code: def is_reducible(circuit, nqubits, begin, end):
      """Determines if a circuit is reducible by checking
      if its subcircuits are scalar values.
  
      Parameters
      ==========
  
      circuit : Gate tuple
          A tuple of Gates representing a circuit.  The circuit to check
          if a gate identity is contained in a subcircuit.
      nqubits : int
          The number of qubits the circuit operates on.
      begin : int
          The leftmost gate in the circuit to include in a subcircuit.
      end : int
          The rightmost gate in the circuit to include in a subcircuit.
  
      Examples
      ========
  
      Check if the circuit can be reduced:
  
      >>> from sympy.physics.quantum.identitysearch import is_reducible
      >>> from sympy.physics.quantum.gate import X, Y, Z
      >>> x = X(0); y = Y(0); z = Z(0)
      >>> is_reducible((x, y, z), 1, 0, 3)
      True
  
      Check if an interval in the circuit can be reduced:
  
      >>> is_reducible((x, y, z), 1, 1, 3)
      False
  
      >>> is_reducible((x, y, y), 1, 1, 3)
      True
      """
  
      current_circuit = ()
      # Start from the gate at "end" and go down to almost the gate at "begin"
      for ndx in reversed(range(begin, end)):
          next_gate = circuit[ndx]
          current_circuit = (next_gate,) + current_circuit
  
          # If a circuit as a matrix is equivalent to a scalar value
          if is_scalar_matrix(current_circuit, nqubits, False):
              return True
  
      return False
  
imports: from collections import deque
  from sympy.core.random import randint
  from sympy.external import import_module
  from sympy.core.basic import Basic
  from sympy.core.mul import Mul
  from sympy.core.numbers import Number, equal_valued
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.physics.quantum.represent import represent
  from sympy.physics.quantum.dagger import Dagger
label_desc: Use image node_id 11 for calling a global function with example usage: is_reducible(circuit, nqubits, begin, end) and returns: False, True