code: def represent(expr, **options):
      """Represent the quantum expression in the given basis.
  
      In quantum mechanics abstract states and operators can be represented in
      various basis sets. Under this operation the follow transforms happen:
  
      * Ket -> column vector or function
      * Bra -> row vector of function
      * Operator -> matrix or differential operator
  
      This function is the top-level interface for this action.
  
      This function walks the SymPy expression tree looking for ``QExpr``
      instances that have a ``_represent`` method. This method is then called
      and the object is replaced by the representation returned by this method.
      By default, the ``_represent`` method will dispatch to other methods
      that handle the representation logic for a particular basis set. The
      naming convention for these methods is the following::
  
          def _represent_FooBasis(self, e, basis, **options)
  
      This function will have the logic for representing instances of its class
      in the basis set having a class named ``FooBasis``.
  
      Parameters
      ==========
  
      expr  : Expr
          The expression to represent.
      basis : Operator, basis set
          An object that contains the information about the basis set. If an
          operator is used, the basis is assumed to be the orthonormal
          eigenvectors of that operator. In general though, the basis argument
          can be any object that contains the basis set information.
      options : dict
          Key/value pairs of options that are passed to the underlying method
          that finds the representation. These options can be used to
          control how the representation is done. For example, this is where
          the size of the basis set would be set.
  
      Returns
      =======
  
      e : Expr
          The SymPy expression of the represented quantum expression.
  
      Examples
      ========
  
      Here we subclass ``Operator`` and ``Ket`` to create the z-spin operator
      and its spin 1/2 up eigenstate. By defining the ``_represent_SzOp``
      method, the ket can be represented in the z-spin basis.
  
      >>> from sympy.physics.quantum import Operator, represent, Ket
      >>> from sympy import Matrix
  
      >>> class SzUpKet(Ket):
      ...     def _represent_SzOp(self, basis, **options):
      ...         return Matrix([1,0])
      ...
      >>> class SzOp(Operator):
      ...     pass
      ...
      >>> sz = SzOp('Sz')
      >>> up = SzUpKet('up')
      >>> represent(up, basis=sz)
      Matrix([
      [1],
      [0]])
  
      Here we see an example of representations in a continuous
      basis. We see that the result of representing various combinations
      of cartesian position operators and kets give us continuous
      expressions involving DiracDelta functions.
  
      >>> from sympy.physics.quantum.cartesian import XOp, XKet, XBra
      >>> X = XOp()
      >>> x = XKet()
      >>> y = XBra('y')
      >>> represent(X*x)
      x*DiracDelta(x - x_2)
      >>> represent(X*x*y)
      x*DiracDelta(x - x_3)*DiracDelta(x_1 - y)
  
      """
  
      format = options.get("format", "sympy")
      if format == "numpy":
          import numpy as np
      if isinstance(expr, QExpr) and not isinstance(expr, OuterProduct):
          options["replace_none"] = False
          temp_basis = get_basis(expr, **options)
          if temp_basis is not None:
              options["basis"] = temp_basis
          try:
              return expr._represent(**options)
          except NotImplementedError as strerr:
              # If no _represent_FOO method exists, map to the
              # appropriate basis state and try
              # the other methods of representation
              options["replace_none"] = True
  
              if isinstance(expr, (KetBase, BraBase)):
                  try:
                      return rep_innerproduct(expr, **options)
                  except NotImplementedError:
                      raise NotImplementedError(strerr)
              elif isinstance(expr, Operator):
                  try:
                      return rep_expectation(expr, **options)
                  except NotImplementedError:
                      raise NotImplementedError(strerr)
              else:
                  raise NotImplementedError(strerr)
      elif isinstance(expr, Add):
          result = represent(expr.args[0], **options)
          for args in expr.args[1:]:
              # scipy.sparse doesn't support += so we use plain = here.
              result = result + represent(args, **options)
          return result
      elif isinstance(expr, Pow):
          base, exp = expr.as_base_exp()
          if format in ("numpy", "scipy.sparse"):
              exp = _sympy_to_scalar(exp)
          base = represent(base, **options)
          # scipy.sparse doesn't support negative exponents
          # and warns when inverting a matrix in csr format.
          if format == "scipy.sparse" and exp < 0:
              from scipy.sparse.linalg import inv
  
