code: 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.
  
      Explanation
      ===========
  
      It will convert Python ints into instances of :class:`~.Integer`, floats
      into instances of :class:`~.Float`, etc. It is also able to coerce
      symbolic expressions which inherit from :class:`~.Basic`. This can be
      useful in cooperation with SAGE.
  
      .. 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.
  
      Examples
      ========
  
      >>> 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 'x***2'"
  
      When attempting to parse non-Python syntax using ``sympify``, it raises a
      ``SympifyError``:
  
      >>> sympify("2x+1")
      Traceback (most recent call last):
      ...
      SympifyError: Sympify of expression 'could not parse '2x+1'' failed
  
      To parse non-Python syntax, use ``parse_expr`` from ``sympy.parsing.sympy_parser``.
  
      >>> from sympy.parsing.sympy_parser import parse_expr
      >>> parse_expr("2x+1", transformations="all")
      2*x + 1
  
      For more details about ``transformations``: see :func:`~sympy.parsing.sympy_parser.parse_expr`
  
      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 :class:`~.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:
  
      >>> 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
      >>> set(_clash1)  # if this fails, see issue #23903
      {'E', 'I', 'N', 'O', 'Q', '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
  
      .. deprecated:: 1.6
  
         ``sympify(obj)`` automatically falls back to ``str(obj)`` when all
         other conversion methods fail, but this is deprecated. ``strict=True``
         will disable this deprecated behavior. See
         :ref:`deprecated-sympify-string-fallback`.
  
      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. If
      argument a is not a string, the mathematical expression is evaluated
      before being passed to sympify, so adding ``evaluate=False`` will still
      return the evaluated result of expression.
  
      >>> sympify('2**2 / 3 + 5')
      19/3
      >>> sympify('2**2 / 3 + 5', evaluate=False)
      2**2/3 + 5
      >>> sympify('4/2+7', evaluate=True)
      9
      >>> sympify('4/2+7', evaluate=False)
      4/2 + 7
      >>> sympify(4/2+7, evaluate=False)
      9.00000000000000
  
      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
      =====
  
      The keywords ``rational`` and ``convert_xor`` are only used
      when the input is a string.
  
      convert_xor
      -----------
  
      >>> sympify('x^y',convert_xor=True)
      x**y
      >>> sympify('x^y',convert_xor=False)
      x ^ y
  
      rational
      --------
  
      >>> sympify('0.1',rational=False)
      0.1
      >>> sympify('0.1',rational=True)
      1/10
  
      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
  
      Parameters
      ==========
  
      a :
          - any object defined in SymPy
          - standard numeric Python types: ``int``, ``long``, ``float``, ``Decimal``
          - strings (like ``"0.09"``, ``"2e-19"`` or ``'sin(x)'``)
          - booleans, including ``None`` (will leave ``None`` unchanged)
          - dicts, lists, sets or tuples containing any of the above
  
      convert_xor : bool, optional
          If true, treats ``^`` as exponentiation.
          If False, treats ``^`` as XOR itself.
          Used only when input is a string.
  
      locals : any object defined in SymPy, optional
          In order to have strings be recognized it can be imported
          into a namespace dictionary and passed as locals.
  
      strict : bool, optional
          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.
  
      rational : bool, optional
          If ``True``, converts floats into :class:`~.Rational`.
          If ``False``, it lets floats remain as it is.
          Used only when input is a string.
  
      evaluate : bool, optional
          If False, then arithmetic and operators will be converted into
          their SymPy equivalents. If True the expression will be evaluated
          and the result will be returned.
  
      """
      # XXX: If a is a Basic subclass rather than instance (e.g. sin rather than
      # sin(x)) then a.__sympy__ will be the property. Only on the instance will
      # a.__sympy__ give the *value* of the property (True). Since sympify(sin)
      # was used for a long time we allow it to pass. However if strict=True as
      # is the case in internal calls to _sympify then we only allow
      # is_sympy=True.
      #
      # https://github.com/sympy/sympy/issues/20124
      is_sympy = getattr(a, "__sympy__", None)
      if is_sympy is True:
          return a
      elif is_sympy is not None:
          if not strict:
              return a
          else:
              raise SympifyError(a)
  
      if isinstance(a, CantSympify):
          raise SympifyError(a)
  
      cls = getattr(a, "__class__", None)
  
      # Check if there exists a converter for any of the types in the mro
      for superclass in getmro(cls):
          # First check for user defined converters
          conv = _external_converter.get(superclass)
          if conv is None:
              # if none exists, check for SymPy defined converters
              conv = _sympy_converter.get(superclass)
          if conv is not None:
              return conv(a)
  
      if cls is type(None):
          if strict:
              raise SympifyError(a)
          else:
              return a
  
      if evaluate is None:
          evaluate = global_parameters.evaluate
  
      # Support for basic numpy datatypes
      if _is_numpy_instance(a):
          import numpy as np
  
          if np.isscalar(a):
              return _convert_numpy_types(
                  a,
                  locals=locals,
                  convert_xor=convert_xor,
                  strict=strict,
                  rational=rational,
                  evaluate=evaluate,
              )
  
      _sympy_ = getattr(a, "_sympy_", None)
      if _sympy_ is not None:
          return a._sympy_()
  
      if not strict:
          # Put numpy array conversion _before_ float/int, see
          # <https://github.com/sympy/sympy/issues/13924>.
          flat = getattr(a, "flat", None)
          if flat is not None:
              shape = getattr(a, "shape", None)
              if shape is not None:
                  from sympy.tensor.array import Array
  
                  return Array(
                      a.flat, a.shape
                  )  # works with e.g. NumPy arrays
  
      if not isinstance(a, str):
          if _is_numpy_instance(a):
              import numpy as np
  
              assert not isinstance(a, np.number)
              if isinstance(a, np.ndarray):
                  # Scalar arrays (those with zero dimensions) have sympify
                  # called on the scalar element.
                  if a.ndim == 0:
                      try:
                          return sympify(
                              a.item(),
                              locals=locals,
                              convert_xor=convert_xor,
                              strict=strict,
                              rational=rational,
                              evaluate=evaluate,
                          )
                      except SympifyError:
                          pass
          elif hasattr(a, "__float__"):
              # float and int can coerce size-one numpy arrays to their lone
              # element.  See issue https://github.com/numpy/numpy/issues/10404.
              return sympify(float(a))
          elif hasattr(a, "__int__"):
              return sympify(int(a))
  
      if strict:
          raise SympifyError(a)
  
      if iterable(a):
          try:
              return type(a)(
                  [
                      sympify(
                          x,
                          locals=locals,
                          convert_xor=convert_xor,
                          rational=rational,
                          evaluate=evaluate,
                      )
                      for x in a
                  ]
              )
          except TypeError:
              # Not all iterables are rebuildable with their type.
              pass
  
      if not isinstance(a, str):
          raise SympifyError(
              "cannot sympify object of type %r" % type(a)
          )
  
      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
  
file_path: sympy/sympy/core/sympify.py
imports: from __future__ import annotations
  from typing import Any, Callable
  from inspect import getmro
  import string
  from sympy.core.random import choice
  from .parameters import global_parameters
  from sympy.utilities.iterables import iterable
  from .basic import Basic
label_desc: Use image node_id 3 for calling a global function with example usage: sympify(a, locals, convert_xor, strict, rational, evaluate) and returns: expr, a, a, conv, a, _convert_numpy_types, type, a, Array, sympify, sympify, sympify