text: """
  This module provides convenient functions to transform sympy expressions to
  lambda functions which can be used to calculate numerical values very fast.
  """
  
  from __future__ import division
  from sympy.external import import_module
  from sympy.core.compatibility import is_sequence
  
  import inspect
  
  # These are the namespaces the lambda functions will use.
  MATH = {}
  MPMATH = {}
  NUMPY = {}
  SYMPY = {}
  
  # Default namespaces, letting us define translations that can't be defined
  # by simple variable maps, like I => 1j
  # These are separate from the names above because the above names are modified
  # throughout this file, whereas these should remain unmodified.
  MATH_DEFAULT = {}
  MPMATH_DEFAULT = {}
  NUMPY_DEFAULT = {"I": 1j}
  SYMPY_DEFAULT = {}
  
  # Mappings between sympy and other modules function names.
  MATH_TRANSLATIONS = {
      "Abs":"fabs",
      "ceiling":"ceil",
      "E":"e",
      "ln":"log",
  }
  
  MPMATH_TRANSLATIONS = {
      "ceiling":"ceil",
      "chebyshevt":"chebyt",
      "chebyshevu":"chebyu",
      "E":"e",
      "I":"j",
      "ln":"log",
      #"lowergamma":"lower_gamma",
      "oo":"inf",
      #"uppergamma":"upper_gamma",
      "LambertW":"lambertw",
      "Matrix":"matrix",
      "conjugate":"conj",
  }
  
  NUMPY_TRANSLATIONS = {
      "Abs":"abs",
      "acos":"arccos",
      "acosh":"arccosh",
      "arg":"angle",
      "asin":"arcsin",
      "asinh":"arcsinh",
      "atan":"arctan",
      "atan2":"arctan2",
      "atanh":"arctanh",
      "ceiling":"ceil",
      "E":"e",
      "im":"imag",
      "ln":"log",
      "Matrix":"matrix",
      "Max":"amax",
      "Min":"amin",
      "oo":"inf",
      "re":"real",
  }
  
  # Available modules:
  MODULES = {
      "math"   : (MATH,   MATH_DEFAULT,   MATH_TRANSLATIONS,   ("from math import *",)),
      "mpmath" : (MPMATH, MPMATH_DEFAULT, MPMATH_TRANSLATIONS, ("from sympy.mpmath import *",)),
      "numpy"  : (NUMPY,  NUMPY_DEFAULT,  NUMPY_TRANSLATIONS,  ("import_module('numpy')",)),
      "sympy"  : (SYMPY,  SYMPY_DEFAULT,  {},                  ("from sympy.functions import *",
                                                                "from sympy.matrices import Matrix",
                                                                "from sympy import Integral, pi, oo, nan, zoo, E, I",)),
  }
  
  def _import(module, reload="False"):
      """
      Creates a global translation dictionary for module.
  
      The argument module has to be one of the following strings: "math",
      "mpmath", "numpy", "sympy".
      These dictionaries map names of python functions to their equivalent in
      other modules.
      """
      try:
          namespace, namespace_default, translations, import_commands = MODULES[module]
      except KeyError:
          raise NameError("'%s' module can't be used for lambdification" % module)
  
      # Clear namespace or exit
      if namespace != namespace_default:
          # The namespace was already generated, don't do it again if not forced.
          if reload:
              namespace.clear()
              namespace.update(namespace_default)
          else:
              return
  
      for import_command in import_commands:
          if import_command.startswith('import_module'):
              module = eval(import_command)
  
              if module is not None:
                  namespace.update(module.__dict__)
                  continue
          else:
              try:
                  exec import_command in {}, namespace
                  continue
              except ImportError:
                  pass
  
          raise ImportError("can't import '%s' with '%s' command" % (module, import_command))
  
      # Add translated names to namespace
      for sympyname, translation in translations.iteritems():
          namespace[sympyname] = namespace[translation]
  
  def lambdify(args, expr, modules=None, printer=None, use_imps=True):
      """
      Returns a lambda function for fast calculation of numerical values.
  
