      >>> class Something(dict):
      ...     pass
      ...
      >>> sympify(Something())
      {}
  
      >>> class Something(dict, CantSympify):
      ...     pass
      ...
      >>> sympify(Something())
      Traceback (most recent call last):
      ...
      SympifyError: SympifyError: {}
  
      """
      pass
  
  
  def sympify(a, locals=None, convert_xor=True, strict=False, rational=False,
          evaluate=None):
      """Converts an arbitrary expression to a type that can be used inside SymPy.
  
      For example, it will convert Python ints into instance of sympy.Rational,
      floats into instances of sympy.Float, etc. It is also able to coerce symbolic
      expressions which inherit from Basic. This can be useful in cooperation
      with SAGE.
  
      It currently accepts as arguments:
         - any object defined in sympy
         - standard numeric python types: int, long, float, Decimal
         - strings (like "0.09" or "2e-19")
         - booleans, including ``None`` (will leave ``None`` unchanged)
         - lists, sets or tuples containing any of the above
  
      .. warning::
          Note that this function uses ``eval``, and thus shouldn't be used on
          unsanitized input.
  
      If the argument is already a type that SymPy understands, it will do
      nothing but return that value. This can be used at the beginning of a
      function to ensure you are working with the correct type.
  
      >>> from sympy import sympify
  
      >>> sympify(2).is_integer
      True
      >>> sympify(2).is_real
      True
  
      >>> sympify(2.0).is_real
      True
      >>> sympify("2.0").is_real
      True
      >>> sympify("2e-45").is_real
      True
  
      If the expression could not be converted, a SympifyError is raised.
  
      >>> sympify("x***2")
      Traceback (most recent call last):
      ...
      SympifyError: SympifyError: "could not parse u'x***2'"
  
      Locals
      ------
  
      The sympification happens with access to everything that is loaded
      by ``from sympy import *``; anything used in a string that is not
      defined by that import will be converted to a symbol. In the following,
      the ``bitcount`` function is treated as a symbol and the ``O`` is
      interpreted as the Order object (used with series) and it raises
      an error when used improperly:
  
      >>> s = 'bitcount(42)'
      >>> sympify(s)
      bitcount(42)
      >>> sympify("O(x)")
      O(x)
      >>> sympify("O + 1")
      Traceback (most recent call last):
      ...
      TypeError: unbound method...
  
      In order to have ``bitcount`` be recognized it can be imported into a
      namespace dictionary and passed as locals:
  
      >>> from sympy.core.compatibility import exec_
      >>> ns = {}
      >>> exec_('from sympy.core.evalf import bitcount', ns)
      >>> sympify(s, locals=ns)
      6
  
      In order to have the ``O`` interpreted as a Symbol, identify it as such
      in the namespace dictionary. This can be done in a variety of ways; all
      three of the following are possibilities:
  
      >>> from sympy import Symbol
      >>> ns["O"] = Symbol("O")  # method 1
      >>> exec_('from sympy.abc import O', ns)  # method 2
      >>> ns.update(dict(O=Symbol("O")))  # method 3
      >>> sympify("O + 1", locals=ns)
      O + 1
  
      If you want *all* single-letter and Greek-letter variables to be symbols
      then you can use the clashing-symbols dictionaries that have been defined
      there as private variables: _clash1 (single-letter variables), _clash2
      (the multi-letter Greek names) or _clash (both single and multi-letter
      names that are defined in abc).
  
      >>> from sympy.abc import _clash1
      >>> _clash1
      {'C': C, 'E': E, 'I': I, 'N': N, 'O': O, 'Q': Q, 'S': S}
      >>> sympify('I & Q', _clash1)
      I & Q
  
      Strict
      ------
  
      If the option ``strict`` is set to ``True``, only the types for which an
      explicit conversion has been defined are converted. In the other
      cases, a SympifyError is raised.
  
      >>> print(sympify(None))
      None
      >>> sympify(None, strict=True)
      Traceback (most recent call last):
      ...
      SympifyError: SympifyError: None
  
      Evaluation
      ----------
  
      If the option ``evaluate`` is set to ``False``, then arithmetic and
      operators will be converted into their SymPy equivalents and the
      ``evaluate=False`` option will be added. Nested ``Add`` or ``Mul`` will
      be denested first. This is done via an AST transformation that replaces
      operators with their SymPy equivalents, so if an operand redefines any
      of those operations, the redefined operators will not be used.
  