              exp = -exp
              base = inv(base.tocsc()).tocsr()
          if format == "numpy":
              return np.linalg.matrix_power(base, exp)
          return base**exp
      elif isinstance(expr, TensorProduct):
          new_args = [represent(arg, **options) for arg in expr.args]
          return TensorProduct(*new_args)
      elif isinstance(expr, Dagger):
          return Dagger(represent(expr.args[0], **options))
      elif isinstance(expr, Commutator):
          A = expr.args[0]
          B = expr.args[1]
          return represent(Mul(A, B) - Mul(B, A), **options)
      elif isinstance(expr, AntiCommutator):
          A = expr.args[0]
          B = expr.args[1]
          return represent(Mul(A, B) + Mul(B, A), **options)
      elif isinstance(expr, InnerProduct):
          return represent(Mul(expr.bra, expr.ket), **options)
      elif not isinstance(expr, (Mul, OuterProduct)):
          # For numpy and scipy.sparse, we can only handle numerical prefactors.
          if format in ("numpy", "scipy.sparse"):
              return _sympy_to_scalar(expr)
          return expr
  
      if not isinstance(expr, (Mul, OuterProduct)):
          raise TypeError("Mul expected, got: %r" % expr)
  
      if "index" in options:
          options["index"] += 1
      else:
          options["index"] = 1
  
      if "unities" not in options:
          options["unities"] = []
  
      result = represent(expr.args[-1], **options)
      last_arg = expr.args[-1]
  
      for arg in reversed(expr.args[:-1]):
          if isinstance(last_arg, Operator):
              options["index"] += 1
              options["unities"].append(options["index"])
          elif isinstance(last_arg, BraBase) and isinstance(
              arg, KetBase
          ):
              options["index"] += 1
          elif isinstance(last_arg, KetBase) and isinstance(
              arg, Operator
          ):
              options["unities"].append(options["index"])
          elif isinstance(last_arg, KetBase) and isinstance(
              arg, BraBase
          ):
              options["unities"].append(options["index"])
  
          next_arg = represent(arg, **options)
          if format == "numpy" and isinstance(next_arg, np.ndarray):
              # Must use np.matmult to "matrix multiply" two np.ndarray
              result = np.matmul(next_arg, result)
          else:
              result = next_arg * result
          last_arg = arg
  
      # All three matrix formats create 1 by 1 matrices when inner products of
      # vectors are taken. In these cases, we simply return a scalar.
      result = flatten_scalar(result)
  
      result = integrate_result(expr, result, **options)
  
      return result
  
imports: from sympy.core.add import Add
  from sympy.core.expr import Expr
  from sympy.core.mul import Mul
  from sympy.core.numbers import I
  from sympy.core.power import Pow
  from sympy.integrals.integrals import integrate
  from sympy.physics.quantum.dagger import Dagger
  from sympy.physics.quantum.commutator import Commutator
  from sympy.physics.quantum.anticommutator import AntiCommutator
  from sympy.physics.quantum.innerproduct import InnerProduct
  from sympy.physics.quantum.qexpr import QExpr
  from sympy.physics.quantum.tensorproduct import TensorProduct
  from sympy.physics.quantum.matrixutils import flatten_scalar
  from sympy.physics.quantum.state import KetBase, BraBase, StateBase
  from sympy.physics.quantum.operator import Operator, OuterProduct
  from sympy.physics.quantum.qapply import qapply
  from sympy.physics.quantum.operatorset import operators_to_state, state_to_operators
label_desc: Use image node_id 2 for calling a global function with example usage: represent(expr) and returns: result, expr, result, unknown, np, TensorProduct, rep_innerproduct, Dagger, rep_expectation, represent, represent, represent, expr, _sympy_to_scalar