      Usage:
      >>> from sympy import sqrt, sin
      >>> from sympy.utilities.lambdify import lambdify
      >>> from sympy.abc import x, y, z
      >>> f = lambdify(x, x**2)
      >>> f(2)
      4
      >>> f = lambdify((x,y,z), [z,y,x])
      >>> f(1,2,3)
      [3, 2, 1]
      >>> f = lambdify(x, sqrt(x))
      >>> f(4)
      2.0
      >>> f = lambdify((x,y), sin(x*y)**2)
      >>> f(0, 5)
      0.0
  
      If not specified differently by the user, Sympy functions are replaced as
      far as possible by either python-math, numpy (if available) or mpmath
      functions - exactly in this order.
      To change this behavior, the "modules" argument can be used.
      It accepts:
       - the strings "math", "mpmath", "numpy", "sympy"
       - any modules (e.g. math)
       - dictionaries that map names of sympy functions to arbitrary functions
       - lists that contain a mix of the arguments above. (Entries that are first
          in the list have higher priority)
  
      Examples:
      (1) Use one of the provided modules:
          >> f = lambdify(x, sin(x), "math")
  
          Attention: Functions that are not in the math module will throw a name
                     error when the lambda function is evaluated! So this would
                     be better:
          >> f = lambdify(x, sin(x)*gamma(x), ("math", "mpmath", "sympy"))
  
      (2) Use some other module:
          >> import numpy
          >> f = lambdify((x,y), tan(x*y), numpy)
  
          Attention: There are naming differences between numpy and sympy. So if
                     you simply take the numpy module, e.g. sympy.atan will not be
                     translated to numpy.arctan. Use the modified module instead
                     by passing the string "numpy":
  
          >> f = lambdify((x,y), tan(x*y), "numpy")
          >> f(1, 2)
          -2.18503986326
          >> from numpy import array
          >> f(array([1, 2, 3]), array([2, 3, 5]))
          [-2.18503986 -0.29100619 -0.8559934 ]
  
      (3) Use own dictionaries:
          >> def my_cool_function(x): ...
          >> dic = {"sin" : my_cool_function}
          >> f = lambdify(x, sin(x), dic)
  
          Now f would look like:
          >> lambda x: my_cool_function(x)
  
      Functions present in `expr` can also carry their own numerical
      implementations, in a callable attached to the ``_imp_``
      attribute.  Usually you attach this using the
      ``implemented_function`` factory:
  
      >>> from sympy.abc import x, y, z
      >>> from sympy.utilities.lambdify import lambdify, implemented_function
      >>> from sympy import Function
      >>> f = implemented_function(Function('f'), lambda x : x+1)
      >>> func = lambdify(x, f(x))
      >>> func(4)
      5
  
      ``lambdify`` always prefers ``_imp_`` implementations to
      implementations in other namespaces, unless the ``use_imps`` input
      parameter is False.
      """
      from sympy.core.symbol import Symbol
  
      # If the user hasn't specified any modules, use what is available.
      if modules is None:
          # Use either numpy (if available) or python.math where possible.
          # XXX: This leads to different behaviour on different systems and
          #      might be the reason for irreproducible errors.
          modules = ["math", "mpmath", "sympy"]
  
          try:
              _import("numpy")
          except ImportError:
              pass
          else:
              modules.insert(1, "numpy")
  
      # Get the needed namespaces.
      namespaces = []
      # First find any function implementations
      if use_imps:
          namespaces.append(_imp_namespace(expr))
      # Check for dict before iterating
      if isinstance(modules, (dict, str)) or not hasattr(modules, '__iter__'):
          namespaces.append(modules)
      else:
          namespaces += list(modules)
      # fill namespace with first having highest priority
      namespace = {}
      for m in namespaces[::-1]:
          buf = _get_namespace(m)
          namespace.update(buf)
  
      if hasattr(expr, "atoms"):
          #Try if you can extract symbols from the expression.
          #Move on if expr.atoms in not implemented.
          syms = expr.atoms(Symbol)
          for term in syms:
              namespace.update({str(term): term})
  
      # Create lambda function.
      lstr = lambdastr(args, expr, printer=printer)
  
      return eval(lstr, namespace)
  
  def _get_namespace(m):
      """
      This is used by _lambdify to parse its arguments.
      """
      if isinstance(m, str):
          _import(m)
          return MODULES[m][0]
      elif isinstance(m, dict):
          return m
      elif hasattr(m, "__dict__"):
          return m.__dict__
      else:
          raise TypeError("Argument must be either a string, dict or module but it is: %s" % m)
  
  def lambdastr(args, expr, printer=None):
      """
      Returns a string that can be evaluated to a lambda function.
  