      >>> sympify('2**2 / 3 + 5')
      19/3
      >>> sympify('2**2 / 3 + 5', evaluate=False)
      2**2/3 + 5
  
      Extending
      ---------
  
      To extend ``sympify`` to convert custom objects (not derived from ``Basic``),
      just define a ``_sympy_`` method to your class. You can do that even to
      classes that you do not own by subclassing or adding the method at runtime.
  
      >>> from sympy import Matrix
      >>> class MyList1(object):
      ...     def __iter__(self):
      ...         yield 1
      ...         yield 2
      ...         return
      ...     def __getitem__(self, i): return list(self)[i]
      ...     def _sympy_(self): return Matrix(self)
      >>> sympify(MyList1())
      Matrix([
      [1],
      [2]])
  
      If you do not have control over the class definition you could also use the
      ``converter`` global dictionary. The key is the class and the value is a
      function that takes a single argument and returns the desired SymPy
      object, e.g. ``converter[MyList] = lambda x: Matrix(x)``.
  
      >>> class MyList2(object):   # XXX Do not do this if you control the class!
      ...     def __iter__(self):  #     Use _sympy_!
      ...         yield 1
      ...         yield 2
      ...         return
      ...     def __getitem__(self, i): return list(self)[i]
      >>> from sympy.core.sympify import converter
      >>> converter[MyList2] = lambda x: Matrix(x)
      >>> sympify(MyList2())
      Matrix([
      [1],
      [2]])
  
      Notes
      =====
  
      Sometimes autosimplification during sympification results in expressions
      that are very different in structure than what was entered. Until such
      autosimplification is no longer done, the ``kernS`` function might be of
      some use. In the example below you can see how an expression reduces to
      -1 by autosimplification, but does not do so when ``kernS`` is used.
  
      >>> from sympy.core.sympify import kernS
      >>> from sympy.abc import x
      >>> -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1
      -1
      >>> s = '-2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1'
      >>> sympify(s)
      -1
      >>> kernS(s)
      -2*(-(-x + 1/x)/(x*(x - 1/x)**2) - 1/(x*(x - 1/x))) - 1
  
      """
      if evaluate is None:
          if global_evaluate[0] is False:
              evaluate = global_evaluate[0]
          else:
              evaluate = True
      try:
          if a in sympy_classes:
              return a
      except TypeError: # Type of a is unhashable
          pass
      try:
          cls = a.__class__
      except AttributeError:  # a is probably an old-style class object
          cls = type(a)
      if cls in sympy_classes:
          return a
      if cls is type(None):
          if strict:
              raise SympifyError(a)
          else:
              return a
  
      # Support for basic numpy datatypes
      if type(a).__module__ == 'numpy':
          import numpy as np
          if np.isscalar(a):
              if not isinstance(a, np.floating):
                  func = converter[complex] if np.iscomplex(a) else sympify
                  return func(np.asscalar(a))
              else:
                  try:
                      from sympy.core.numbers import Float
                      prec = np.finfo(a).nmant
                      a = str(list(np.reshape(np.asarray(a),
                                              (1, np.size(a)))[0]))[1:-1]
                      return Float(a, precision=prec)
                  except NotImplementedError:
                      raise SympifyError('Translation for numpy float : %s '
                                         'is not implemented' % a)
  
      try:
          return converter[cls](a)
      except KeyError:
          for superclass in getmro(cls):
              try:
                  return converter[superclass](a)
              except KeyError:
                  continue
  
      if isinstance(a, CantSympify):
          raise SympifyError(a)
  
      try:
          return a._sympy_()
      except AttributeError:
          pass
  
      if not isinstance(a, string_types):
          for coerce in (float, int):
              try:
                  return sympify(coerce(a))
              except (TypeError, ValueError, AttributeError, SympifyError):
                  continue
  
      if strict:
          raise SympifyError(a)
  
      try:
          from ..tensor.array import Array
          return Array(a.flat, a.shape)  # works with e.g. NumPy arrays
      except AttributeError:
          pass
  
      if iterable(a):
          try:
              return type(a)([sympify(x, locals=locals, convert_xor=convert_xor,
                  rational=rational) for x in a])
          except TypeError:
              # Not all iterables are rebuildable with their type.
              pass
      if isinstance(a, dict):
          try:
              return type(a)([sympify(x, locals=locals, convert_xor=convert_xor,
                  rational=rational) for x in a.items()])
          except TypeError:
              # Not all iterables are rebuildable with their type.
              pass
  
