code: def _dict_from_expr(expr, opt):
      """Transform an expression into a multinomial form."""
      if expr.is_commutative is False:
          raise PolynomialError(
              "non-commutative expressions are not supported"
          )
  
      def _is_expandable_pow(expr):
          return (
              expr.is_Pow
              and expr.exp.is_positive
              and expr.exp.is_Integer
              and expr.base.is_Add
          )
  
      if opt.expand is not False:
          if not isinstance(expr, (Expr, Eq)):
              raise PolynomialError("expression must be of type Expr")
          expr = expr.expand()
          # TODO: Integrate this into expand() itself
          while any(
              _is_expandable_pow(i)
              or i.is_Mul
              and any(_is_expandable_pow(j) for j in i.args)
              for i in Add.make_args(expr)
          ):
              expr = expand_multinomial(expr)
          while any(
              i.is_Mul and any(j.is_Add for j in i.args)
              for i in Add.make_args(expr)
          ):
              expr = expand_mul(expr)
  
      if opt.gens:
          rep, gens = _dict_from_expr_if_gens(expr, opt)
      else:
          rep, gens = _dict_from_expr_no_gens(expr, opt)
  
      return rep, opt.clone({"gens": gens})
  
imports: from __future__ import annotations
  from sympy.external.gmpy import GROUND_TYPES
  from sympy.core import S, Add, Mul, Pow, Eq, Expr, expand_mul, expand_multinomial
  from sympy.core.exprtools import decompose_power, decompose_power_rat
  from sympy.core.numbers import _illegal
  from sympy.polys.polyerrors import PolynomialError, GeneratorsError
  from sympy.polys.polyoptions import build_options
  import re
label_desc: Use image node_id 14 for calling a global function with example usage: _dict_from_expr(expr, opt) and returns: rep,  opt, unknown