      >>> from sympy.abc import x, y, z
      >>> from sympy.utilities.lambdify import lambdastr
      >>> lambdastr(x, x**2)
      'lambda x: (x**2)'
      >>> lambdastr((x,y,z), [z,y,x])
      'lambda x,y,z: ([z, y, x])'
  
      """
      if printer is not None:
          if inspect.isfunction(printer):
              lambdarepr = printer
          else:
              if inspect.isclass(printer):
                  lambdarepr = lambda expr: printer().doprint(expr)
              else:
                  lambdarepr = lambda expr: printer.doprint(expr)
      else:
          #XXX: This has to be done here because of circular imports
          from sympy.printing.lambdarepr import lambdarepr
  
      # Transform everything to strings.
      expr = lambdarepr(expr)
      if isinstance(args, str):
          pass
      elif hasattr(args, "__iter__"):
          args = ",".join(str(a) for a in args)
      else:
          args = str(args)
  
      return "lambda %s: (%s)" % (args, expr)
  
  def _imp_namespace(expr, namespace=None):
      """ Return namespace dict with function implementations
  
      We need to search for functions in anything that can be thrown at
      us - that is - anything that could be passed as `expr`.  Examples
      include sympy expressions, as well as tuples, lists and dicts that may
      contain sympy expressions.
  
      Parameters
      ----------
      expr : object
         Something passed to lambdify, that will generate valid code from
         ``str(expr)``.
      namespace : None or mapping
         Namespace to fill.  None results in new empty dict
  
      Returns
      -------
      namespace : dict
         dict with keys of implemented function names within `expr` and
         corresponding values being the numerical implementation of
         function
  
      Examples
      --------
      >>> from sympy.abc import x, y, z
      >>> from sympy.utilities.lambdify import implemented_function, _imp_namespace
      >>> from sympy import Function
      >>> f = implemented_function(Function('f'), lambda x : x+1)
      >>> g = implemented_function(Function('g'), lambda x : x*10)
      >>> namespace = _imp_namespace(f(g(x)))
      >>> sorted(namespace.keys())
      ['f', 'g']
      """
      # Delayed import to avoid circular imports
      from sympy.core.function import FunctionClass
      if namespace is None:
          namespace = {}
      # tuples, lists, dicts are valid expressions
      if is_sequence(expr):
          for arg in expr:
              _imp_namespace(arg, namespace)
          return namespace
      elif isinstance(expr, dict):
          for key, val in expr.items():
              # functions can be in dictionary keys
              _imp_namespace(key, namespace)
              _imp_namespace(val, namespace)
          return namespace
      # sympy expressions may be Functions themselves
      func = getattr(expr, 'func', None)
      if isinstance(func, FunctionClass):
          imp = getattr(func, '_imp_', None)
          if not imp is None:
              name = expr.func.__name__
              if name in namespace and namespace[name] != imp:
                  raise ValueError('We found more than one '
                                   'implementation with name '
                                   '"%s"' % name)
              namespace[name] = imp
      # and / or they may take Functions as arguments
      if hasattr(expr, 'args'):
          for arg in expr.args:
              _imp_namespace(arg, namespace)
      return namespace
  
  def implemented_function(symfunc, implementation):
      """ Add numerical `implementation` to function `symfunc`
  
      `symfunc` can by a Function, or a name, in which case we make an
      anonymous function with this name.  The function is anonymous in the
      sense that the name is not unique in the sympy namespace.
  
      Parameters
      ----------
      symfunc : str or ``sympy.FunctionClass`` instance
         If str, then create new anonymous sympy function with this as
         name.  If `symfunc` is a sympy function, attach implementation to
         function
      implementation : callable
         numerical implementation of function for use in ``lambdify``
  
      Returns
      -------
      afunc : sympy.FunctionClass instance
         function with attached implementation
  
      Examples
      --------
      >>> from sympy.abc import x, y, z
      >>> from sympy.utilities.lambdify import lambdify, implemented_function
      >>> from sympy import Function
      >>> f = implemented_function(Function('f'), lambda x : x+1)
      >>> lam_f = lambdify(x, f(x))
      >>> lam_f(4)
      5
      """
      # Delayed import to avoid circular imports
      from sympy.core.function import UndefinedFunction
      # if name, create anonymous function to hold implementation
      if isinstance(symfunc, basestring):
          symfunc = UndefinedFunction(symfunc)
      # We need to attach as a method because symfunc will be a class
      symfunc._imp_ = staticmethod(implementation)
      return symfunc
  