      # At this point we were given an arbitrary expression
      # which does not inherit from Basic and doesn't implement
      # _sympy_ (which is a canonical and robust way to convert
      # anything to SymPy expression).
      #
      # As a last chance, we try to take "a"'s normal form via unicode()
      # and try to parse it. If it fails, then we have no luck and
      # return an exception
      try:
          from .compatibility import unicode
          a = unicode(a)
      except Exception as exc:
          raise SympifyError(a, exc)
  
      from sympy.parsing.sympy_parser import (parse_expr, TokenError,
                                              standard_transformations)
      from sympy.parsing.sympy_parser import convert_xor as t_convert_xor
      from sympy.parsing.sympy_parser import rationalize as t_rationalize
  
      transformations = standard_transformations
  
      if rational:
          transformations += (t_rationalize,)
      if convert_xor:
          transformations += (t_convert_xor,)
  
      try:
          a = a.replace('\n', '')
          expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate)
      except (TokenError, SyntaxError) as exc:
          raise SympifyError('could not parse %r' % a, exc)
  
      return expr
  
  
  def _sympify(a):
      """
      Short version of sympify for internal usage for __add__ and __eq__ methods
      where it is ok to allow some things (like Python integers and floats) in
      the expression. This excludes things (like strings) that are unwise to
      allow into such an expression.
  
      >>> from sympy import Integer
      >>> Integer(1) == 1
      True
  
      >>> Integer(1) == '1'
      False
  
      >>> from sympy.abc import x
      >>> x + 1
      x + 1
  
      >>> x + '1'
      Traceback (most recent call last):
      ...
      TypeError: unsupported operand type(s) for +: 'Symbol' and 'str'
  
      see: sympify
  
      """
      return sympify(a, strict=True)
  
  
  def kernS(s):
      """Use a hack to try keep autosimplification from joining Integer or
      minus sign into an Add of a Mul; this modification doesn't
      prevent the 2-arg Mul from becoming an Add, however.
  
      Examples
      ========
  
      >>> from sympy.core.sympify import kernS
      >>> from sympy.abc import x, y, z
  
      The 2-arg Mul allows a leading Integer to be distributed but kernS will
      prevent that:
  
      >>> 2*(x + y)
      2*x + 2*y
      >>> kernS('2*(x + y)')
      2*(x + y)
  
      If use of the hack fails, the un-hacked string will be passed to sympify...
      and you get what you get.
  
      XXX This hack should not be necessary once issue 4596 has been resolved.
      """
      import re
      from sympy.core.symbol import Symbol
  
      hit = False
      if '(' in s:
          if s.count('(') != s.count(")"):
              raise SympifyError('unmatched left parenthesis')
  
          kern = '_kern'
          while kern in s:
              kern += "_"
          olds = s
          # digits*( -> digits*kern*(
          s = re.sub(r'(\d+)( *\* *)\(', r'\1*%s\2(' % kern, s)
          # negated parenthetical
          kern2 = kern + "2"
          while kern2 in s:
              kern2 += "_"
          # step 1:  -(...)  -->  kern-kern*(...)
          target = r'%s-%s*(' % (kern, kern)
          s = re.sub(r'- *\(', target, s)
          # step 2: double the matching closing parenthesis
          # kern-kern*(...)  -->  kern-kern*(...)kern2
          i = nest = 0
          while True:
              j = s.find(target, i)
              if j == -1:
                  break
              j = s.find('(')
              for j in range(j, len(s)):
                  if s[j] == "(":
                      nest += 1
                  elif s[j] == ")":
                      nest -= 1
                  if nest == 0:
                      break
              s = s[:j] + kern2 + s[j:]
              i = j
          # step 3: put in the parentheses
          # kern-kern*(...)kern2  -->  (-kern*(...))
          s = s.replace(target, target.replace(kern, "(", 1))
          s = s.replace(kern2, ')')
          hit = kern in s
  
      for i in range(2):
          try:
              expr = sympify(s)
              break
          except:  # the kern might cause unknown errors, so use bare except
              if hit:
                  s = olds  # maybe it didn't like the kern; use un-kerned s
                  hit = False
                  continue
              expr = sympify(s)  # let original error raise
  
      if not hit:
          return expr
  
      rep = {Symbol(kern): 1}
      def _clear(expr):
          if isinstance(expr, (list, tuple, set)):
              return type(expr)([_clear(e) for e in expr])
          if hasattr(expr, 'subs'):
              return expr.subs(rep, hack2=True)
          return expr
      expr = _clear(expr)
      # hope that kern is not there anymore
      return expr
  