code: def _sep_const_coeff(expr):
      """
      Example
      =======
  
      >>> from sympy.logic.algorithms.lra_theory import _sep_const_coeff
      >>> from sympy.abc import x, y
      >>> _sep_const_coeff(2*x)
      (x, 2)
      >>> _sep_const_coeff(2*x + 3*y)
      (2*x + 3*y, 1)
      """
      if isinstance(expr, Add):
          return expr, sympify(1)
  
      if isinstance(expr, Mul):
          coeffs = expr.args
      else:
          coeffs = [expr]
  
      var, const = [], []
      for c in coeffs:
          c = sympify(c)
          if len(c.free_symbols) == 0:
              const.append(c)
          else:
              var.append(c)
      return Mul(*var), Mul(*const)
  
imports: from sympy.solvers.solveset import linear_eq_to_matrix
  from sympy.matrices.dense import eye
  from sympy.assumptions import Predicate
  from sympy.assumptions.assume import AppliedPredicate
  from sympy.assumptions.ask import Q
  from sympy.core import Dummy
  from sympy.core.mul import Mul
  from sympy.core.add import Add
  from sympy.core.relational import Eq, Ne
  from sympy.core.sympify import sympify
  from sympy.core.singleton import S
  from sympy.core.numbers import Rational, oo
  from sympy.matrices.dense import Matrix
label_desc: Use image node_id 1 for calling a global function with example usage: _sep_const_coeff(expr) and returns: Mul,  Mul, expr,  sympify